 D Schöngen

 K J Koziol

Maike Andresen

Wolfgang Stahl

Martin Schwell

Isabelle Kleiner

H V L Nguyen

Maike Andresen Ha

Vinh Lam Nguyen

Ha Vinh

Lam Nguyen

"Struktur und Dynamik der Pheromone

Keywords: Strukturen und interne Dynamik von Ketonen untersucht mittels microwave spectroscopy, quantum chemistry, ketones, internal rotation Mikrowellenspektroskopie, Quantenchemie, Ketone, interne Rotation spectroscopie micro-onde, chimie quantique, cétones, rotation interne die eine Acetylmethylgruppe enthalten, mikrowellenspektroskopisch untersucht, wobei besonders Effekte interner Rotationen betrachtet wurden welches eine andere spezifische Spektren, die auf die interne Rotation der Methylgruppe am Ende der jeweiligen Alkylkette zurück zu führen sind, ergeben eine Barrierenhöhe von ungefähr

In this dissertation, diverse ketones containing an acetyl methyl group were studied by microwave spectroscopy with the main focus on the effects of internal rotations. As a result a "barrier class system" was introduced, which firmly links the barrier to internal rotation of the acetyl methyl group to the characteristic structure of the molecule. The acetyl methyl barrier thus functions as a "structural detector". The analysis was supplemented by quantum chemical calculations of molecular parameters.

For a series of methyl n-alkyl ketones, including pentan-2-one, hexan-2-one, heptan-2-one and octan-2-one, at least two conformers could be identified in the spectrum of each of these aliphatic ketones: one with C 1 and one with C s symmetry. The barriers to internal rotation of the acetyl methyl group of the C 1 conformers were determined to always be about 240 cm -1 .

In case of the C s conformers, the barrier heights are found to be approximately 180 cm -1 . These conformers are hence members of the "C 1 " and "C s class", respectively. Only for hexan-2-one, a third conformer showing another specific C 1 structure and a barrier height of 182 cm -1 was assigned. Furthermore, spectral splittings caused by the internal rotation of the methyl group at the end of the respective alkyl chain were observed. Here, the barriers are about 1000 cm -1 for each conformer.

E-3-Penten-2-one and 3-methyl-3-buten-2-one are α,β-unsaturated ketones and members of

Zusammenfassung

In dieser Dissertation wurden verschiedene Ketone,

First of all, I like to thank Prof. Dr. Wolfgang Stahl and Prof. Dr. Martin Schwell to be my PhD supervisors at the RWTH Aachen University and the UPEC, respectively. Their cooperation made this joint thesis possible.

Prof. Stahl is especially thanked for his patient explanations and his fast fixes of the spectrometers. I will fondly remember him. He will be missed.

Prof. Schwell is sincerely thanked for his assistance in fighting the immense bureaucracy of the collaboration. I am very grateful for Prof. Dr. Arne Lüchow's readiness to stand in as German supervisor, and that he agreed to support the finalisation of this dissertation.

Furthermore, I thank all members of the examination committee for enabling an international public defence despite the problems caused by the Corona crisis.

Heartfelt gratitude goes to Dr. Ha Vinh Lam Nguyen for her guidance during the research process and her involvement in the corrections of several scientific papers.

Isabelle Kleiner is gracefully acknowledged for introducing me to the BELGI program and helping me with the French language.

All my colleagues in Germany and France are thanked for the tips they provided, as well as for the great atmosphere and entertaining moments they created.

Likewise, I am deeply grateful for my friends and family and their support. Fabian Draber is especially thanked for his patience with my demotivated phases.

Finally, I like to acknowledge Dr. Ha Vinh Lam Nguyen, Christina Dindic, Kenneth Koziol and Martin Andresen, as well as Jens Kothe and Andreas Ohligschläger for proofreading this document.

Thanks to you all.

the "mesomeric class". They exhibit complicated splitting patterns in the spectrum arising due to the internal rotation of the acetyl methyl group, as well as of the methyl group attached to the propenyl or isopropenyl group, respectively. For E-3-penten-2-one, two conformers were assigned, one with antiperiplanar (ap) and one with synperiplanar (sp) structure. In case of 3-methyl-3-buten-2-one, only the ap conformer could be identified. The acetyl methyl torsional barriers range from 350 cm -1 to 520 cm -1 , while they are about 600 cm -1 for the propenyl and isopropenyl methyl groups.

In the microwave spectrum of 3-methylbutan-2-one, a branched ketone, additional splittings beside those due to internal rotation were observed. They are probably caused by a tunnelling motion between two enantiomeric versions of the molecule. Therefore, 3-methylbutan-2-one is a member of the "tunnelling class".

Im Mikrowellenspektrum von 3-Methylbutan-2-on, einem verzweigtem Keton, gibt es neben den Aufspaltungen der internen Rotationen noch zusätzliche Aufspaltungen. Diese werden wahrscheinlich von einer Tunnelbewegung zwischen zwei Enantiomerversionen des Moleküls verursacht. 3-Methylbutan-2-on ist folglich ein Mitglied der "Tunnel-Klasse".

Résumé

Cette thèse présente les travaux de recherche sur diverses cétones contenant un groupe acétyle par la spectroscopie micro-onde, en particulier, sur les effets de rotations internes dus au groupe méthyle de ce groupe acétyle, appelé groupe acétyle méthyle. Pour ces cétones, un "système des classes des barrières" a été établi, reliant clairement la hauteur des barrières empêchant la rotation interne du groupe acétyle méthyle à la structure caractéristique de la molécule. Ainsi, la barrière du groupe acétyle méthyle fonctionne comme un "détecteur structurel". Cette étude a été étoffée par des calculs de chimie quantique de certains des paramètres moléculaires.

Pour les molécules de la série des méthyle-n-alkyle cétones, comprenant les molécules de pentan-2-one, d'hexan-2-one, d'heptan-2-one et d'octan-2-one, au moins deux conformères ont pu être identifiés dans le spectre de chacune de ces cétones aliphatiques: l'un avec une symétrie C 1 et l'autre avec une symétrie C s . Les barrières de rotation interne du groupe acétyle méthyle des conformères C 1 ont été déterminées à une valeur d'environ 240 cm -1 . Dans le cas des conformères C s , la hauteur de barrière est d'environ 180 cm -1 . Ces conformères appartiennent donc à la "classe C 1 " ou la "classe C s " respectivement. Seulement dans le cas de la molécule d'hexan-2-one, un troisième conformère avec une structure C 1 différente et une hauteur de barrière de 182 cm -1 a été attribuée. De surcroît, la rotation interne du groupe méthyle de l'extrémité de la chaîne alkyle produit des dédoublements supplémentaires dans les spectres avec une barrière à la rotation d'environ 1000 cm -1 pour chaque conformère.

Les molécules de E-3-pentène-2-one et de 3-méthyl-3-butène-2-one sont des cétones α,β-insaturées et appartiennent à la "classe mésomérique". Elles présentent des dédoublements

I Introduction

Microwave spectroscopy is an analysis method for molecules in the gas phase. Since its earliest applications in the first half of the 20 th century, the accuracy of the spectrometers, as well as the understanding of microwave spectroscopic theory, constantly evolved. Today, countless microwave spectroscopic studies on different types of molecules exist. As one of many examples a series of acetates shall be mentioned. The gas phase structures of diverse aliphatic [5] [6] [7] [8] [9] [10], branched [11] [12] [13] and unsaturated acetates [14] [15]

[16] [17] have been thoroughly investigated due to their interesting odorant characteristics, with one of the biggest advantages of microwave spectroscopy being that it allows for the distinction between different conformations of a molecule. In a few rare cases, it is even possible to separate different enantiomers via microwave spectroscopy [18].

A phenomenon with major implications for microwave spectroscopy is the so-called internal rotation. Internal rotation is a large amplitude motion, where one part of the molecule, normally a small functional group such as a methyl group, rotates against the rest of the molecule. This rotation causes each of the lines in the microwave spectrum to split into multiplets. Hence, a deep understanding of internal rotation is essential for a successful spectral analysis. The width of the splittings depends on numerous influences, i. a. transition type, orientation of the internal rotor in the molecule and barrier to internal rotation.

Especially the barrier height of an internal rotor can be used to quantify the effects of internal rotation, since its value is often connected to a specific functional group or conformation. For example, the barrier height of the acetyl methyl group in the above mentioned series of acetates is always about 100 cm -1 [5] [6] [7] [8] [9] [10] [11] [13] [16], while esters containing a methoxy methyl group undergoing internal rotation show barrier values of around 420 cm -1 [5] [19] [20] [21] [22] [23] [24] [25].

Ketones constitute one of the biggest substance classes and are widely used in organic chemistry. Unsurprisingly, numerous microwave spectroscopic investigations of ketones with different structures have been performed. For example, there are studies on branched ketones, such as methyl isobutyl ketone [26], methyl neopentyl ketone [27], pinacolone [28], and diisopropyl ketone [29], as well as on unsaturated ketones like methyl vinyl ketone [30] and allyl acetone [31]. Works on diverse ring containing ketones, either aromatic [32] [33] [34] [35] [36] or not [37] [38] [39] [40], also exist. Moreover, there are analyses of molecules like cyclobutanone [41], cyclohexanone [42], diacetyl [43] and trifluoroacetone [44] forming complexes with water. In the cases of acetylacetone [45], trifluoroacetone [46] and hexafluoroacetylacetone [47], microwave spectroscopy provided insights into the two structural versions of their keto-enol tautomerism.

Despite this large pool of literature, the behaviour of functional groups undergoing internal rotations within the ketone class remains somewhat unclear. In ketones containing an acetyl methyl group as an internal rotor, one of the lowest barriers is found in acetylacetone with a value of 57.0 cm -1 [45], while in acetophenone the barrier is as high as 627.0 cm -1 [33].

Although the barrier to internal rotation of the acetyl methyl group appears to depend strongly on the substitution on the other side of the carbonyl group, no conclusive trends could be drawn [48]. The aim of this thesis is to determine general rules and to explain the rather wide range of the barriers of ketones containing an acetyl methyl group. For this purpose, systematic microwave spectroscopic studies on aliphatic, unsaturated and branched ketones were carried out. The key question to be answered is: Is the barrier height of an acetyl methyl group in a ketone linked to the overall structure of the molecule?

As will be shown throughout this dissertation, this question can be answered with a firm yes, and the connection of the barrier height to the structure of the molecule will be thoroughly explored and categorised. The remainder of this document is organised as follows: Part II gives an overall summary of the relevant microwave spectroscopic theory and the general analysis procedure applied. In Part III, IV and V the investigated molecules according to the different barrier classes eventually identified are presented. The conformers of the linear aliphatic methyl alkyl ketones propan-2-one (Chapter 3), hexan-2-one (Chapter 4), heptan-2one (Chapter 5) and octan-2-one (Chapter 6) belong to the ketones of the "C 1 " and "C s class" (Part III). The results of these chapters have already been published in Ref. [START_REF] Andresen | [END_REF], [2], [3],

and [4], respectively. The unsaturated molecules E-3-penten-2-one (Chapter 7) and 3-methyl-3-buten-2-one (Chapter 8) are representatives of the "mesomeric class" (Part IV). The "tunnelling class" (Part V) is explained with the example of 3-methylbutan-2-one (Chapter 9).

Lastly, a general discussion and a final conclusion are given in Part VI and Part VII, respectively. The Appendix is marked as Part VIII.

II Theoretical Foundations and Methods

Theoretical Foundations

In this chapter, a summary of the microwave spectroscopic theory relevant for this thesis is given, paraphrasing mainly the descriptions by Gordy and Cook (Ref. [START_REF] Gordy | Microwave Molecular Spectra[END_REF]). Operators of parameters are printed with a bold symbol.

Microwaves are radiations with wavelengths in the order of 30 cm to 0.3 mm (1 GHz to 1 THz). In this dissertation, an energy range from 2 to 40 GHz is utilised. The microwave spectra measured here are hence rotational spectra. The transition j ← i between the rotational energy levels i and j is allowed if the transition dipole moment μ ij is unequal zero.

μ ij = ∫ Ψ i * μ Ψ j dτ ≠ 0 (1.1)
Ψ is the wave function of the energy level and μ the transition dipole moment operator. The energy E of a rotational level can be determined by solving the Schrödinger equation. In the principal axis system, the coordinates are chosen in such a way that the moment of inertia tensor I does not exhibit any off-diagonal elements, which simplifies many calculations.

H Ψ = E Ψ

I = (

I a 0 0 0 0

I b 0 0 I c ) (1.6)
Nevertheless, in theory any coordinate system with the coordinates x, y, z can be chosen. A general expression for I in a body-fixed, gravity-centred, rectangular coordinate system is given in Eq. (1.7). Here, the matrix elements are defined as:

I xx = ∑ m i (y 2 + z 2 ) n i
(1.8)

I yy = ∑ m i (z 2 + x 2 ) n i
(1.9)

I zz = ∑ m i (x 2 + y 2 ) n i
(1.10)

I xy = I yx = -∑ m i x y n i
(1.11)

I yz = I zy = -∑ m i y z n i
(1.12)

I zx = I xz = -∑ m i z x n i
(1.13)

Symmetric Top

In the so-called rigid-rotor model it is assumed that the molecule does not experience any distortion or internal motion. H hence only contains the kinetic energy T, which can be expressed with the total angular momentum P.

H = T = P 2 2I
(1.14)

In vector notation P is defined with the angular momentum components P a , P b and P c as:

P = ( P a P b P c ) (1.15)
Consequently, the value of P 2 can be determined as:

P 2 = P a 2 + P b 2 + P c 2 (1.16)
Using the operators P a , P b and P c , the Hamiltonian operator can be written as:

H = P a 2 2I a + P b 2 2I b + P c 2 2I c
(1.17)

For a symmetric top molecule, Eq. (1.17) can be further simplified, as shown for the case of a prolate top (I a < I b = I c ), where a is the main principal axis.

H = P 2 2I b + P a 2 2 ( 1 I a - 1 I b ) (1.18)
Since the respective operators P 2 and H commute with each other, as well as with either operator P a , P b or P c , the operators share a common set of eigenfunctions, containing the Schrödinger equation (Eq. (1.2)) and the following equations.

P 2 Ψ J,K = ħ 2 J (J+1) Ψ J,K (1.19)
P a Ψ J,K = ħ K Ψ J,K

(1.20)

P a 2 Ψ J,K = ħ 2 K 2 Ψ J,K
(1.21) J = 0, 1, 2, ... is the rotational quantum number, while K = 0, ±1, ..., ±J is the projection quantum number. h and ħ are the Planck constant and the reduced Planck constant, respectively. With the definition of the rotational constants A, B and C given in Eq. (1.23) to

Eq. (1.25), the energy eigenvalues of a rotational level can be deduced as: Analogously, the energy eigenvalues of an oblate top (I a = I b < I c ), where c is the main principal axis, are obtained as:

E J,K = B J (J + 1) + (A -B) K 2
E J,K = B J (J + 1) + (C -B) K 2 (1.26)
Furthermore, special selection rules for a transition J' K' ← J K of the symmetric top can be derived from the general selection rule (Eq. (1.1)). These special rules are ΔJ = J' -J = 0, ±1

and ΔK = K' -K = 0, with lines in the spectrum being separated in different branches, called P-(ΔJ = -1), R-(ΔJ = +1) and Q-branches (ΔJ = 0).

Asymmetric Top

In case of an asymmetric top, each principal moment of inertia exhibits a different value (I a < I b < I c ), and H does not commute with either operator P a , P b or P c , since no main axis can be defined. For this reason, using commutation rules to solve the Schrödinger equation (Eq. (1.2)) is not possible. Instead, the wave function of an asymmetric top is expressed by a combination of eigenfunctions Ψ n 0 , for which energy eigenvalues are obtainable.

Ψ = ∑ c n Ψ n 0 n (1.27)
Here, c n are weighting constants and insertion in the Schrödinger equation (Eq. (1.2)) leads to a linear set of equations (Eq. (1.28)) and a matrix eigenvalue problem.

∑ c n [H mn -E δ mn ] n = 0 (1.28)
The value of δ mn is δ mn = 0 when m ≠ n and δ mn =1 when m = n. H mn is the Hamiltonian matrix element defined as:

H mn = ∫ Ψ m 0 H Ψ n 0 dτ (1.29)
The energy eigenvalues E can thus be acquired by diagonalising the Hamiltonian matrix.

A more figurative explanation of the asymmetric top is the idea of placing it between a prolate and an oblate symmetric top, with the degree of asymmetry being expressed by Ray's parameter κ.

κ = 2 B -A -C A -C (1.30)
κ takes values between -1 and +1 with κ = -1 representing the prolate top and κ = +1 the oblate top. Consequently, "near prolate" and "near oblate" tops with values of κ ≈ -1 and κ ≈ +1, respectively, also exist.

Analogously, the energy levels of an asymmetric top can be labelled with so-called pseudoquantum numbers. In this notation, J K a K c is the asymmetric level energetically located between the level J K a of the prolate top and the level J K c of the oblate top.

Centrifugal Distortion

The rigid-rotor model is a good starting point to set up the Hamiltonian. Nevertheless, real molecules are not rigid but experience a distortion by centrifugal forces upon rotation. Thus, the rigid-rotor Hamiltonian H R needs to be expanded by a distortion term H D . Distortion is hence a correction to the rigid rotor.

H = H R + H D (1.31)
The term H D is set up by combinations of the angular momentum components and specific centrifugal constants. One way to express H D following Watson's A reduction in I r representation is given in Eq. (1.32).

H D = -Δ J P 4 -Δ JK P 2 P a 2 -Δ K P a 4 -2δ J P 2 (P b 2 -P c 2 )

δ K [P a 2 (P b 2 -P c 2 ) + (P b 2 -P c 2 ) P a 2 ]

(1.32)

In case of Watson's S reduction, H D is defined as: 4 -D JK P 2 P a 2 -D K P a 4 + d 1 P 2 (P + 2 -P - 2 )

H D = -D J P
+ d 2 (P + 4 + P - 4 )

(1.33)

With P + and P -being the respective step-up and step-down operator:

P + = P b + iP c
(1.34)

P -= P b -iP c (1.35)
Δ J , Δ JK , Δ K , δ J and δ K or D J , D JK , D K , d 1 and d 2 , respectively, are the quartic distortion constants, but H D can be further extended with sextic, octic etc. distortion constants, if these corrections are needed.

Internal Rotation

Besides the overall rotation of the entire molecule, there can also be a large amplitude motion hindered by a barrier within a molecule. In the case of internal rotation, a rigid top, for example a methyl group, rotates against a rigid frame, e.g. the rest of the molecule. As illustrated in Figure 1.1, this torsion, expressed through the torsional angle α, results in a potential energy curve with a maximum at an eclipsed position and a minimum at a staggered position. In general, there are N equivalent positions and the potential energy V is defined by a Fourier series expansion.

V(α) = a 0 + ∑ a k cos kNα ∞ k=1
(1.36)

For a methyl group with its three hydrogen atoms and many other internal rotors with C 3 symmetry, there are three equivalent positions (N = 3), and Eq. (1.36) can be written as Eq. (1.37), with the first two terms of the Fourier series being often enough to accurately describe the internal rotation.

V(α) = V 3 2 (1 -cos 3α) + V 6 2
(1 -cos 6α) + …

(1.37) Figure 1.1: Schematic threefold potential energy curve dependent on the torsional angle α. The quantum number v refers to the different vibrational states. The energy levels split into (0) and (1) species levels.

In the microwave spectrum, the phenomenon of internal rotation of a methyl group leads to interesting effects. Depending on the height of the barrier hindering the torsion, three different cases are distinguished:

(i) For an infinite high barrier, the internal torsion is rather considered as back and forth oscillations at the three equivalent positions, which are expressed through three separate harmonic oscillators. Each vibrational energy level with the quantum number v = 0, 1, 2, ... is hence threefold degenerated and the rotational microwave spectrum behaves like that of a rigid rotor, where centrifugal distortion might also be included (see Section 1.3.).

(ii) Free rotation is achieved if the barrier height is zero. In this case, all energy levels except the first one are twofold degenerated, since the rotation can be clockwise or counter clockwise, as shown with the quantum number m = 0, ±1, ±2, ....

(iii) If, however, the barrier height shows a value in between those of cases (i) and (ii), tunnelling effects occur and the threefold degeneracy of the torsional motion is partly removed. The three degenerated energy levels then split in a non-degenerated species, often called A species, and a double degenerated species called E species. In another notation, the non-degenerated species corresponding to the back and forth oscillation is labelled σ = 0 ((0) species), while the double degenerated species referring to a clockwise and counter clockwise internal rotation are labelled σ = ±1 ((1) species). Only transitions from a (0) to a (0) species level or from a (1) to a (1) species level are allowed. Because of Coriolis interactions, the splittings of the energy levels are slightly different for different species and different transitions, which leads to splittings of the lines in the microwave spectrum. The energy U of the split vibrational energy level can be determined with Eq. (1.38), where A (v) is a normalisation factor.

U(α) = ∑ A k (v) e i(3k + σ) α ∞ k=-∞ (1.38)
To calculate the energy of the rotational levels of each species, the Hamiltonian of the rigid rotor must be expanded to include the internal rotation effects, which will be explained in the next paragraphs following the descriptions by Lin and Swalen in Ref. [START_REF] Lin | [END_REF] rather than those by Gordy and Cook (Ref. [START_REF] Gordy | Microwave Molecular Spectra[END_REF]).

In principle, for a molecule experiencing internal rotation, the total angular momentum P is extended by the angular momentum of the internal rotor P α . Analogously, the moment of inertia I now includes the component I α . It is noteworthy that in the principal axis system the tensor I no longer is a diagonal matrix, with λ g denoting the direction cosine of the angle between the internal rotor axis i and the principal axis g = a, b, c. λ g = cos ∡(i,g)

P = (

(1.41)
The Hamiltonian H needs to be constructed from three parts: The part for the overall rotation H R , which might also be extended to include centrifugal distortion (see Section 1.3.), the part for the internal torsion H T and the part for the interaction between those two H RT .

H = H R + H T + H RT (1.42)
With Eq. (1.39) and Eq. (1.40), these parts result to: The additional parameters are defined as: Finding solutions for the Schrödinger equation (Eq. (1.2)) including internal rotation (Eq. (1.42)) is not trivial, and there are different programs available, which are able to calculate rotational energy levels including internal rotation, as well as predict microwave spectra. Each of these programs follows slightly different approaches to solve the occurring mathematical problems. The strategies of the programs XIAM [51] and BELGI [52] [53] are explained in Section 2.3.1. and Section 2.3.2., respectively. In some cases, it might be necessary to include higher-order parameters for a correct description of the overall-rotationinternal-rotor interactions. These parameters are similarly set up as distortion parameters are treated in a rigid-rotor model (see Section 1.3.)

H R = ( 1 2I a + Z aa ) P a 2 + ( 1 2I b + Z bb ) P b 2 + ( 1 2I c + Z cc ) P c
Z gh = Fρ g ρ h
If a molecule exhibits more than one internal rotor, for example two methyl groups undergoing internal rotation labelled with the indices i = 1 and i = 2, the potential energy becomes:

V(α 1 ,α 2 ) = V 3,1 2
(1 -cos 3α 1 )

+ V 3,2 2
(1 -cos 3α 2 ) + V' 12 sin 3α 1 sin 3α 2 + V 12 cos 3α 1 cos 3α 2 + …

(1.51)

V 12 and V' 12 are top-top coupling parameters. If there are no or only small interactions between the two rotors, these parameters are negligibly small and the different rotors can be treated separately.

The lines in the microwave spectrum of a two-top molecule split into five species. These species can be called AA, AE, EA, EE and EE* species in Dreizler's notation [54], or A, E1, E2, E3, and E4 species using the permutation-inversion formalism of the G 18 group [START_REF] Bunker | Molecular Symmetry and Spectroscopy[END_REF]. In this dissertation the same notation as in Ref. [START_REF] Ferres | [END_REF] is used, with the five species being labelled as (σ 1 σ 2 ) = (00), ( 01), (10), (11) and (12). Illustratively, (00) refers to a state without internal rotation and for the (01) and (10) species only one top rotates, respectively. ( 11) and ( 12) can be considered to describe two rotating tops either in the same or in opposite directions to each other.

Inversion Tunnelling

Internal rotation is not the only large amplitude motion, which might be observed in a molecule. In this section, the motion connecting two identical but inverted configurations shall be further explored. Such an inversion motion is most famously known for the example of ammonia (NH 3 ), where there are two equivalent pyramidal configurations separated only by a small barrier. Hence, a tunnelling between the two configurations occurs. A schematic depiction of the potential energy curve for a general inversion tunnelling motion is given in For an infinitely high barrier dividing the two minima of the potential energy curve, corresponding to the two inverted configurations, there would be two degenerated energy levels for each value of v. However, for a small barrier, tunnel effects lift the degeneracy and cause a splitting of each rotational level into two respective levels of opposite symmetry called (+) and (-). The (+) level and the (-) level are separated by a defined energy ΔE t and the wave function Ψ + or Ψ -of the respective level is determined by a linear combination of the wave functions ϕ 1 and ϕ 2 of the two equivalent configurations, respectively.

Ψ + = 1 √2
(ϕ 1 + ϕ 2 )

(1.52)

Ψ -= 1 √2
(ϕ 1 -ϕ 2 )

(1.53) Figure 1.2: Schematic potential energy curve of an inversion motion along the coordinate x.

The energy level at each vibrational level v splits into a (+) and a (-) species level.

Mathematically, the tunnelling motion may induce a change of sign of the dipole moment components describing the different inversion configurations. This is especially interesting for the general selection rule (Eq. (1.1)), since it leads to the deduction of special selection rules for the two tunnel levels. The selection rules are (+) ↔ (+) and (-) ↔ (-) if the sign of the dipole moment component μ g with g = a, b, c stays the same. In this case, there are no splittings in the microwave spectrum. But if the signs change upon the tunnelling motion, the selection rules are (+) ↔ (-) and (-) ↔ (+), as illustrated in Figure 1.3. The resulting splittings are hence 2ΔE t .

In general, ΔE t can theoretically be obtained from the potential energy curve and experimentally from the splittings in the spectrum. Nevertheless, the determination can be difficult to achieve due to effects of e.g. centrifugal distortion or Coriolis interactions influencing the tunnel splittings. As also depicted in Figure 1.3, in a molecule experiencing inversion tunnelling as well as internal rotation, the effects of both phenomena can be separately dealt with. However, if the two large amplitude motions couple and have a significant impact on each other, there is currently no program code for a global treatment available.

Methods

All microwave spectroscopic studies performed in this dissertation follow the same general scheme, as is illustrated in Figure 2.1. First of all, the microwave spectrum of the target substance is measured. Short descriptions of the spectrometers in use are given in Section 2.1.

In a next step, characteristic parameters, such as the rotational constants and barriers to internal rotation of any given conformer (see Chapter 1), are calculated. In Section 2.2., wellestablished quantum chemical methods suitable for such calculations are summarised. The calculated parameters are then used to predict the microwave spectrum. A predicted spectrum is necessary to interpret and assign the lines of the experimental spectrum correctly, as well as to fit experimentally deduced parameters. To predict and/or fit the lines of a spectrum, various specific programs are available, for example SPFIT/SPCAT [57], ERHAM [58] and RAM36 [59]. In this thesis, only the XIAM [51] and the BELGI [52] [53] program have been applied and are further explained in Section 2.3.1. and Section 2.3.2., respectively. Depending on the accuracy of the calculated parameters, several iterative cycles of prediction and assignment might be needed to finally achieve fits with experimental accuracy.

Microwave Spectrometers

To record the microwave spectra, two molecular jet Fourier transform microwave spectrometers have been used, one as described in Ref. [60] working in the frequency range of 2.0 to 26.5 GHz, the other operating between 26.5 and 40.0 GHz, as described in Ref. [61].

In principle, both spectrometers work in the same way. Microwave radiation with the frequency υ is created by a microwave synthesizer and up-converted by a single side band mixer to a frequency of υ + 160 MHz. A single-pole double-throw (SPDT) PIN diode switch then generates a pulse, which is guided into the Fabry-Pérot resonator of the spectrometer.

The Fabry-Pérot resonator is an evacuated cavity at a pressure about 10 -7 mbar with two curved mirrors. One of these mirrors is tuneable to create a standing wave. The target substance is mixed with a carrier gas, usually helium or argon, and inserted into the cavity through a nozzle, typically at a pressure ranging from about 100 to 200 kPa, resulting in a cooling of the gas jet to very low temperatures in the order of a few Kelvin. The microwave pulse excites the substance molecules, which afterwards relax back to their original state. The free induction decay (FID) of this relaxation is detected by an antenna, and the detected frequency now shows an off-resonance component δ. The frequency is subsequently down-

Quantum Chemical Tools

Calculating the energy of a molecule with any given electronic structure is a basic operation in quantum chemistry. Likewise, it is trivial to find energetically stable conformers via socalled geometry optimisations. A fundamental background of quantum chemical calculations will hence not be further explained here. In this dissertation, calculations were performed using the Gaussian package, either in its Gaussian09 [62] or Gaussian16 [63] version. The methods applied are MP2, B3LYP, B3PW91, M06-2X, B3LYP-D3 and B3LYP-D3BJ.

MP2 is a perturbation theoretical approach, where a Hartree-Fock calculation is corrected by a second-order correlation energy correction as first introduced by Møller and Plesset [64] and later expanded and implemented in the Gaussian program by multiple authors [65] [66] [67] [68] [69].

B3LYP, B3PW91 and M06-2X are functionals of the density functional theory (DFT). DFT uses the electron density as foundation for the calculations and is based on the Hohenberg-Kohn theorems [70] and the Kohn-Sham equations [71]. Different functionals follow different approaches to model the exchange and correlation interactions of the molecule. B3LYP and B3PW91 are both hybrid functionals as developed by Becke [72], with B3LYP being further devised by Stephens et al. [73]. M06-2X is a hybrid meta exchange-correlation functional introduced by Zhao and Truhlar [74]. D3 and D3BJ are add-ons to certain DFT functionals to account for London dispersion interactions, called Grimme's dispersion correction [75] [76].

The D3BJ method supplementary uses so-called Becke-Johnson (BJ) damping [76].

All of these methods can be operated with different basis sets. In this work, mainly triple split Pople basis sets (6-311G) in different combinations with diffuse (+ or ++) and polarisation functions (e.g. (d,p), (df,pd) or (3df,3pd)) are being utilised [77]. Moreover, polarised valence double-(cc-pVDZ) and triple-zeta (cc-pVTZ) Dunning basis sets are applied [78].

Diffuse functions are included in the augmented basis sets called aug-cc-pVDZ and aug-cc-pVTZ [78]. In the principal axis system, the rigid-rotor part is easy to deal with and the meaning of the parameters is clear. However, in the cases where internal rotations are included, the choice of the coordinate system has a big impact on the appearance of the Hamiltonian matrix and the mathematical procedure to handle it. In the principal axis system, large coupling components between the internal and the overall rotation appear in the form of off-diagonal elements, and the treatment becomes more difficult (see Section 1.4.). An alternative axis system is the rho axis system, where the main axis z is chosen in such a way that it aligns with the vector ρ of the internal rotor axis. This leads to an elimination of all couplings between P α , P x and P y , and only interactions between P α and P z remain.

Fitting Programs

The XIAM code [51] is a program capable to predict and fit the microwave spectrum of a molecule with up to three internal rotors using the so-called combined axis method (CAM). This method applies two general steps.

Starting from the principal axis system, a transformation to a rho axis system is performed, with the Hamiltonian matrix of each internal rotor being set up in its own rho axis system.

The transformation is defined by the angles β and γ, referring to a rotation about the y and x axis, respectively.

cos β = ρ z √ρ x 2 + ρ y 2 + ρ z 2 (2.1) cos γ = ρ x √ρ x 2 + ρ y 2 (2.2)
In the rho axis system the Hamiltonian matrix is diagonal in K, making it easy to obtain eigenvalues and eigenfunctions connected to the internal torsion parts of the Hamiltonian H T and H RT (see Eq. (1.42)).

In a second step, a retransformation in the principal axis system is performed and the elements of the global energy matrix, consisting of rigid-rotor parts, transformed eigenvalues of each internal top and top-top coupling operators, can be determined.

Because the three angles ∡(i,g) with g = x, y, z are not independent of each other, XIAM uses the angles δ and ε instead. BELGI is a program for predicting and fitting the microwave spectrum of molecules with one internal rotor of C 3v symmetry. It exists in two versions, the BELGI-C s version [52] for molecules with a planar frame of C s symmetry, as well as the BELGI-C 1 version [53] for molecules without any symmetry constraints.

According to the information on the PROSPE website [79], the Hamiltonian matrix is set up in a rho axis system and BELGI follows a two-step diagonalisation procedure: First, a 21 x 21 matrix for each K quantum number and each species ((0) species or (1) species) is created, resulting in eigenvalues and eigenfunctions describing the internal torsion parts of the Hamiltonian. In the second step, a matrix for each J value is set up also including the overall rotation, centrifugal distortion and rotation-torsion coupling terms. This Hamiltonian matrix is diagonalised. The matrix dimension is of the order 9 • (2J + 1) x 9 • (2J + 1), since the nine lowest vibrational states v are taken into account.

Comparing the BELGI-C 1 with the BELGI-C s version, different group-theoretical considerations due to the different molecular symmetries lead to complex matrix elements in the C 1 version. An example for an imaginary component is the parameter D aci , multiplying {P a ,P c }.

In comparison to the XIAM program (see Section 2.3.1.), BELGI allows the use of many higher order parameters, different from those in XIAM. The specific sets of parameters used in this dissertation are given in the respective molecule chapters (Chapter 3 to Chapter 6).

III Ketones of the C 1 and C s Class

To investigate the connection between the molecular structure of a ketone and the internal rotation of its acetyl methyl group, at first, systematic studies on a series of rather simple linear aliphatic ketones containing an acetyl methyl group were conducted. The smallest ketone is acetone, which consists of a carbonyl group and two acetyl methyl groups. Acetone may also be one of the most analysed molecules in the microwave spectroscopic community with studies published every few years, starting with a first detection in 1949 by Bak et al. [80]. The first time that the barrier heights of the acetyl methyl groups have been determined was in 1959 by Swalen et al. [81]. Due to expanding data sets, the value of 274 cm -1 found there was corrected multiple times over the years [82] [83] [84] [85] [86],

more recently in 2013 in a paper by Ilyushin et al. where a barrier height of 242.09 cm -1 has been reported [87]. The next smallest ketone in the series is methyl ethyl ketone, also called butan-2-one. This molecule has already been thoroughly investigated, as well [88] [89] [90].

As published by Nguyen et al. in 2014 [91], the barrier to internal rotation of the acetyl methyl group is 183.170 cm -1 . Moreover, the barrier height of the ethyl methyl group has been determined to be 765 cm -1 .

If the ethyl group of methyl ethyl ketone is further extended, the next members of the saturated methyl n-alkyl ketone series are obtained, which are methyl propyl ketone, methyl butyl ketone, methyl pentyl ketone and methyl hexyl ketone, or, following the IUPAC nomenclature, pentan-2-one, hexan-2-one, heptan-2-one and octan-2-one (see Figure 1).

These four molecules are analysed in the following chapters (see Chapter 3, Chapter 4, Chapter 5 and Chapter 6) and the results have already been published in Ref. [START_REF] Andresen | [END_REF], [2], [3],

and [4], respectively.

All methyl alkyl ketones feature two methyl groups undergoing internal rotation: The acetyl methyl group, which this dissertation is particularly focused on, and the methyl group at the end of the alkyl chain. Splittings due to both methyl groups are expected in the microwave spectrum. In general, methyl alkyl ketones can be used in organic chemistry as reagents in many reactions, especially in nucleophilic additions [START_REF] Brückner | Reaktionsmechanismen -Organische Reaktionen, Stereochemie, Moderne Synthesemethoden[END_REF]. In nature, they are found in the pheromone cocktail of different species, for example in bees [START_REF] Shearer | [END_REF] [94] [95] [96] and mice [97] [98]. Pheromones are signal substances conveying information from one individual of a species to another. They exist within all animals and trigger behavioural changes. The effects and tasks of pheromones are numerous, among other they function as attack triggers, territory markers, and sex fragrances [99]. Since pheromones are detected in olfactory receptors, using microwave spectroscopy for gas phase and conformational analyses might bring further insights to the complex odorant-receptor interplay. Although it is known that the composition of the pheromone mixture and the presence of certain functional groups play the most decisive role [99], an important aspect might also be the preference of a given receptor to a certain conformational structure of the pheromone substance. The results from this dissertation might be a first step for further investigations in this direction. However, combined efforts of chemistry, biology and theoretical calculations will be necessary in the future to finally unveil this mystery. the contents of the manuscript. Dr. Layla Tulimat and Jade Turrel are thankfully acknowledged for the measurements and preliminary calculations they carried out to contribute to this work. Preliminary studies on this chapter's topic were performed within the Master thesis titled "Microwave Spectroscopic and Quantum Chemical Investigations on Methyl Alkyl Ketones" by Maike Andresen presented to the RWTH Aachen University.

Quantum Chemical Calculations

Geometry Optimisations 3.1.1.

To obtain possible conformers of pentan-2-one, also called methyl propyl ketone (MPK), we created various starting geometries by setting the dihedral angles θ 1 = ∡(C 1 ,C 5 ,C 7 ,C 10 ) and θ 2 = ∡(C 5 ,C 7 ,C 10 ,C 13 ) (for atom numbering, see Figure 3.1) to 180°, 60°, and -60° and optimised all geometry parameters including θ 1 and θ 2 . The dihedral angle ∡(A,B,C,D) is defined as the angle between the ABC plane and the BCD plane. When looking from B to C, a clockwise rotation refers to a positive angle, while the value is negative for the counter clockwise direction. The rotations about the C 1 -C 5 and C 10 -C 13 axes are equivalent to the internal rotation of the acetyl and propyl methyl group, respectively, and do not create new conformations. The nine starting geometries were optimised to a local energy minimum at the MP2/6-311++G(d,p) level of theory using the Gaussian09 package [62], yielding four conformers, which are illustrated in Figure 3.2. This level of theory was chosen since it calculated rotational constants close to the experimental ones in many of our previous works [100] [101] [102]. Additional harmonic frequency calculations proved that all of the conformers are stable ones and not saddle points. The calculated energies, rotational constants, dipole moment components, and optimised dihedral angles θ 1 and θ 2 are listed in Table 3.1. The nuclear coordinates in the principal axis system of all conformers are available in Table 13.1 in the Appendix. The global minimum conformer, conformer I, occurs at (θ 1 , θ 2 ) = (161.4, -69.5°, see Table 3.1) and has the propyl methyl group tilted out of the plane spanned by the C 1 , C 5 , O 6 , C 7 atoms (which make up the acetyl group). Similar structures where the γ-carbon is in a nearly synclinal position have been observed for molecules containing a propyl group, such as n-propyl acetate [7] and methyl butyrate [20]. For the former molecule, the tilt angle is 63.0° and for the latter 68.5°.

The conformer with the second lowest energy (called conformer II) seems to possess C s symmetry, but a closer look at the structure reveals that the real symmetry is not C s . The propyl chain is tilted out of the C s plane at the α-carbon position by an angle of about 10° (θ 1 = 170.1°, see Table 3.1). This "pseudo-C s " structure has been frequently observed in previous investigations on aliphatic ketones. For example, a tilt angle out of the C-(C=O)-C plane of about 10° was calculated for each ethyl group in diethyl ketone [103]. A similar tilt angle was found for the tert-butyl group in methyl neopentyl ketone [27] and the ethyl group in methyl ethyl ketone [91], while pinacolone features a larger tilt angle of 16° [28]. The two other conformers, conformer III and IV, both show a value of θ 1 ≈ ±60° and are, respectively, about 2 and 4 kJ mol -1 higher in energy than conformer I. We expected that they cannot be observed in the microwave spectrum under the molecular jet conditions described in Section 3.2.1., and therefore, we did not consider them for the spectral analysis. Table 3.1: Relative energies at equilibrium and with zero-point corrections (in kJ mol -1 ), rotational constants (in GHz), dipole moment components (in Debye), and optimised dihedral angles θ 1 = ∡(C 1 ,C 5 ,C 7 ,C 10 ), θ 2 = ∡(C 5 ,C 7 ,C 10 ,C 13 ) (in degree) of the four conformers (I-IV) of methyl propyl ketone calculated at the MP2/6-311++G(d,p) level of theory. E [a] E ZPE [c] 8.336 1.795 1.534 [a] Referring to the absolute energy of E = -271.047861 Hartree of conformer I. [b] Referring to the zero-point corrected energy of E = -270.905256 Hartree of conformer I. [c] Experimentally deduced rotational constants obtained from the XIAM(1Top) fits; see Table 3.2.

Basis Set Variation 3.1.2.

Full geometry optimisations were first carried out at the MP2/6-311++G(d,p) level. However, since the calculated structures and consequently the rotational constants of the conformers depend strongly on the level of theory in use [17] [104], the optimisations were redone for the two assigned conformers (see Section 3.2.3.) using a series of MP2 and DFT calculations with different basis sets (for more information see Section 2.2.). A comparison of the calculated and the experimental values explores the level of theory that best matches the experimental rotational constants. The results are summarised in Table 13.2 and Table 13.3 for conformer I and in Table 13.4 and Table 13.5 for conformer II (see Appendix). The results will be discussed in Section 3.3. and in detail in Chapter 11.

Internal Rotation 3.1.3.

MPK has two inequivalent methyl rotors, the acetyl methyl and propyl methyl group. Each rotational transition of such a molecule splits into five torsional species labelled as (σ 1 σ 2 ) = (00), (01), (10), (11), and (12) [START_REF] Ferres | [END_REF]. The numbers σ = 0, 1, 2 represent the three symmetry species A, E a , E b of the C 3 groups of the internal rotors, respectively [54]. They correspond to the transformation properties of the C 3 -adapted planar rotor wave functions e i(3k+σ)α with k ∈ ℤ and the torsional angle α. In this notation, σ 1 refers to the acetyl methyl group and σ 2 to the propyl methyl group.

The barriers to internal rotation of the acetyl and propyl methyl group were calculated for the lowest energy conformers, conformers I and II, by varying the dihedral angle α 1 = ∡(H 2 ,C 1 ,C 5 ,C 7 ) and α 2 = ∡(C 7 ,C 10 ,C 13 ,H 15 ), respectively in 10° increments, while all other parameters were optimised at the MP2/6-311++G(d,p) and B3LYP/6-311++G(d,p) levels of theory. Because of the symmetry of the methyl group, a range of only 120° was sufficient.

The corresponding energies were parametrised with a one-dimensional Fourier expansion, and the resulting coefficients are given in Table 13.6 in the Appendix.

Acetyl Methyl Group 3.1.3.1.

Figure 3.3 depicts the potential energy curve of the rotation of the acetyl methyl group of conformer I with a threefold potential as expected. However, the shape of the curve is not entirely symmetric, and significant contributions of higher order potential terms are necessary. This is due to the fact that any change in the position of the acetyl methyl group significantly influences the position of the β-carbon of the propyl chain and the dihedral angle θ 1 changes by up to 16.1° during this methyl rotation. Obviously, the one-dimensional curve is not suitable to fully describe this two-dimensional problem. Nevertheless, it is an easy method to obtain an estimate of the corresponding barrier heights, which are 229.8 cm -1 and 168.3 cm -1 calculated with the MP2 and the B3LYP methods, respectively. Figure 3.4 shows the potential energy curve of the acetyl methyl group of conformer II of MPK, where double minima with small local maxima in between them exist. For a closer investigation of these minima, we reduced the step width of the dihedral angle α 1 to a grid of 1° in a range of ±20° around a local maximum and observed a deviation of the position of the minima from the local maximum of up to 15°. The presence of the double minima is also due to the coupling of the acetyl methyl group with the position of the β-carbon of the alkyl chain. Since conformer II features a "pseudo-C s " symmetry with the alkyl chain tilted by about 10° (see Section 3.1.1.), the double minimum represents the two enantiomers of the conformer. The barrier heights calculated at the MP2/6-311++G(d,p) and B3LYP/6-311++G(d,p) levels are 147.6 cm -1 and 115.7 cm -1 , respectively.

Propyl Methyl Group

3.1.3.2.

In contrast, the potential energy curves of the rotation of the propyl methyl group illustrated in Figure 13.1 and Figure 13.2 in the Appendix show an almost pure V 3 potential for both conformers at all method and basis set combinations. The Fourier coefficients are available in Table 13.6 in the Appendix. The barrier heights calculated at the MP2/6-311++G(d,p) and B3LYP/6-311++G(d,p) levels of theory are 990.9 cm -1 and 978.9 cm -1 , respectively, for conformer I, while being 1111.1 cm -1 and 1038.0 cm -1 for conformer II.

Microwave Spectrum

Experimental Setup 3.2.1.

The microwave spectrum of MPK was recorded using modified versions of the molecular jet Fourier transform microwave spectrometers described in Ref. [60] and [61] operating in a frequency range from 2.0 to 40.0 GHz (for more information see Section 2.1.). The substance was purchased from Alfa Aesar GmbH & Co KG, Karlsruhe, Germany. The stated purity was more than 99%, and no further purifications were carried out. A mixture of 1% MPK in helium at a stagnation pressure of 100 kPa was expanded through a pulsed nozzle into the cavity. At the beginning, a series of overlapping spectra from 9.9 to 14.4 GHz was recorded in a step width of 0.25 MHz. In a second step, all fitted signals were measured at higher resolution.

Spectral Analysis 3.2.2.

The splittings between the (00) and (10) species arising from the acetyl methyl rotation with a calculated barrier height of about 100 cm -1 to 230 cm -1 (see Section 3.1.3.) range from some MHz up to several GHz, and the (00) and (10) species are well-separated in the broadband scan. The additional splittings of these two components into the (00), (01) species and the (10), (11), (12) species, respectively, due to the propyl methyl group are very small and range from several 100 kHz down to less than 4 kHz. These narrow splittings correspond well with the rather high calculated barrier of around 1000 cm -1 . However, they are not resolvable for all transitions, especially in case of the (00) and (01) species. 00) and (10) species is not resolvable (Ref. [START_REF] Andresen | [END_REF], figure modified for consistent formatting).

Spectral Assignment 3.2.3.

Conformer II 3.2.3.1.

To start the spectrum analysis, the internal rotation effects were neglected, and MPK was considered as a rigid rotor. The rotational constants of conformer II calculated at the MP2/6-311++G(d,p) level of theory given in Table 3.1 were inserted in the XIAM program [51] in its rigid-rotor mode to predict the frequencies of the (00) species for a comparison with the experimental broadband scan. Though quantum chemistry calculated that the dipole moment component in a-direction is much smaller than that in b-direction (see Table 3.1), we still began with searching for a-type transitions, due to their characteristic pattern. Several a-type lines could be identified straightforwardly in the experimental spectrum. Based on this assignment, further a-type and afterward b-type lines could be assigned. This enabled us to predict the whole rigid-rotor spectrum with sufficient accuracy to find all remaining (00) species lines in the frequency range from 2.0 to 40.0 GHz. As a next step, the internal rotation of the acetyl methyl group was considered with a prediction of the (00) and (10) species transitions. The starting value for the angle between the internal rotor axis and the principal axis a was taken from ab initio results at the MP2/6-311++G(d,p) level. The initial V 3 potential was set to 183 cm -1 , which is the value found in methyl ethyl ketone [91]. By comparing the theoretical and experimental broadband scan, the assignment was straightforward for some a-type transitions, where the splittings between the (00) and (10) species were relatively small (less than 50 MHz). The assignment of b-type lines with much larger splittings was more difficult, however successful by trial and error. A total of 174 torsional lines were finally assigned and fitted with the XIAM program to a rootmean-square (rms) deviation of 8.7 kHz, given as XIAM(1Top) fit in Table 3.2. It is notable that this deviation is only achievable by fitting the three higher order parameters D pi2J , D pi2K , and D pi2-. The barrier to internal rotation is 188.3843(50) cm -1 . Since the analysis only includes transitions in the ground torsional state, a strong correlation between V 3 and F 0 is present. Therefore, F 0 was fixed to 158 GHz, corresponding to I α = 3.1986 uÅ 2 , a value often found for methyl groups.

The BELGI-C s [52] fit of the same data set with 14 parameters decreased the rms deviation value to 3.5 kHz. The starting values of the rotational constants A, B, and C were derived by a transformation of the values obtained from the XIAM(1Top) fit into the rho axis system. The initial values of the internal rotation parameters V 3 , ρ, and F were taken directly from the XIAM(1Top) fit, whereby only V 3 and ρ were fitted and F was fixed to the XIAM value. The off-diagonal element D ab (multiplying the off-diagonal {P a ,P b } term) of the moment of inertia tensor was present due to the use of the non-principal axis system and was calculated from the results of the XIAM(1Top) fit. To achieve the measurement accuracy, three centrifugal distortion constants and five higher order parameters (F V , L V , k 1 , k 2 , and c 1 ) were also floated.

The BELGI-C s parameters in the rho axis system are available in Table 13.7 in the Appendix.

Parameters, which can be transformed into the principal axis system, are summarised as BELGI-C s fit in Table 3.2. A list of all fitted transition is given in Table 13.8.

Conformer I 3.2.3.1.

After conformer II was assigned, a large number of lines remained in the scan. For the assignment process of conformer I, the same scheme as mentioned in Section 3.2.3.1. was applied. Nevertheless, it turned out to be much more difficult, because the predicted spectrum did not, at first, match the experimental one. After many trials and errors, the rigid-rotor spectrum containing the (00) species could be assigned. Subsequently, we attempted to assign the (10) species. The angles between the internal rotor axis and the principal axes from ab initio and the V 3 potential of 188 cm -1 found for conformer II were used as initial values.

However, again, no agreement between the theoretical and the experimental spectra could be observed. Hence, the barrier height was increased in steps of 10 cm -1 until the calculated spectrum reasonably matched the experimental one at a surprisingly high value of 240 cm -1 .

A total of 264 torsional lines was finally assigned and fitted with the XIAM program to an rms deviation of 21.0 kHz.

The BELGI-C 1 code [53] improved the deviation of the same data set to 4.6 kHz with 16 parameters, where in this case, parameters such as D aci allowed for molecules with C 1 symmetry were included. A summary of all molecular parameters for the XIAM(1Top) fit and BELGI-C 1 fit is also given in Table 3.2, a list of all fitted transition in Table 13.9 in the Appendix. The BELGI-C 1 parameters in the rho axis system are available in Table 13.7.

Two-Top Fits 3.2.3.2.

Splittings due to the internal rotation of the propyl methyl group are small but resolvable for about half of the rotational transitions. In a XIAM two-top fit, the (01), (11), and (12) species lines were added, and thereby, the number of lines increased to 294 for conformer II and 388 for conformer I (see XIAM(2Tops) fits in Table 3.2). The experimentally deduced barrier height of the propyl methyl group is 978.7(68) cm -1 for conformer I and 1031.6(21) cm -1 for conformer II, which is close to the calculated values (see Section 3.1.3.2.). For both conformers, the F 0 value of the propyl methyl group was also fixed to 158 GHz as for the acetyl methyl group. The angles between the propyl methyl rotor axis and the principal axes could not be fitted and were fixed to the ab initio values derived from the optimised geometries mentioned in Section 3.1.1. The rms deviations of the two-top fits are slightly higher than those of the one-top fits. If the (01), (11), and (12) species lines are referred to the position of the respective (00) or (10) line, the rms deviation of such a relative XIAM fit is 8.0 kHz for conformer I and 7.0 kHz for conformer II by fitting only one parameter, the barrier height of the propyl methyl group. The residuals of these absolute and relative two-top fits are listed in Table 13.8 and Table 13.9 in the Appendix. [c] XIAM(2Tops) All parameters refer to the principal axis system. [b] Parameters obtained by transformation from rho axis system to principal axis system. [c] Watson's A reduction and I r representation were used. [d] Internal rotation parameters of the second rotor are fixed to F 0,2 = 158.0 GHz, ∡(i 2 ,a) = 110.5°, ∡(i 2 ,b) = 68.6°, and ∡(i 2 ,c) = 30.4°. [e] For this conformer, F 0,2 = 158.0 GHz, ∡(i 2 ,a) = 153.0°, ∡(i 2 ,b) = 117.0°, and ∡(i 2 ,c) = 90.0°. [f] Total number of lines. [g] Number of lines of each symmetry species. [h] Root-mean square deviation of the fit.

XIAM(1Top)

Pentan-2-one -

Discussion

According to the XIAM(1Top) fits, the torsional barrier of the acetyl methyl group is 238.145(21) cm -1 for conformer I and 188.3843(50) cm -1 for conformer II. The values obtained by BELGI agree within 1%, while improving the rms deviation to measurement accuracy for both conformers (see Table 3.2). Both XIAM fits show larger rms deviations due to the limited number of parameters available in this program, which is proven by some branches of lines with systematic deviations. We notice that the residuals of some lines in the BELGI fits are higher than the average deviation because these transitions show large splittings arising from the internal rotation of the propyl methyl group, which are not considered by the BELGI model.

Conformer I with the barrier to internal rotation of the acetyl methyl group of 238.145(21) cm -1 exhibits a bent structure with C 1 symmetry, where the γ-carbon of the propyl chain is in a nearly synclinal position. For conformer II, the barrier height of 188.3843(50) cm -1 is much smaller. The structure of conformer II is "pseudo-C s ", where the entire propyl chain is tilted out of the heavy atom acetyl plane by about 10° (see Section 3.1.1.). By comparing the results of the present chapter with other ketones investigated in the literature, we found a scheme with two different classes. The first class contains ketones featuring a "pseudo-C s " structure where the torsional barrier is always close to 180 cm -1 . Examples are conformer II of MPK (≈ 188 cm -1 ) and methyl ethyl ketone (≈ 183 cm -1 ) [91]. Even if the alkyl chain is branched, as in the case of methyl neopentyl ketone, the barrier height seems to be almost unaffected (≈ 174 cm -1 ) [27]. The second class comprises molecules with a real C 1 symmetry and a higher barrier height of about 240 cm -1 .

Conformer I of MPK (≈ 238 cm -1 ), allyl acetone (≈ 225 cm -1 ) [31], and methyl isobutyl ketone (250 cm -1 ) [26] belong to this class. In the following chapters of this dissertation, this "two class concept" will be verified and expanded.

Geometry optimisations of conformer II have shown that the propyl group is slightly tilted out of the plane containing the acetyl group. Nevertheless, despite carefully searching for c-type transitions, none of them were found. The absence of c-type transitions suggests the following possibilities: (i) The real structure features C s symmetry. (ii) The real structure is not C s ; however, the dipole moment component in c-direction is too small, and thus, c-type lines are too weak to be detected with the sensitivity of the spectrometer. (iii) The enantiomers are separated by a low barrier, and the tunnelling ground state is above this barrier causing an "effective C s " geometry. In this case, the expectation value of the dipole moment in c direction would be zero. Indeed, calculations at the MP2/6-311++G(d,p) level of theory yield a tunnelling barrier height of 15.0 cm -1 , while the ground state lies at about 30.0 cm -1 .

The V 6 contribution in the potential of the acetyl methyl group of conformer II, as presented in Figure 3.4, would generate additional splittings of the A and E torsional species of the threefold rotor, if the lowest torsional level lay below the local maxima, as it is, for example the case for pinacolone [28]. This is clearly not the case for MPK because no additional splittings rather than those of the propyl methyl torsion are observed in the spectrum. A further support for a C s or an "effective C s " symmetry is that the fit achieved with BELGI-C s , which reproduced the experimental data within measurement accuracy, did not require any out-of-plane terms. Finally, the inertial defect Δ c = I c -I a -I b of -12.688 uÅ 2 confirms that the heavy atom skeleton effectively is planar. This value is almost the same as that found in methyl butyrate (Δ c = -13.018 uÅ 2 ) [20], which also contains four pairs of out-of-plane hydrogen atoms.

The observed rotational constants of conformer II agree within approximately 1% with the calculated values obtained at different method and basis set combinations (see Table 13.4 and Table 13.5 in the Appendix). They differ more significantly for conformer I, especially for the A rotational constant (see Table 13.2 and Table 13.3 in the Appendix). At some levels of theory with the MP2 method, the calculated A rotational constant is up to 4% smaller than the experimental value. The deviations are in general better with DFT based levels, which is probably due to error compensation.

Most of the lines in the microwave spectrum of MPK were assigned to either conformer I or conformer II. In the range of the broadband scan, which spans 4.5 GHz, only 16 weak lines remained unassigned. They might be due to conformer III or IV of MPK, 13 C isotopologues, or impurities.

Conclusions

MPK was investigated by quantum chemical calculations, and the two energetically most favourable conformers were assigned in the rotational spectrum. The barrier to internal rotation of the acetyl methyl group is about 238 cm -1 for conformer I and 189 cm -1 for conformer II. These values could be linked to the geometry of the respective conformer.

Hexan-2-one

The main text passages of Chapter 4 have already been published as: Maike Andresen, Isabelle Kleiner, Martin Schwell, Wolfgang Stahl, Ha Vinh Lam Nguyen

Sensing the Molecular Structures of Hexan-2-one by Internal Rotation and Microwave

Spectroscopy

ChemPhysChem 2019, 20,[2063][2064][2065][2066][2067][2068][2069][2070][2071][2072][2073] In this dissertation, the paper is referred to as Ref. [2]

Quantum Chemical Calculations

Geometry Optimisations 4.1.1.

A total of 27 starting geometries of hexan-2-one, or methyl butyl ketone (MBK), were created by varying each of the dihedral angles θ 1 = ∡(C 1 ,C 5 ,C 7 ,C 10 ), θ 2 = ∡(C 5 ,C 7 ,C 10 ,C 13 ), and θ 3 = ∡(C 7 ,C 10 ,C 13 ,C 16 ) (for atom numbering, see Figure 4.1) to 180°, 60° and -60°. Changing the dihedral angles α 1 = ∡(H 2 ,C 1 ,C 5 ,C 7 ) and α 2 = ∡(C 10 ,C 13 ,C 16 ,H 18 ) corresponds to the internal rotation of the acetyl methyl and the butyl methyl group, respectively, and does not lead to new conformational isomers. Using the Gaussian09 package [62], the starting geometries were optimised at the MP2/6-311++G(d,p) level of theory to local energy minima, yielding 11 different conformers, each of which exists as an enantiomeric pair. Frequency calculations confirmed that all conformers obtained refer to local minima rather than saddle points. To determine the energetically most favourable conformers, not only the calculated electronic energies but also the zero-point energies (ZPE) were considered. The energies relative to that of the lowest energy conformer, rotational constants, dipole moment components, and optimised dihedral angles are summarised in Table 4.1. The angles between the principal axes of inertia and the internal rotor axes are given in Table 14.1 in the Appendix. The MP2/6-311++G(d,p) level of theory was chosen, because it has predicted rotational constants which were in good agreement with the experimental ones in many previous studies [21] [105] [106] [107]. However, since all assignment attempts using the rotational constants predicted at this level of theory as initial values failed (see Section 4.2.2.1.), this level turns out to be inadequate in the case of MBK. This observation is consistent with the results from our studies on the similar molecule methyl propyl ketone (for more information see Chapter 3, here referred to as Ref. [START_REF] Andresen | [END_REF]). Therefore, the 11 conformers were reoptimised at the B3LYP/6-311++G(d,p) level of theory with the results also given in Table 4.1. The order in energy of the conformers obtained from calculations with the MP2 and the B3LYP method is very different. The structures of the three energetically most favourable conformers obtained with the latter method, called conformer I, II and III, are illustrated in Figure 4.2, since they are the conformers eventually identified in the experimental spectrum (see Section 4.2.). Their nuclear coordinates are given in [a] Referring to the absolute energy of E = -310.243919 Hartree of conformer II. [b] Referring to the zero-point corrected energy of E = -310.072583 Hartree of conformer II. [c] Referring to the absolute energy of E = -311.191516 Hartree of conformer I. [d] Referring to the zero-point corrected energy of E = -311.023059 Hartree of conformer I. [e] Experimentally deduced rotational constants of the XIAM(1Top) fit (see Table 4.2). [f] Corrected rotational constants A, B, and C of the respective conformer (see Section 4.2.2.1.).

-

-

Hexan-2-one

Hexan-2-one -40 - Conformer I with a straight butyl chain seems to possess C s symmetry, but the dihedral angles optimised at the MP2 and B3LYP levels shown in Table 4.1 reveal that the whole butyl group is slightly tilted out of the C-(C=O)-C plane by an angle of about 10° (θ 1 = 169.4°) and 5° (θ 1 = 174.5°), respectively. The same phenomenon could be observed in many other aliphatic ketones, as for example in diethyl ketone [103], pinacolone [28], and methyl neopentyl ketone [27] with respective tilt angles of approximately 12°, 16°, and 10°.

Moreover, this tilt-distorted C s structure, hereafter called "pseudo-C s ", is also found for the "straight" conformers of the shorter linear methyl alkyl ketones, methyl ethyl ketone (9°) [91] and methyl propyl ketone (10°) [START_REF] Andresen | [END_REF]. This will be further discussed in Section 4.3.1.

In conformer II, the γ-carbon C 13 (for atom numbering, see Figure 4.1) is in a nearly synclinal position with respect to the C-(C=O)-C plane. The symmetry of this conformer is C 1 and curiously, it contains the C 1 conformer of methyl propyl ketone as a sub-structure [START_REF] Andresen | [END_REF]. In this comparison, the alkyl chain of MBK is by one CH 2 group longer and the supplementary carbon atom is added at the end of the propyl group of methyl propyl ketone in an antiperiplanar position (θ 3 ≈ 180°). This has also been observed for a series of microwave spectroscopic studies on n-alkyl acetates and methyl alkanoates [5]

[6] [7] [8] [9] [10] [19] [20].
Finally, in conformer III only the butyl methyl group is bent to a synclinal position.

Interestingly, for the dihedral angles θ 1 , the values of 171.1° and 173.1° calculated with the MP2 and B3LYP levels, respectively, are similar to those found for conformer I. This indicates that conformer III also exhibits a "pseudo-C s "-like environment in the vicinity of the carbonyl group, as will be further explored in Section 4.3.2.

Basis Set Variation 4.1.2.

Because all assignment attempts using the rotational constants predicted by our most frequently used level of theory MP2/6-311++G(d,p) have failed (see Section 4.2.2.1.), the geometry optimisations were redone for conformer I, II and III at different levels of theory (see Section 2.2.) to achieve a better agreement between the predicted and experimental value.

The results are summarised in Table 14.5 to Table 14.10 in the Appendix, and will be discussed in detail in Chapter 11.

Internal Rotation 4.1.3.

Not only the acetyl methyl group CH 3 CO-, but also the methyl group located at the end of the butyl chain, called the butyl methyl group -C 3 H 6 CH 3 , undergoes internal rotation. Therefore, each rotational transition splits into five torsional species, called (σ 1 σ 2 ) = (00), (01), (10), (11), and (12) [START_REF] Ferres | [END_REF], which, respectively, correspond to the AA, AE, EA, EE and EE* species in Dreizler's notation [54] or the respective A, E1, E2, E3, and E4 species using the permutation-inversion formalism of the G 18 group [START_REF] Bunker | Molecular Symmetry and Spectroscopy[END_REF]. The numbers σ=0, 1, 2 represent the three symmetry species A, E a , E b of the C 3 group, respectively. In the case of MBK, σ 1 refers to the acetyl methyl group, σ 2 to the butyl methyl group.

To calculate the barriers to internal rotation of these two methyl groups at the MP2/6-311++G(d,p) and B3LYP/6-311++G(d,p) level of theory, the respective dihedral angles

α 1 = ∡(H 2 ,C 1 ,C 5 ,C 7
) and α 2 = ∡(C 10 ,C 13 ,C 16 ,H 18 ) were fixed to values in 10° increments. All other geometry parameters were allowed to relax during the optimisations. Due to the symmetry of the methyl group, a rotation of 120° was sufficient. The resulting energies were then parameterised with a one-dimensional Fourier expansion. The coefficients of this expansion are given in Table 14.11 and Table 14.12 in the Appendix.

Acetyl Methyl Group 4.1.3.1.

Only for conformer II, an almost pure V 3 potential is obtained, as illustrated in the upper trace of Figure 4.3, even though higher order potential terms are needed, because the potential curve is not entirely symmetric. This strange shape can be explained by the oscillation of the entire butyl group of up to 20° upon the acetyl methyl rotation (see the lower trace of For conformer III, the barrier values of 148.7 cm -1 (MP2) and 119.0 cm -1 (B3LYP), respectively, are very similar to those of conformer I. However, the two pits of the double minimum are not equivalent and therefore do not refer to an enantiomeric pair. Thus overall, there are three global (conformer III a ) and three local minima (conformer III b ) (see the inset of In summary, the barrier to internal rotation of the acetyl methyl group is estimated to be about 150-250 cm -1 , which is in agreement with observations from previous studies on linear methyl alkyl ketones [91] [START_REF] Andresen | [END_REF]. Torsional splittings in the order of several MHz up to some GHz are expected in the experimental spectrum for molecules featuring similar barrier heights.

Butyl Methyl Group 4.1.3.2.

The potential energy curves of the butyl methyl group, as illustrated in Figure 14.1 and Figure 14.2 in the Appendix, have a normal threefold shape with a nearly pure V 3 potential.

The barrier height is always around 1000 cm -1 , as it is also the case for ethyl chloride [108].

The values predicted at the MP2/6-311++G(d,p) level of theory are 1057.6 cm -1 , 1067.6 cm -1 , and 995.5 cm -1 for conformers I to III, respectively. The respective values predicted at the B3LYP/6-311++G(d,p) level are 994.6 cm -1 , 1002.6 cm -1 , and 942.3 cm -1 .

The calculated torsional barrier of approximately 1000 cm -1 is much higher compared to that of the acetyl methyl group. A similar value was found for the propyl methyl group of methyl propyl ketone [START_REF] Andresen | [END_REF]. Comparing the microwave spectrum of MBK to that of methyl propyl ketone, we expect that splittings arising from the butyl methyl group are small, in the order of a few kHz, but resolvable with our experimental setup.

Microwave Spectrum

Experimental Setup 4.2.1.

MBK was purchased from Alfa Aesar GmbH & Co KG, Karlsruhe, Germany with a stated purity of more than 98% and no further purification steps were carried out. The sample was placed on a piece of pipe cleaner under a helium flow with a pressure of about 200 kPa. The helium-substance mixture was expanded through a pulsed nozzle into the vacuum chamber. A series of overlapping spectra from 9.0 to 14.6 GHz was recorded with a step size of 0.25 MHz using a modified version of the molecular jet Fourier transform microwave (MJ-FTMW) spectrometer described in Ref. [60], which operates in a frequency range from 2.0 to 26.5 GHz. Afterwards, the transitions were measured or remeasured at high resolution, whereby a second MJ-FTMW spectrometer operating from 26.5 to 40.0 GHz was used [61].

For further information on the spectrometers see Section 2.1.

Spectral Assignment 4.2.2.

Rigid-Rotor Fits 4.2.2.1.

To assign the microwave spectrum of MBK, we first neglected the internal rotation effects and only considered the (00) species transitions predicted using the XIAM code [51] in its rigid-rotor mode. The rotational constants calculated at the MP2/6-311++G(d,p) level of theory were taken as initial values (see Section 4.1.1.). We compared the experimental and the theoretical spectra predicted for all 11 conformers listed in Table 4.1, but all assignment attempts failed. Using the rotational constants from the B3LYP calculations as initial values did not improve the situation. Therefore, we suspected that the predicted rotational constants are not sufficiently accurate. This suspicion was strongly supported by the same observation in our previous studies on methyl propyl ketone [START_REF] Andresen | [END_REF], in which the alkyl group is one methylene group shorter than that of MBK. We assumed that, for methyl alkyl ketones, there was some kind of systematic error in the calculations at the levels of theory in use.

To quantify these errors, the relative deviations ΔA, ΔB, and ΔC in percent between the experimental rotational constants of methyl propyl ketone [START_REF] Andresen | [END_REF] and those predicted at different levels of theory in the basis set variation were calculated (for constant A see Eq. (4.1)), and all values were averaged. In a next step, we came back to MBK and averaged the values of the rotational constants predicted at all levels of theory (see Section 4.1.2.), given in Table 14.5, Table 14.7, and Table 14.9 in the Appendix. Lastly, we corrected the mean values of the rotational constants of MBK with the respective relative deviations obtained in the first step with the results from methyl propyl ketone by using Eq. (4.2). B and C were similarly calculated.

Hexan-2-one

-46 - ΔA = (A cal -A exp ) • 100 A exp (4.1) A MBK = A ̅ MBK • 100 ΔA ̅ MPK + 100 (4.2)
This procedure was an attempt to compensate the errors in quantum chemical calculations at the used levels of theory, through which we obtained the rotational constants given in Table 4.1. These corrected rotational constants turned out to be surprisingly accurate, finally allowing the straightforward assignment of all three conformers.

One-Top Fits 4.2.2.2.

Conformer I

As a next step, the internal rotation of the acetyl methyl group was considered. Here, an initial value for the torsional barrier is needed in the XIAM code [51]. We first tried the values of 147.6 cm -1 and 115.5 cm -1 calculated at the MP2/6-311++G(d,p) and the B3LYP/6-311++G(d,p) level of theory, respectively (see Section 4.1.3.1.). However, the assignment of the (10) species transitions with these starting values turned out to be difficult, which led to the suspicion that they are not sufficiently accurate, either. In methyl propyl ketone, we found a torsional barrier of 188.3843(50) cm -1 for the "pseudo-C s " conformer [START_REF] Andresen | [END_REF]. Trying this as initial value for conformer I of MBK resulted in a successful assignment. The initial values of the angles between the internal rotor axis i 1 and the principal axes a, b, c are also needed. In contrast to the other initial parameters, the values calculated at the MP2/6-311++G(d,p) level of theory were sufficiently accurate. We note that the angle ∡(i 1 ,c) could not be fitted and was fixed to 90°, a value which usually corresponds to a structure with an undistorted C s symmetry. Finally, 345 rotational transitions belonging to the (00) and ( 10) torsional states could be assigned to conformer I and fitted with the XIAM program (called XIAM(1Top) fit in Table 4.2). The deduced barrier to the internal rotation of the acetyl methyl group is 186.9198(50) cm -1 and the root-mean-square (rms) deviation of the fit is 9.1 kHz. N [d] 345 345 563 380 555 234 244 N (00)/ (10) [e] [a] For conformer I the internal rotation parameters of the second rotor are fixed to F 0,2 = 158.0 GHz, ∡(i 2 ,a) = 35.81°, ∡(i 2 ,b) = 54.19°, and ∡(i 2 ,c) = 90.00°. [b] For conformer II, F 0,2 = 158.0 GHz, ∡(i 2 ,a) = 20.61°, ∡(i 2 ,b) = 105.90°, and ∡(i 2 ,c) = 102.77°. [c] For conformer III, F 0,2 = 158.0 GHz, ∡(i 2 ,a) = 112.58°, ∡(i 2 ,b) = 39.82°, and ∡(i 2 ,c) = 120.83°. [d] Total number of lines. [e] Number of the (00)/(10) torsional transitions, respectively. [f] Number of the (01)/(11)/(12) torsional transitions, respectively. [g] Root-mean-square deviation of the fit.

-47 -

Hexan-2-one

Hexan-2-one

-48 -
The experimental accuracy of the spectrometers for unblended lines is 1-2 kHz, as determined for carbonyl sulphide [109]. In the case of MBK, the resolution of a measured line can be much lower, for some transitions up to 10 kHz due to unresolved splittings of the butyl methyl rotor and additional spin-spin and spin-rotation couplings, which broaden the signals.

The average line width (FWHH) of about 35 kHz indicates a measurement accuracy of approximately 4 kHz. The rms deviation of the fit is thus more than twice the measurement accuracy. We noticed some systematic deviations of several branches (mainly b-type and forbidden c-type lines with K a ≥ 2), where the experimental and predicted frequencies always differ by almost the same value of up to 30 kHz. This most likely indicates that one or several interaction terms are unaccounted for in the Hamiltonian.

The same set of data was refitted with the BELGI-C s program [52] in order to include higher order parameters. By floating 14 parameters, an rms deviation of 4.7 kHz was obtained. The barrier height is 186.7345(88) cm -1 . The BELGI parameters which can be transformed into the principal axis system are summarised in Table 4.2. The parameters in the original rho axis system are given in Table 14.13 in the Appendix. A list of the fitted frequencies along with their residuals obtained for both fits are available in Table 14.14.

Conformer II

Conformer II possesses a C 1 symmetry with the butyl group bent out of the C-(C=O)-C plane, where the γ-carbon is in a nearly synclinal position (see Section 4.1.1.). Using the same strategy as that for conformer I, we tried to match conformer II of MBK with the C 1 conformer of methyl propyl ketone, which has a similar structure [START_REF] Andresen | [END_REF]. The initial barrier to internal rotation of 238 cm -1 was used, and the assignment was straightforward. The 380 assigned torsional transitions were fitted in a XIAM(1Top) fit, yielding a torsional barrier of 233.5913(97) cm -1 (see Table 4.2). Although a few systematic deviations were observed, the XIAM(1Top) fit is quite satisfactory with an rms deviation of 3.9 kHz, which is within the measurement accuracy. The same 380 lines were refitted with the BELGI-C 1 code [53]. A fit with the same quality as the XIAM(1Top) fit was achieved by floating 16 parameters. The BELGI parameters in the rho axis system are given in Table 14.13 in the Appendix. The fitted frequencies along with their residuals obtained for both fits are listed in Table 14.15.

Conformer III

After conformer I and II were assigned, only transitions with medium or weak intensity remained in the broadband scan, which could be assigned to conformer III. According to calculations at the B3LYP/6-311++G(d,p) level of theory, this conformer is about 3-4 kJ mol -1 higher in energy than conformer I and II (see Table 4.1). Therefore, only 234 transitions could be measured and fitted here. Conformer III shows a C 1 structure, where the methyl group at the end of the butyl chain is in a synclinal position with respect to the C-(C=O)-C plane. Both, the XIAM(1Top) fit given in Table 4.2 and the BELGI-C 1 fit given in Table 14.13 in the Appendix yield rms deviations within the measurement accuracy (3.0 kHz and 3.2 kHz, respectively). The fitted frequencies and their residuals obtained for both fits are listed in Table 14.16.

Two-Top Fits 4.2.2.3.

While the splittings between the (00) and ( 10) symmetry species arising from the internal rotation of the acetyl methyl group are clearly resolved in the broadband scan, additional splittings of the (00) species into the (00) and (01) species, as well as of the (10) species into the (10), (11) and (12) species, due to the internal rotation of the butyl methyl group, are small, ranging from only 100 kHz down to less than 2 kHz. Therefore, they are only resolved in high resolution measurements and only in about half of the transitions. In the other half, they broaden the signals, as mentioned in Section 4.2.2.2.1. Figure 4.6 and Figure 4.7 illustrate two typical spectra of the 5 14 ← 4 13 transition of conformer I with its clearly visible (10), (11) and (12) torsional components, while the splitting in (00) and (01) is not resolvable.

We expanded the XIAM(1Top) fits described in Section 4.2.2.2. to the XIAM(2Tops) fits also given in Table 4.2 by including the (01), ( 11) and ( 12) torsional species of rotational transitions with resolvable splittings. The initial values for the barrier heights and the angles between the internal rotor axis i 2 and the principal axes are taken from calculations at the MP2/6-311++G(d,p) level (see Table 14.1 in the Appendix.). The total numbers of lines increase to 563 for conformer I, 555 for conformer II and 244 for conformer III. Only 10 new lines are added in the two-top fit of conformer III, which is due to the weak intensities of all its transitions. The deduced barriers to internal rotation of the butyl methyl group of conformer I to III are 979.99(88) cm -1 , 1016.30(77) cm -1 and 961.9(32) cm -1 , respectively. The values of all other fitted parameters are very similar to those of the one-top fits. The angles ∡(i 2 ,g), with g = a, b, c, could not be fitted and were fixed to the calculated values. The respective rms deviation is 10.1 kHz, 5.1 kHz, and 3.3 kHz, which is always about 1 kHz higher than the value found for the corresponding one-top fit. There are two main reasons for this: (i) The measurement accuracy of the (01), (11) and (12) torsional transitions is lower than that of the (00) and (01) species, and (ii) among the 15 fitted parameters, only one parameter, the V 3 potential of the butyl methyl group, accounts for the (00)-( 01) and ( 10)-( 11)-( 12) splittings.

To check for convergence, we carried out further XIAM(2Tops) fits where the relative frequencies υ (01) -υ (00) , υ (11) υ (10) and υ (12) υ (10) instead of the absolute line frequencies, i. e. only the torsional splittings, were fitted. Here, only the V 3 potential of the butyl methyl group was floated and all other parameter values, such as the rotational constants and the angles between the internal rotor axes and the inertial axes, were fixed to those of the XIAM(1Top) fit. The relative XIAM fit was only better in the case of conformer I with an rms deviation of 5.6 kHz. For conformers II and III, the deviations are 5.7 kHz and 5.1 kHz, respectively. The fitted frequencies and their residuals are given in Table 14.14, Table 14.15, and Table 14.16 in the Appendix.

Discussion

We could assign all lines in the microwave spectrum of MBK to conformer I, II, and III, except a few lines of extremely weak intensity, which might belong to impurities or 25) cm -1 for conformer I, II, and III, respectively (according to the XIAM(1Top) fits). The following sections will be divided in respective paragraphs giving detailed discussions on all of the statements above.

Geometries of the Three Observed Conformers 4.3.1.

Only the energetically most favourable conformers are expected to be observed in the microwave spectrum under the measurement conditions described in Section 4.2.1. As shown in Section 4.1.1., the order in energy of the conformers is very different in calculations with the MP2 and the B3LYP methods. The experimental rotational constants of the observed conformers clearly agree with those of the three lowest energy conformers calculated at the B3LYP/6-311++G(d,p) level of theory. Therefore, we conclude that for MBK, the energies calculated with DFT using the functional B3LYP are in better agreement with the experimental results. Special attention should be paid to the structure of conformer I. Calculations at both levels of theory, the MP2/6-311++G(d,p) and the B3LYP/6-311++G(d,p) level, stated that not all heavy atoms are located on a symmetry plane (C s structure), but the entire butyl group is slightly tilted out of the C-(C=O)-C plane ("pseudo-C s " structure) (see Section 4.1.1.).

However, the BELGI-C s code, which is specially designed for a molecule with a plane of symmetry at equilibrium, could reproduce the experimental data to measurement accuracy. Moreover, no c-type transitions were observed for the (00) species. This discrepancy confronts us with three possibilities for the structure of conformer I. First, the calculated C 1 structure is correct, but due to a very small dipole moment component in c direction, the ctype transitions are too weak and cannot be observed. Second, the equilibrium structure is C s and the calculations have failed to find the correct minima. Third, the enantiomers are separated by only a small barrier and the tunnelling ground state lies above this barrier. In this case, the effective structure is C s , the dipole moment in c direction would be zero and thus, no c-type transitions are visible.

The potential energy curves for the acetyl methyl rotation illustrated in Figure 4.4 strongly support the last possibility. The height of the local maxima located in between the double minima is 18.1 cm -1 and 1.4 cm -1 calculated with the MP2 and the B3LYP method, respectively. The respective tunnelling ground state is calculated to be 29 cm -1 and 23 cm -1 , clearly higher than the tunnelling barrier. Another observation backing a C s or an "effective C s " structure is the inertial defect Δ c = I c -I a -I b with an experimental value of approximately -16.00 uÅ 2 . If the heavy atom skeleton is planar and there are five pairs of outof-plane hydrogens, the inertial defect is -15.60 uÅ2. The inertial defects obtained for the "pseudo-C s " structures calculated at the MP2/6-311++G(d,p) and the B3LYP/6-311++G(d,p) level of theory are -16.72 uÅ2 and -15.76 uÅ2, respectively.

The symmetry of conformer II is C 1 and contains the C 1 conformer of methyl propyl ketone as a sub-structure [START_REF] Andresen | [END_REF]. This can also be observed for a series of microwave spectroscopic studies on n-alkyl acetates and methyl alkanoates [5] [20].

[6] [7] [8] [9] [10] [19]
In case of conformer III, the butyl methyl group is bent to a synclinal position. The experimentally deduced rotational constants for this conformer are very similar to those of conformer II (see Table 4.2), which might complicate the distinction between those two. However, the angles between the internal rotor axis and the principal axes give helpful hints, The experimental rotational constants obtained with the XIAM(1Top) fits agree within 1-2% with the values calculated at different levels of theory (see Section 4.1.2) for all three assigned conformers. Only the rotational constant A of conformer II is not calculated well with deviations of up to 5% at some levels of theory using the MP2 method. It is interesting that the deviations between the experimental and predicted rotational constants are very similar to those found in methyl propyl ketone [START_REF] Andresen | [END_REF]. This seems to support our assumption given in Section 4.2.2.1 about some systematic errors in the quantum chemical calculations of linear methyl alkyl ketones, at least at the current levels of theory in use. A more detailed discussion is given in Chapter 11.

The BELGI rotational constants are in agreement (within 1%) with the XIAM values. However, they do not agree within the standard errors. The most significant difference is that of the A rotational constant (Δ ≈ 15 MHz in the case of conformer I). This is probably due to the different approaches used in BELGI and XIAM. While the BELGI program is a pure rho axis method code, the XIAM program uses a combined axis method, which is a combination of the principal axis method and the rho axis method (for further information see Section 2.3.). Furthermore, different sets of parameters are fitted, and the physical meaning of some parameters becomes less clear. Especially in the BELGI program, the A rotational constant is rather sensitive and can become an effective parameter in the fitting process. This is not a seldom observation, as has been found in many previous studies with BELGI-XIAM comparisons, for example in methyl ethyl ketone (Δ ≈ 40 MHz) [91], propyl methyl ketone (Δ ≈ 30-55 MHz) [START_REF] Andresen | [END_REF], ethyl acetate (Δ ≈ 40 MHz) [6], vinyl acetate (Δ ≈ 25 MHz) [14], and 4-hexyn-3-ol (Δ ≈ 35 MHz) [110]. This problem also occurs when XIAM is compared to other programs treating internal rotations, such as ERHAM [58], for example in studies on methyl isobutyl ketone (Δ ≈ 8 MHz) [26] and isopropenyl acetate (Δ ≈ 7 MHz) [15].

Torsional Barriers of the Acetyl Methyl Group 4.3.2.

The acetyl methyl group of conformer I features a barrier to internal rotation of approximately 180 cm -1 , while the value found for conformer II is about 240 cm -1 . For the two conformers assigned in the microwave spectrum of methyl propyl ketone, the same observation with the respective values of 188.3843(50) cm -1 and 238.145(21) cm -1 can be made [START_REF] Andresen | [END_REF]. In the literature, further ketones containing an acetyl methyl group support a classification for the barrier height of the acetyl methyl group in ketones, as illustrated in 12) cm -1 ) [31] and methyl isobutyl ketone (250.3(19) cm -1 ) [26]. The second class includes ketones in which the torsional barrier of the acetyl methyl group is always around 180 cm -1 , such as conformer I of MBK (186.9198(50) cm -1 ), the C s conformer of methyl propyl ketone (188.3843(50) cm -1 ) [START_REF] Andresen | [END_REF], methyl ethyl ketone (183.1702(82) cm -1 ) [91] and methyl neopentyl ketone (174.11(27) cm -1 ) [27]. The "pseudo-C s " structure seems to be responsible for this value. This class is thus called the "C s class". (1) methyl propyl ketone [START_REF] Andresen | [END_REF], (2) MBK (this chapter), (3) allyl acetone [31], (4) methyl isobutyl ketone [26], (5) methyl ethyl ketone [91], and (6) methyl neopentyl ketone [27] (Ref. [2], figure modified for consistent formatting).

Obviously, the barrier of about 240 cm -1 found for the C 1 structure is significantly higher than that linked to the "pseudo-C s " structure, but the reason behind this is not obvious. One could argue that the C 1 structure with the γ-carbon of the alkyl chain in a synclinal position would cause higher steric hindrance and consequently higher barriers. But if this argument were correct, the barrier height found in methyl neopentyl ketone, which possesses a branched alkyl chain (see Figure 4.8), should not be 174.11(27) cm -1 , but about 240 cm -1 [27].

Therefore, we suspect that electronic effects have more influence on the acetyl methyl torsion than steric effects do. The electronic configuration on the other side of the carbonyl group is not the same in case of a C s or "effective C s " structure compared to a C 1 structure.

The barrier height of 182.2481(25) cm -1 found for conformer III of MBK yields another key observation. Although this conformer has a C 1 structure, it falls into the second class where all the molecules feature C s symmetry. Looking at its potential energy curves given in in all molecules stated in the "C s class" above. We thus conclude that the electrostatic interactions only stretch to the γ-carbon of the alkyl chain and not further.

To summarise, the torsional barrier of the acetyl methyl group is influenced by the configuration of the alkyl chain but only up to the γ-carbon. If the alkyl chain is "cut-off" at the γ-carbon and the "rest" features a "pseudo-C s " structure, the barrier height is around 180 cm -1 . If the "rest" is C 1 symmetric, the barrier height is approximately 240 cm -1 . Further linear aliphatic ketones will be investigated in the next chapters to verify this "two-class" concept.

Finally, we note that the simplest ketone containing an acetyl methyl group, acetone, is not considered in our comparison. The alkyl chain of acetone with only one methyl group is not long enough to support our classification into "pseudo-C s " and C 1 . Furthermore, the two equivalent methyl groups in acetone with their strong coupled large amplitude motion make this molecule a special case [87].

There are also ketones which do not belong to either of the two classes mentioned above. For example, the high torsional barrier of the acetyl methyl group of methyl vinyl ketone is 433.8(1) cm -1 for the ap conformer and 376.6(2) cm -1 for the sp conformer [30], probably because of mesomeric effects. If a bulky group is present on the other side of the carbonyl group, e. g. in cyclopropyl methyl ketone [40], phenylacetone [35], and acetovanillone [34], as well as in α-ionone and β-ionone [111], different effects occurring from steric hindrance cause the torsional barriers to range from about 240 cm -1 to 620 cm -1 . Further ketone studies are required to create a classification for these molecules.

Conclusions

Three conformers of MBK were assigned in the jet-cooled microwave spectrum. Conformer I possesses a straight butyl chain, whereas conformer II shows a C 1 structure with the butyl group bent out of the C-(C=O)-C plane to a nearly synclinal position. In conformer III, the methyl group at the end of the butyl chain is in a synclinal position. The barrier heights of the acetyl methyl group deduced by fitting the torsional splittings in the spectrum with the program XIAM are 187.2303(49) cm -1 , 233.911(12) cm -1 , and 182.2581(27) cm -1 for conformer I, II, and III, respectively. The BELGI code was also used to fit the same data set and reduced the rms deviation to measurement accuracy. The barrier to internal rotation of the butyl methyl group could be deduced from the XIAM two-top fits to be about 1000 cm -1 for all three conformers. The results serve as a milestone for a two-class concept linking the acetyl methyl torsional barrier to the conformational geometry, whereby electrostatic interactions from the alkyl chain seem to influence the acetyl methyl torsion, but only up to the γ-carbon. If the relevant parts of the alkyl chain show a "pseudo-C s " structure, the barrier height is approximately 180 cm -1 , as found for conformer I and III. If the relevant part is C 1 symmetric, as in the case of conformer II, the barrier height is around 240 cm -1 .

Heptan-2-one

The main text passages of Chapter 5 have already been published as: In this dissertation, the paper is referred to as Ref. [3] Heptan-2-one, also called methyl pentyl ketone, is a medium-sized molecule with a relatively long alkyl chain. Therefore, a large number of different conformational isomers are possible, which can be described by four dihedral angles, θ 1 = ∡(C 1 ,C 5 ,C 7 ,C 10 ), θ 2 = ∡(C 5 ,C 7 ,C 10 ,C 13 ), θ 3 = ∡(C 7 ,C 10 ,C 13 ,C 16 ), and θ 4 = ∡(C 10 ,C 13 ,C 16 ,C 19 ) (for atom numbering see Figure 5.1). The variation of the dihedral angles α 1 = ∡(H 2 ,C 1 ,C 5 ,C 7 ) and α 2 = ∡(C 13 ,C 16 ,C 19 ,H 21 ) refers to the internal rotation of the acetyl methyl and the pentyl methyl group, respectively, and does not create different conformers. Each of the four angles θ i (i = 1-4) was set to +180°, +60° and -60°, resulting in 3 4 = 81 starting geometries. Under the experimental conditions described in Section 5.2.1., we expected that only the energetically most favourable conformers are visible in the measured spectrum. Previous studies on pentan-2-one (or methyl propyl ketone, for more information see Chapter 3, here referred to as Ref. [START_REF] Andresen | [END_REF]) and hexan-2-one (hereafter called MBK for methyl butyl ketone to avoid confusion with the word heptan-2-one, for more information see Chapter 4, here referred to as Ref. [2]) have shown that the energetically most favourable conformers of MBK contain the energetically most favourable conformers of pentan-2-one as substructures. Therefore, we extrapolate that the energetically most favourable conformers of heptan-2-one contain the energetically most favourable conformers of MBK as substructures as well. Hence, the number of starting geometries could be reduced to 33, when the 11 conformers of MBK reported in Ref. [2] were taken as starting points and only the additional dihedral angle θ 4 of heptan-2-one was set to +180°, +60° and -60°. With these 33 starting structures, geometry optimisations using the Gaussian09 package [62] were performed. Calculations at the MP2/6-311++G(d,p) level of theory yielded 32 stable conformers and frequency calculations confirmed them to be true minima rather than saddle points. The above-mentioned level was chosen due to its reasonable balance between speed of calculations and accuracy of the results, as can be seen in many previous studies [21] [101] [102]. Nevertheless, in the case of MBK [2], the B3LYP/6-311++G(d,p) level of theory has predicted a more reliable energetic order of the conformers. Therefore, the whole optimisation procedure for heptan-2-one was redone at the B3LYP/6-311++G(d,p) level, yielding 30 stable conformers. In this work, we focus on the two energetically most favourable conformers predicted with the B3LYP method, hereafter called conformer I and conformer II, which could eventually be identified in the microwave spectrum (see Section 5.2.3). The two conformers are illustrated in Figure 5.2. Their relative energies, rotational constants, dipole moment components, and optimised dihedral angles are collected in Table 5.1. The nuclear coordinates are given in Table 15.1 in the Appendix. Table 5.1: Rotational constants, dipole moment components, and optimised dihedral angles, as well as the relative equilibrium and zero-point corrected energies of the two assigned conformers of heptan-2-one calculated at the MP2/6-311++G(d,p) and B3LYP/6-311++G(d,p) levels of theory.

Parameter

Conformer I Conformer II MP2 B3LYP Exp. [a] MP2 B3LYP Exp. [ 2.44 [b] 0.00 [c] 0.00 [b] 0.73 [c] E ZPE / kJ mol - 1 1.64 [d] 0.00 [e] 0.00 [d] 1.19 [e] [a]

Experimental rotational constants obtained from the XIAM(1Top) fits, see Table 5.2. [b] Relative to the absolute energy of E = -349.439836 Hartree of conformer II. [c] Relative to the absolute energy of E = -350.515894 Hartree of conformer I. [d] Relative to the zero-point corrected energy of E ZPE = -349.239778 Hartree of conformer II. [e] Relative to the zero-point corrected energy of E ZPE = -350.319097 Hartree of conformer I.

All the heavy atoms of conformer I seem to lie in one plane and the molecular symmetry should be C s . However, calculations with both the MP2 and B3LYP methods suggest that the entire n-pentyl chain is slightly tilted out of the C-(C=O)-C plane by approximately 10° (θ 1 = 169.4°) and 5° (θ 1 = -174.9°), respectively. A conformer with such a tilt-distorted symmetry, hereafter called "pseudo-C s ", has been observed for all shorter alkyl methyl ketones [91] [1] [2] and some other ketones like diethyl ketone [103] and methyl neopentyl ketone [27]. This tilt-distorted symmetry will be further discussed in Section 5.3.2.

Conformer II shows a C 1 symmetry where the γ-carbon (C 13 ) of the alkyl chain (see Figure 5.1) is in a nearly synclinal position. As expected, it contains the C 1 conformers of pentan-2-one [START_REF] Andresen | [END_REF] and MBK [2] as a substructure. Similar observations have been found in a series of systematic microwave spectroscopic studies on n-alkyl acetates [5]

[6] [7] [8] [9]
[10] and methyl alkanoates [19] [20].

Basis Set Variation 5.1.2.

The very dense microwave spectrum of heptan-2-one, as will be presented in Section 5.2.1., in combination with its rich conformational landscape requires precisely predicted rotational constants for a successful assignment. Unfortunately, results from the calculations at the MP2/6-311++G(d,p) and B3LYP/6-311+ +G(d,p) level of theory provide this quality only to a limited extend (see Section 5.2.3.). To find better alternatives, further geometry optimisations with the MP2, B3LYP, and B3PW91 methods in combination with different basis sets were carried out. Moreover, calculations with the Gaussian16 package [63] were also performed, using the M06-2X method, as well as the B3LYP functional including Grimme's dispersion correction without (DFT-D3) or with Becke-Johnson damping (DFT-D3BJ) (for more information see Section 2.2.). The results for both conformers are listed in Table 15.2, Table 15.3, Table 15.4 and Table 15.5 in the Appendix and discussed in Section 5.3.1. and Chapter 11.

Internal Rotation 5.1.3.

Heptan-2-one possesses two methyl groups undergoing internal rotation, the acetyl methyl group CH 3 CO-and the pentyl methyl group -C 4 H 8 CH 3 , causing each rotational transition to split into a quintet of lines. The five torsional species are called (σ 1 σ 2 ) = (00), (01), (10), (11) and (12) [START_REF] Ferres | [END_REF], with σ 1 referring to the acetyl methyl and σ 2 to the pentyl methyl group. The designations σ = 0, 1, 2 represent the A, E a , and E b symmetry species of the C 3 group, respectively [54].

To determine the barriers to the internal rotation of the two methyl groups, the respective dihedral angles α 1 = ∡(H 2 ,C 1 ,C 5 ,C 7 ) and α 2 = ∡(C 13 ,C 16 ,C 19 ,H 21 ) were each varied in a grid of 10° increments, while all other parameters were optimised at the MP2/6-311++G(d,p) and the B3LYP/ 6-311++G(d,p) level. Because the symmetry of a methyl group is C 3 , a rotation of 120° was sufficient to describe its threefold potential curve. In a next step, the resulting energies were parametrised with a one-dimensional Fourier expansion. The corresponding Fourier coefficients are listed in Table 15.6 in the Appendix.

Acetyl Methyl Group 5.1.3.1.

In case of conformer I, the potential energy curve, as illustrated in Figure 5.3, shows a significant V 6 contribution, and each of the three potential wells is divided by a local barrier into a pair of minima. For a closer look at this phenomenon, calculations at both, the MP2 and the B3LYP level, were repeated in a range of ±20° around a local maximum using a finer step width of 1°, (see the inset of Figure 5.3). The heights of the local barriers are 18.2 cm -1 and 1.0 cm -1 , respectively. The global barrier heights are 146.8 cm -1 (MP2) and 114.0 cm -1 (B3LYP). The two pits of a double minimum refer to the two enantiomers of conformer I.

Upon the rotation of the acetyl methyl group, there is an oscillation motion of the entire n-pentyl group, changing between the enantiomeric structures, as depicted in the lower trace of Figure 5.3. This observation substantiates the "pseudo-C s " geometry of this conformer (see Section 5.1.1.) and will be discussed in detail Section 5.3.2.

In Figure 5.4 the respective potential energy curve of conformer II is given. Although, as expected, we observe a threefold potential with single minima, the potential shape is not entirely symmetric and higher order terms are necessary to parametrise the energy curve. In this case, there also is an oscillation of the entire n-pentyl group, now up to 17° (see the lower Pentyl Methyl Group 5.1.3.2.

For the pentyl methyl group, the threefold curves of both conformers are of almost pure V 3 shape each and only very small contributions of higher order exist, as shown in Figure 15.1 and Figure 15.2 in the Appendix. In case of conformer I, the barrier height predicted at the MP2 level is 1059.2 cm -1 , and 995.8 cm -1 with the B3LYP method. The respective values for conformer II are 1066.8 cm -1 and 999.6 cm -1 .

Microwave Spectrum Experimental Setup 5.2.1.

The microwave spectrum of heptan-2-one was recorded using two molecular jet Fourier transform microwave spectrometers as described in Ref. [60] and Ref. [61], which cover a frequency range from 2.0 to 40.0 GHz (for more information on the spectrometers see Section 2.1.). The substance was placed on a piece of a pipe cleaner. Helium at a pressure of about 200 kPa was allowed to flow over the sample, and the helium-substance mixture was expanded into the Fabry-Pérot resonator. Heptan-2-one was purchased from Alfa Aesar GmbH & Co KG, Karlsruhe, Germany, with a stated purity of 99%, and no further purification steps were performed.

There are two operating modes of the spectrometers. First, a series of adjacent spectra in the so-called scan mode was measured from 9.7 to 13.7 GHz, as shown in Figure 15.3 in the Appendix, revealing a very dense spectrum, especially in the range of 9.7 to 12.2 GHz. Subsequently, measurements were performed in the high resolution mode for the scan region.

After successful assignment, signals beyond the scan range were also recorded.

Measurement Accuracy 5.2.2.

The chosen step width of 0.25 MHz decides the resolution of the broadband scan. The predicted barriers to internal rotation of the acetyl methyl group range from about 100 cm -1 to 250 cm -1 (see Section 5.1.3.1.). In the microwave spectrum of other methyl alkyl ketones, like butan-2-one [91], pentan-2-one [START_REF] Andresen | [END_REF], and MBK [2] this caused splittings into the (00) and (10) species of several MHz up to some GHz. Therefore, we expect splittings in the same order of magnitude for 2-heptanone, which are thus well-resolvable in the broadband scan.

Additionally, the internal rotation of the pentyl methyl group causes all (00) species lines to split into the (00) and (01) species, while all (10) species transitions split into (10), (11), and (12) species lines. Quantum chemistry predicts barrier heights of about 1000 cm -1 for this methyl group (see Section 5.1.3.2.), and our experiences from the microwave spectra of other methyl alkyl ketones have shown that such a torsional barrier leads to splittings in the order of a few hundred down to less than 2 kHz [91] [1] [2]. Those splittings are only resolvable in the high resolution mode. For heptan-2-one, about 30% of all transitions feature resolvable splittings. In case of the other 70%, a line broadening is observed. Consequently, the measurement accuracy of the heptan-2-one spectra is estimated to be approximately 3-4 kHz, while the instrumental accuracy achievable in the high resolution mode is approximately 1 to 2 kHz [109]. In Figure 5.5 two typical high resolution measurements of the 4 22 ← 3 13 transition of conformer II are given. At the beginning, the internal rotations of both terminal methyl groups were neglected and the molecule was considered to be a rigid rotor. The rotational constants of conformer I calculated at the MP2/6-311++G(d,p) level of theory (see Table 5.1) were inserted as initial values in the XIAM program [51]. Despite the high density of the spectral lines (see Section 5.2.1.), several a-and b-type transitions could be assigned after some cycles of trial and error. In a second step, the internal rotation of the acetyl methyl group was also taken into account. The initial angles between the internal rotor axis i 1 and the principal axes a, b, and c were obtained from calculations at the MP2/6-311++G(d,p) level, but it is noteworthy that in the final fit ∡(i 1 ,c) had to be fixed to 90°. For the potential barrier height of the acetyl methyl group, here called the V 3,1 potential, the starting value of 187 cm -1 was taken, which is the value found for the "pseudo-C s " conformer of MBK [2]. Previous studies on pentan-2-one [START_REF] Andresen | [END_REF] and MBK [2] have shown that this value should be much more reliable than the values calculated at the MP2/6-311++G(d,p) or the B3LYP/6-311++G(d,p) level of theory (see Section 5.1.3.1.).

Eventually, a total of 285 (00) and (10) species lines could be assigned to conformer I. The experimentally deduced parameters are listed in Table 5.2 as XIAM(1Top) fit with a rootmean-square (rms) deviation of 6.5 kHz, which is about twice the measurement accuracy (see Section 5.2.2.). This elevated rms deviation is mainly caused by systematic deviations of certain branches, indicating that some higher order parameters are missing in the Hamiltonian.

To validate the XIAM(1Top) fit, the same data set of 285 lines was refitted using the BELGI-C s code [52]. By floating 13 parameters, some of them belonging to higher order terms (see Table 15.7 in the Appendix), the rms deviation decreases to 3.5 kHz, a value in good agreement with the measurement accuracy. BELGI parameters which are transformable into the principal axis system are also given in Table 5.2. A list of all frequencies and their residuals is shown in Table 15.8 in the Appendix.

Conformer II (C 1 ) 5.2.3.2.

Following the same general strategy as for conformer I, conformer II could be identified and fitted. Nevertheless, using the rotational constants calculated at the MP2/6-311++G(d,p) or B3LYP/6-311++G(d,p) level of theory (see Table 5.1) did not result in sufficiently precise predictions for a successful assignment. This problem also occurred in other methyl alkyl ketones, such as MBK, where a discrepancy between the experimentally deduced and calculated constants of up to 5% has been observed [2]. Assuming the same error compensation in geometry optimisation calculations of MBK and heptan-2-one, the deviations ΔX between the predicted and the experimental rotational constants (X = A, B, and C) relative to the experimental values (in percent) should be similar for both molecules. Thus, we could deduce "guessed" rotational constants of heptan-2-one using the following relation (which is a variation of Eq. (4.2)):

X guess = X cal • 100 ΔX MBK + 100
(5.1) Table 5.2: Molecular parameters of conformers I and II of heptan-2-one obtained from the XIAM and BELGI codes. The BELGI and XIAM(1Top) fits include only the internal rotation of the acetyl methyl group. The XIAM(2Tops) fits contain the internal rotation of both methyl groups.

Parameter [a] Unit All parameters refer to the principal axis system. I r representation and Watson's A reduction was used.

[b] Parameters of the BELGI fits were transformed from the rho axis system into the principal axis system. -Finally, the "guessed" values turned out to be very accurate. The barrier to internal rotation of the acetyl methyl group observed for the C 1 conformer of MBK is 234cm -1 [2], and for the same reason as stated in Section 5.2.3.1., this barrier was taken as initial value for this parameter of heptan-2-one. The final XIAM(1Top) fit includes 448 lines and shows an rms deviation of 5.9 kHz. The BELGI-C 1 code [53] decreases this value to 2.3 kHz by fitting 16 parameters. The molecular parameters are summarised in Table 5.2 and Table 15.7 in the Appendix, all assigned frequencies are listed in Table 15.9 in the Appendix.

Two-Top Fits 5.2.3.3.

To include the internal rotation of the pentyl methyl group, resolvable transitions of the (01), (11), and (12) species were added to the XIAM(1Top) fits described in the preceding sections.

The parameters of these new fits, which we call XIAM(2Tops), are also stated in Table 5.2.

The total number of lines increases to 406 and 545 for conformer I and II, respectively, while the rms deviations are 7.1 kHz and 7.0 kHz. If only V 3,2 and the (01), (11), and (12) species lines are fitted, and the line positions are considered relative to that of their respective (00) and (10) transition, the rms deviation decreases to 3.7 kHz for conformer I and 4.9 kHz for conformer II. The fitted frequencies are given in Table 15.8 and Table 15.9 in the Appendix.

Discussion

Geometry Parameters 5.3.1.

The microwave spectra of conformer I and conformer II of heptan-2-one were assigned and fitted to measurement accuracy. The parameters obtained from the XIAM fits agree with the BELGI values within 1%, but not within their standard errors. These discrepancies can be traced back to the use of certain higher order parameters in the BELGI fits to treat branches that are not properly reproduced with XIAM (see Section 5.2.3.).

If the experimentally deduced rotational constants are compared with the rotational constants calculated at different levels of theory (see Section 5.1.2.), the values are in good agreement for conformer I (within 1% or less). For conformer II, however, the constants coincide less, especially the A rotational constants calculated at certain MP2 levels, where the experimental and theoretical values differ up to 5%. This has also been observed for other linear methyl alkyl ketones [91] [1] [2], suggesting that some kind of interactions in this type of molecules are not correctly captured at those levels. The best calculation-experiment agreements (within 0.5%) are found for Grimme's dispersion calculations in combination with polarization function while excluding diffuse functions. Hence, dispersion might be an important effect to be considered due to the relative long carbon chain of heptan-2-one. Nevertheless, a good agreement might just be explained by error compensation. The inaccurately calculated rotational constants cause more problems, if the line density of the experimental spectrum is very high, as it is the case for heptan-2-one (see Section 5.2.1.), because then reliable predictions of the rotational constants are even more crucial for a successful assignment. Using Eq. (5.1) to obtain the "guessed" rotational constants for the assignment of conformer II is essentially a calibration to correct the errors of a certain level of theory.

Although such a calibration has led to convincing results while going from pentan-2-one [START_REF] Andresen | [END_REF] to MBK [2] and on to heptan-2-one (this chapter), the application is very limited, since every different set of substance class, conformer, rotational constant and level of theory in use would need its own calibration. An alternative way to circumvent this problem is the modulation and analysis of line intensities using the strong field coherence breaking (SFCB) method, as has been applied by Fritz et al. for the chirped-pulse microwave spectrum of MBK [112]. There, it has led to the assignment of three conformers, similar to our own results investigating MBK by using the calibration method [2].

The experimental spectra of the C s and the C 1 conformer are very similar in intensity. The comparable a-and b-dipole moment components predicted from quantum chemistry suggest a population ratio of approximately 1:1. However, a quantitative statement on the conformational intensity and stability is not attempted due to the lack of dipole moment measurements and the absence of trust in both, calculated dipole moments and intensity ratio obtained from the experimental setup (see Section 5.2.1.). A chirped pulse spectrum [113] of heptan-2-one would be helpful to access more reliable intensity for quantitative comparison.

After the assignment of conformer I and conformer II, several lines of medium and weak intensity still remain in the microwave spectrum of heptan-2-one (see Figure 15.3 in the Appendix). These signals might arise from impurities, but also from one or several conformers, which are higher in energy. However, we were not able to find another assignment. Quantum chemistry yielded up to 15 conformers as possible candidates, all close in energy. Depending on the level of theory employed, the type and energy order of the conformers varies strongly. Additionally, the above-mentioned problem of unprecise predictions of the calculated rotational constants observed for conformer II might appear for the higher energy conformers as well. Moreover, the strongest lines of these conformers are expected to appear in the frequency region from 9 to 12 GHz, where the spectra of conformer I and II are very dense and might mask many signals of the less abundant conformers. Finally, several conformers other than conformer I and II probably exist simultaneously in the spectrum, each of them with only a few strong lines. Consequently, there are not enough lines belonging to one conformer left, to verify any assignment attempt.

Acetyl Methyl Internal Rotation 5.3.2.

Concerning the internal rotation of the acetyl methyl group, our recent studies on pentan-2one [START_REF] Andresen | [END_REF] and MBK [2] propose a link between the barrier height of this torsion and the structural environment on the other side of the carbonyl group (see Section 4.3.2).

Apparently, there are two classes of ketones containing an acetyl methyl group. The ketones of the first class always show a barrier height of approximately 240 cm -1 and a characteristic bent geometry with C 1 symmetry, thus called the "C 1 class". Conformer II of heptan-2-one with its barrier height of 233.380(28) cm -1 (see XIAM(1Top) fit), where the γ-carbon atom of the pentyl group is bent to a nearly synclinal position (see Section 5.1.1.), belongs to this class as well. The second class encloses molecules where the barrier height is about 180 cm -1 and a "pseudo-C s " structure is observed. Hence, we call this the "C s class", which also comprises conformer I of heptan-2-one with a torsional barrier of 185.469(16) cm -1 (according to the XIAM(1Top) fit).

The "pseudo-C s " structures observed for the latter class are interesting to discuss. As described in Section 5.1., all heavy atoms of conformer I of heptan-2-one seem to lie in a C s symmetry plane, but calculations at the MP2/6-311++G(d,p), B3LYP/6-311++G(d,p), and many other levels of theory yield a structure with the entire n-pentyl group tilted out of this plane by up to 10°, leading to a double minimum in the potential energy curve of the acetyl methyl group (see Figure 5.3). Interestingly, conformer I of heptan-2-one, and all the other examples of the "C s class", while showing "pseudo-C s " geometries in the calculations, were fitted with the XIAM and BELGI programs as "true C s " molecules, i.e. ∡(i 1 ,c) = 90°, use of the BELGI-C s code, and no measurement of c-type transitions (see Section 5.2.3.1). We note that the presence of a "pseudo-C s " geometry is firmly linked to a barrier height of about 180 cm -1 , and that there are three possibilities for the real structure: (i) The symmetry of the conformer is C s and the calculations fail to reproduce that correctly. (ii) The calculated "pseudo-C s " geometry is correct, but the dipole moment component in c-direction is too small, so that ctype transitions are not observable in the spectrum. And (iii) the two enantiomers of the "pseudo-C s " structure are only separated by a small barrier and the zero point energy of the tunnelling ground state lies above this barrier, thus leading to an "effective C s " structure.

There are also examples of molecules matching neither the "C 1 " nor the "C s class". Acetone, the smallest methyl alkyl ketone, does not fit because of two acetyl methyl groups undergoing coupled internal rotations [87]. Moreover, molecules featuring mesomeric effects, such as methyl vinyl ketone [30] and ionone [111], or ring containing molecules like, i.e. cyclopropyl methyl ketone [40], 2-acetyl-5-methylfuran [48], phenylacetone [35], acetovanillone [34], and 6-hydroxy-3-methoxyaceto-phenone [34] show the acetyl methyl barrier to be up to about 620 cm -1 . Future studies to validate and expand this two-class concept will thus be necessary (see the following chapters). Nevertheless, our results found for heptan-2-one strongly support the classification made for the other aliphatic methyl alkyl ketones of the series.

Pentyl Methyl Internal Rotation 5.3.3.

The calculated barrier to the internal rotation of the pentyl methyl group is approximately 1000 cm -1 (see Section 5.1.3.2.), which is in good agreement with the experimentally deduced barriers of 982.22(86) cm -1 for conformer I and 979.2(21) cm -1 for conformer II. In general, all parameters of the XIAM(2Tops) fits coincide with those of the XIAM(1Top) fits (see Table 5.2). However, the rms deviations of the former are about 1 kHz higher for both conformers, because (i) the signals of the (01), (11), and (12) transitions show overall weaker intensities than the (00) and (10) ones, thereby reducing the achievable frequency accuracy, and (ii) among the 15 parameters used in the XIAM(2Tops) fits, only the potential barrier V 3,2 accounts for the splittings caused by the pentyl methyl rotor. In the relative fits, where only the pentyl methyl torsional splittings are fitted instead of the absolute frequencies, the rms deviation decreases to almost measurement accuracy. Moreover, V 3,2 is determined more precisely with values of 980.81(25) cm -1 and 979.72(64) cm -1 for conformer I and conformer II, respectively.

Conclusions

The two energetically most favourable conformers of heptan-2-one were identified in the microwave spectrum and fitted to rms deviations close to measurement accuracy. The geometry of conformer I is C s or "pseudo-C s ", while conformer II features a C 1 structure with the γ-carbon of the n-pentyl chain bent to a nearly synclinal position. The torsional barrier of the acetyl methyl group is 185.666(14) cm -1 for the former and 233.418(32) cm -1 for the latter. Similar to the cases of other methyl alkyl ketones, such as butan-2-one [91], pentan-2one [START_REF] Andresen | [END_REF] and MBK [2], these barrier heights can be linked to the respective conformational structures, confirming the observations found in previous studies of the series. Splittings arising from the internal rotation of the pentyl methyl group could also be resolved, yielding barrier heights of 982.22(86) cm -1 and 979.2(21) cm -1 for conformers I and II, respectively.

Octan-2-one

The main text passages of Chapter 6 have already been published as: In this dissertation, the paper is referred to as Ref. [4]

Quantum Chemical Calculations

Geometry Optimisations 6.1.1.

Octan-2-one, or methyl hexyl ketone, with its long hexyl chain supports a large number of conformational structures. The conformational landscape is defined by five dihedral angles: . The atom numbering is given in Figure 6.1. By setting each of the θ i values (i = 1 -5) to ±60° and 180°, 3 5 = 243 staggered starting geometries can be created for optimisations to locate the energy minima. To diminish calculation time, only the energetically most favourable conformers will be focused on, as they are the ones expected to be present under the measurement conditions described in Section 6.2.1. From previous studies, we know that the energetically lowest conformers of longer methyl alkyl ketones always contain the conformers of the shorter ones as sub-structure (see Chapter 3 to Chapter 5, hereafter referred to as Ref. [START_REF] Andresen | [END_REF], [2] and [3]). For example, the C 1 conformer of hexan-2-one [2] contains the C 1 conformer of pentan-2-one [START_REF] Andresen | [END_REF]. Based on the two conformers identified for heptan-2-one [3], called the C s and the C 1 conformer, the geometry optimisations could hence be reduced to two calculations. For the C s configuration, all starting θ i values of octan-2-one were set to 180°. In the case of the C 1 conformer, θ 2 was set to -60°, while the other initial angles were also set to 180°.

θ 1 = ∡(C 1 ,C 5 ,C 7 ,C 10 ), θ 2 = ∡(C 5 ,C 7 ,C 10 ,C 13 ), θ 3 = ∡(C 7 ,
Optimisations were performed at the MP2/6-311++G(d,p) level of theory using the Gaussian09 package [62]. The optimised geometries are shown in Figure 6.2. Frequency calculations confirm them to be true minima and not saddle points. The two obtained conformers both exist as an enantiomeric pair. Their rotational constants, dipole moment components, optimised dihedral angles, and relative energies with and without zero-point corrections are summarised in Table 6.1. The nuclear coordinates are given in Table 16.1 in the Appendix.

In the case of the C 1 conformer, the γ-carbon (C 13 ) of the hexyl chain is in a synclinal position (θ 2 = -70.2°). For the C s conformer, all heavy atoms seem to lie in a symmetry plane, but actually they do not. The entire hexyl group is tilted out of the C-(C=O)-C plane by approximately 10° (θ 1 = 169.3°). Therefore, this conformer also exists as an enantiomeric pair consisting of an image and a mirror image. Hereafter, its structure will be referred to as "pseudo-C s ". These structural peculiarities have been observed in all other members of the methyl n-alkyl series as well [91] [1] [2] [3], and will be discussed in Section 6.4.1. 0.00 [b] 0.64 [c] 2.59 [b] 0.00 [c] E ZPE / kJ mol -1 0.00 [d] 1.21 [e] 1.76 [d] 0.00 [e] [a] Rotational constants obtained from the XIAM(1Top) fit, see Table 6.2. [b] Referring to the absolute energy E = -388.635634 Hartree of the C 1 conformer. [c] Referring to the absolute energy E = -389.840232 Hartree of the C s conformer. [d] Referring to the zero-point corrected energy E = -388.406884 Hartree of the C 1 conformer. [e] Referring to the zero-point corrected energy E = -389.615084 Hartree of the C s conformer.

Basis Set Variation 6.1.2.

The MP2/6-311++G(d,p) level of theory has been chosen for the geometry optimisations, since it has provided a good balance between speed of calculation and reliability in predicting rotational constants for assignment purposes in a variety of molecules, as shown in many of our own investigations [101] [114] [115] and studies in the literature [116] [117] [118].

Nevertheless, for methyl n-alkyl ketones [START_REF] Andresen | [END_REF] [2] [3], especially their C 1 conformers, the accuracy of the rotational constants predicted at this level does not satisfy the experimental requirements which are crucial for a successful assignment of the microwave spectrum (see Section 6.2.). Therefore, geometry optimisations were repeated applying different combinations of methods and basis sets to find better alternatives (for more information see Section 2.2.). The calculated rotational constants of the C 1 and the C s conformer are given in Table 16.2, Table 16.3, Table 16.4 and Table 16.5 in the Appendix, respectively. The results of the calculations at the B3LYP/6-311++G(d,p) level of theory are also given in Table 6.1, since it was used for the other methyl alkyl ketones previously studied as well [91] [1] [2] [3].

Internal Rotation 6.1.3.

In octan-2-one, the acetyl methyl group CH 3 (C=O)-and the methyl group at the end of the hexyl chain -C 5 H 10 CH 3 , hereafter called hexyl methyl group, both undergo internal rotation, causing each rotational transition to split into five torsional species. These species are labelled as σ 1 σ 2 = (00), (01), (10), (11), and (12) [START_REF] Ferres | [END_REF]. σ 1 refers to the acetyl and σ 2 to the hexyl methyl group. The numbers σ = 0, 1, 2 are equivalent to the respective A, E a , and E b symmetry species of the C 3 group [54].

To calculate the barrier to internal rotation of the acetyl methyl group, the dihedral angle α 1 = ∡(H 2 ,C 1 ,C 5 ,C 7 ) was varied in a grid of 10°, while all other geometry parameters were optimised at the MP2/6-311++G(d,p) and B3LYP/6-311++G(d,p) level of theory. A variation of α 1 of more than 120° was not necessary due to the symmetry of the methyl group. The obtained energies were then parametrised with a one-dimensional Fourier expansion. For the hexyl methyl group, the same procedure was applied for the dihedral angle α 2 = ∡(C 16 ,C 19 ,C 22 ,H 24 ). The Fourier coefficients are given in Table 16.6 in the Appendix.

Acetyl Methyl Group 6.1.3.1.

As illustrated in Figure 6.3, the energy curve of the C 1 conformer shows an expected threefold potential for the internal rotation of the acetyl methyl group. Nevertheless, the shape of this curve is not symmetric. This can be traced back to an oscillation of the entire hexyl group upon rotation of the acetyl methyl group, as depicted with the deviations of the dihedral angle θ 1 in the lower trace of Figure 6.3. This observation indicates a certain degree of flexibility of the hexyl chain about the C 5 -C 7 bond. Higher order terms are included in the parametrisation of the energy curve and the estimated barriers to internal rotation are 227.3 cm -1 and 167.2 cm -1 with the MP2 and B3LYP methods, respectively. Figure 6.4 shows the respective potential energy curve of the C s conformer along with the oscillation of its hexyl group (θ 1 ) upon the rotation of the acetyl methyl group. Here, the oscillation switches between the two enantiomers, which exist due to the "pseudo-C s " structure of the C s conformer (see Section 6.1.1.). Consequently, the curve shows three-fold shaped double minima with low local barriers at α max = α 1 = 60°, 180°, and 300°. The double minimum at α 1 = 60° was explored by reducing the step width of the calculations to 1° (see the inset of Figure 6.4). Major V 6 contributions were obtained in the Fourier expansions. The local barrier height of 18.4 cm -1 was calculated with the MP2 method, and a significantly smaller value of 0.8 cm -1 was obtained with the B3LYP method. The respective values of the global barriers are 147.1 cm -1 and 114 cm -1 .

Hexyl Methyl Group 6.1.3.2.

In contrast to the behaviour of the acetyl methyl group, the internal rotation of the hexyl methyl group is quite regular. All potential energy curves show an undistorted threefold shape, as depicted in Figure 16.1 and Figure 16.2 in the Appendix, and only small higher order contributions were needed to parametrise them. For the C 1 conformer, the barrier heights predicted at the MP2 and B3LYP levels are 1057.5 cm -1 and 995.7 cm -1 , respectively.

The respective values of the C s conformer are 1053.2 cm -1 and 995.4 cm -1 .

Microwave Spectrum

Experimental Setup 6.2.1.

Octan-2-one was purchased from TCI Europe, Zwijndrecht, Belgium. The stated purity was over 98.0% and no further purification steps were carried out. Two molecular jet Fourier transform microwave spectrometers covering a frequency range from 2.0 to 40.0 GHz as described in Ref. [60] and [61] (for more information see Section 2.1.) were used to record the microwave spectrum. A piece of a pipe cleaner soaked in liquid octan-2-one was placed under a helium flow at a pressure of about 200 kPa, and the helium-substance mixture was expanded into the Fabry-Pérot cavity of the spectrometers. First, a broadband scan from 9.0 to 14.0 GHz with a step width of 0.25 MHz was measured. After the spectra were assigned, high resolution measurements between 2.0 and 40.0 GHz were recorded.

Spectral Assignment 6.2.2. C 1 Conformer 6.2.2.1.

To assign the microwave spectrum recorded under the measurement conditions described in Section 6.2.1., the internal rotations of both methyl groups were neglected at first, and octan-2-one was considered to be a rigid molecule. The rotational constants of the C 1 conformer obtained at the MP2/6-311++G(d,p) level of theory (see Table 6.1) were used as input in the XIAM code [51] to calculate a theoretical spectrum. The predicted spectrum, however, did not match the experimental one. This is a repeatedly occurring problem within the methyl alkyl ketone series, as found in pentan-2-one [START_REF] Andresen | [END_REF], hexan-2-one [2], and heptan-2-one [3], since the values of the experimentally deduced and calculated rotational constants deviate by up to 5%.

In general, quantum chemical calculations yield equilibrium rotational constants X e (with X = A, B, C), while with microwave spectroscopy rotational constants of the vibrational ground state X 0 are obtained. Nevertheless, a good agreement between X e and X 0 is often accidentally achieved at the MP2/6-311++G(d,p) level due to error compensation [101] [114] [115] [116] [117] [118]. This does not apply for the C 1 conformers of methyl n-alkyl ketones. Good starting values for the rotational constants of octan-2-one can instead be determined with a semi-empirical correction using experimental data of other methyl alkyl ketones, like for example heptan-2-one [3], and the following equation (which is a variation of Eq. (4.2) and Eq. (5.1)):

X start = X cal • 100 ΔX heptan-2-one + 100 (6.1)
X cal are the values of octan-2-one calculated at the MP2/6-311++G(d,p) level of theory.

ΔX heptan-2-one is the deviation in percent between the calculated and the experimentally deduced values of the C 1 conformer of heptan-2-one. Using X start for predictions of the rotational constants, the (00) species lines of the C 1 conformer of octan-2-one could be assigned.

Considering the effects arising from the internal rotation of the acetyl methyl group, the barrier height of 233 cm -1 found for the C 1 conformer of heptan-2-one [3] was used as initial value for the V 3 term of octan-2-one. This led to a straight forward assignment of the (10) species transitions, where splittings in the order of several tens to hundreds of MHz were observed. Finally, a dataset containing 380 lines could be fitted to a root-mean-square (rms) deviation of 3.6 kHz. The molecular parameters of the fit are collected in Table 6.2 in the column named XIAM(1Top). The barrier to internal rotation of the acetyl methyl group is 233.202(27) cm -1 .

Due to the internal rotation of the hexyl methyl group, all (00) species lines split into the (00) and (01) species and all (10) lines into (10), (11), and (12). These splittings are in the order of a few kHz, which is close to the resolution limit of 2 kHz of the spectrometers under ideal conditions [109]. Hence, they are only resolved for about one quarter of all measured transitions. Otherwise, the lines are either broadened, or the (01), (11), or (12) species lines appear as shoulders of their respective (00) and ( 10) lines. In some transitions, small additional splittings are observed, probably due to spin-spin and spin-rotation coupling. The attainable measurement accuracy is estimated to be about 3-4 kHz. A typical high-resolution measurement is depicted in Figure 6.5 for the 7 26 ← 6 15 transition of the C 1 conformer. The rms deviation of 3.6 kHz of the XIAM(1Top) fit is in good agreement with the measurement accuracy. However, it is noteworthy that some branches in the fit show much larger residuals of up to 20 kHz, probably due to missing parameters in the Hamiltonian. To prove the correct assignment, the dataset was refitted using the BELGI-C 1 code [53], a program working in the rho axis system. Floating 16 parameters yielded an rms deviation of 2.8 kHz and a barrier height of 227.78(73) cm -1 . The large residuals observed in the XIAM(1Top) fit disappeared. BELGI parameters which can be transformed into the principal axis system are also summarised in Table 6.2. The complete set of fitted parameters is given in Table 16.7 in the Appendix. Table 6.2: Molecular parameters of the two assigned conformers of octan-2-one. The BELGI and XIAM(1Top) fits contain only the internal rotation of the acetyl methyl group, while the XIAM(2Tops) fits include the internal rotations of the acetyl methyl group and the hexyl methyl group. All parameters refer to the principal axis system. I r representation and Watson's A reduction were used. The BELGI parameters were transformed from the rho axis system into the principal axis system. [b] The internal rotation parameters of the second rotor are fixed to F 0,2 = 158.0 GHz, ∡(i 2 ,a) = 156.92°, ∡(i 2 ,b) = 87.94°, and ∡(i 2 ,c) = 67.02°. [c] The internal rotation parameters of the second rotor are fixed to F 0,2 = 158.0 GHz, ∡(i 2 ,a) = 144.22°, ∡(i 2 ,b) = 54.22°, and ∡(i 2 ,c) = 90.00°. [d] Total line number. [e] Line number of the respective species.

Parameter

[f] Root-mean-square deviation of the fit.

-80 -

Octan-2-one

Octan-2-one -81 -To include the internal rotation of the hexyl methyl group in the fit, 135 resolved (01), (11), and ( 12) species lines were added to the XIAM(1Top) fit. This XIAM(2Tops) fit with an rms deviation of 3.8 kHz is given in Table 6.2 as well. The barrier heights are 233.340(28) cm -1 for the acetyl methyl group and 973.17(60) cm -1 for the hexyl methyl group. The fitted frequencies and the residuals of the XIAM(1Top), XIAM(2Tops), and BELGI-C 1 fit are listed in Table 16.8 in the Appendix.

C s Conformer 6.2.2.1.

The assignment of the C s conformer followed the same general procedure as that applied for the C 1 conformer. Here, a semi-empirical correction was not necessary, since the rotational constants calculated at the MP2/6-311++G(d,p) level of theory were reasonable starting values. After some cycles of trial and error, several (00) species transitions of a-and b-type transitions could be assigned. No c-type lines were observed, as is expected for a molecule with C s symmetry.

The barrier to internal rotation of the acetyl methyl group of 185 cm -1 , obtained for the C s conformer of heptan-2-one [3], was used as starting value for octan-2-one, with which the (10) species lines could be straightforwardly assigned. In total, 244 (00) and ( 10 17) cm -1 . The results of the fits are also given in Table 6.2. The 13 floated BELGI parameters are collected in Table 16.7 in the Appendix. For this conformer, the BELGI-C s version [52] was used, which deals with molecules where the molecular frame to which the rotor is attached has C s symmetry. BELGI-C s does not include parameters associated with imaginary matrix elements, for example D aci .

The XIAM(1Top) fit was expanded to the XIAM(2Tops) fit by including 87 resolvable (01), (11), and (12) lines. The rms deviation is 3.9 kHz. The barrier heights are 185.3490(81) cm -1 for the acetyl and 979.62(69) cm -1 for the hexyl methyl group. All frequencies and the residuals of the XIAM(1Top), XIAM(2Tops), and BELGI-C s fits are listed in Table 16.9 in the Appendix.

After the assignment of the C 1 and C s conformers, only a few lines of very low intensity remained in the broadband scan. They may be transitions of other conformers or caused by impurities, but the line numbers and intensities were not sufficient for another successful identification.

Discussion

Two conformers could be assigned in the microwave spectrum of octan-2-one. If the molecular parameters of the different fits are compared to each other (see Table 6.2), the values of the parameters obtained with the XIAM(1Top) and XIAM(2Tops) fits are very similar, but they differ slightly from those of the BELGI fit. These divergences can be traced back to the different Hamiltonian approaches used by the two codes, and also to the inclusion of higher order parameters in the BELGI fits. Substantially, the results agree with each other, and measurement accuracy was reached by all fits.

The calculated rotational constants of the C s conformer (see Section 6.1.2.) are in good agreement with the experimental values (deviations of about 1% or less). For the C 1 conformer, however, the deviations are much larger. Especially, calculations using the MP2 method yield values of the A rotational constant up to 5% lower than the experimental value. This discrepancy between calculation and experiment has been found for other methyl n-alkyl ketones as well [START_REF] Andresen | [END_REF] [2] [3], but also for alkyl esters which are long enough to support a C 1 geometry. For example, deviations of up to 9% have been reported for methyl butyrate [20]. This is not surprising, since the structure of methyl butyrate is very similar to that of pentan-2-one [START_REF] Andresen | [END_REF], where the acetyl methyl group is exchanged with a methoxy group. In the study on methyl butyrate, Hernandez-Castillo et al. pointed out that the bond between the carbonyl group and the rest of the carbon chain causes most of the problems for the calculations with a wide variety of values found for the corresponding dihedral angle at different levels of theory [20]. For methyl n-alkyl ketones, this dihedral angle, called θ 1 here, also shows a degree of unexpected flexibility (see the lower diagram of Figure 6.3 and Figure 6.4 in Section 6.1.3.1.), and might indeed be responsible for the failure of the calculations. For the C 1 conformer, the best accordance is achieved by using dispersion corrections in combination with polarisation functions, but without diffuse functions, as can for example be seen at the B3LYP-D3BJ/6-311(df,pd) level of theory (see Table 16.3 in the Appendix). The error compensations at the B3LYP-D3BJ/cc-pVDZ level of theory yield X e constants which are in almost exact agreement with the experimental values of both conformers of octan-2-one, and all other methyl alkyl ketones in the series. Though comparing predicted X e constants with experimental X 0 constants is not physically meaningful, here, the B3LYP-D3BJ/cc-pVDZ level offers cost-efficient calculations with accidentally good accuracy and is therefore recommended for the assignment of other methyl n-alkyl ketones with longer alkyl chains.

In the case of the barrier heights, accurate calculations are difficult to achieve, as shown for example in N-acetyl alanine methyl ester where differences between the experimentally deduced and the calculated barriers of up to 80% were observed [119]. For octan-2-one, the deviations are about 3 to 40 % and 2 to 9 % for the internal rotation of the acetyl methyl and the hexyl methyl group, respectively (see Section 6.1.3.).

As mentioned in the preceding paragraphs, finding a quantum chemical method which systematically yields reliable starting values for microwave spectroscopic analyses is a challenging task. In the present work, this problem was circumvented by using available experimental data to correct the calculated rotational constants with a semi-empirical calibration factor (see Section 6.2.2.1.). Alternatively, intensity patterns can be modulated and analysed using strong-field coherence breaking (SFCB), as has been done for methyl butyrate [20] and hexan-2-one [112]. Other approaches aim at improving the quantum chemical calculations. One example is how basis set superposition errors of the MP2 method can be estimated by the so-called atomic counterpoise method [120]. In another example, diffusion quantum Monte Carlo is used to calculate barriers [121]. Nevertheless, more elaborated and consequently more time-consuming and expensive calculations do not guarantee better results, and low-cost levels with error compensations might give the right answers for the wrong reasons. So far, a "golden method" for all molecules and problems is not available. Therefore, any new class of molecules requires its own assessment and benchmark tests to find the best method to use, which can then be applied for all following investigations in the series.

Methyl Alkyl Ketones: An Overview

Structural Aspects of the Conformations 6.4.1.

In this section, the structural aspects of the conformers generally observed in methyl n-alkyl ketones will be reviewed [91] [1] [2] [3]. The different atom positions of the alkyl chain attached to the carbonyl group are labelled with α, β, γ, etc. (see Figure 6.1). Tilt angles will be given relative to the all-trans conformation, where all θ i dihedral angles are 180° and all heavy atoms lie in a mirror plane.

The C s or "Pseudo-C s " Conformer 6.4.1.1.

Independent of the length of the alkyl chain, one conformer is always present in the gas phase spectrum of all methyl n-alkyl ketones, which appears to possess an all-trans geometry and is therefore called the C s conformer. However, calculations at different levels of theory suggest that the β-carbon, and thereby the entire alkyl chain, is tilted out of the C-(C=O)-C plane by about 10° (see Section 6.1.1.). This "pseudo-C s " structure cannot be confirmed nor disproven with the available data sets. As described in Section 6.2.2.1. for octan-2-one and observed in general for all other methyl alkyl ketones in the series [91] [1] [2] [3], no c-type transitions were identified and the spectrum could be fitted with a satisfactory rms deviation using the BELGI-C s code. Moreover, in the XIAM fits the angles between the internal rotor axes and the principal c-axis were fixed to ∡(i 1 ,c) = ∡(i 2 ,c) = 90°. These are indications for a "true C s " symmetry. Nevertheless, the possibility for a "pseudo-C s " structure cannot be excluded either, as a "pseudo-C s " conformer behaves like an "effective C s " conformer if the barrier dividing the enantiomeric pair is smaller than the zero-point energy of the tunnelling ground state. In a recent investigation on 2-propionylthiophene, where an ethyl group is attached on one side of the carbonyl group and the planar thiophene ring on the other side, Dindic et al. observed a tiny, but non-zero tilt angle of the ethyl group, proving that the ethyl group is not located in the thiophene plane. Using isotopic substitutions, the deduced experimental heavy atom skeleton convincingly confirmed the non-planarity of 2-propionylthiophene [122].

Unfortunately, no 13 C isotopologues could be measured in the spectrum of any methyl alkyl ketone in the series. Other molecules exhibiting "pseudo-C s " geometries are e.g. methyl neopentyl ketone [27], cat ketone [123], and diethyl ketone [103].

The C 1 Conformer 6.4.1.2.
The second type of conformer identified in the microwave spectrum of all methyl alkyl ketones is one with C 1 symmetry and a configuration where the β-carbon is slightly tilted out of the C-(C=O)-C plane (θ 1 ≈ 160°), while the γ-carbon is in a synclinal position (θ 2 ≈ 70°).

Butan-2-one is not sufficiently long to support such a structure [91]. In the case of hexan-2-one [2], heptan-2-one [3], and octan-2-one (this chapter), the supplementary δ, ε, and ζ-carbon atoms are all in trans positions (θ i ≈ 180°, with i = 3, 4, 5, respectively).

Conformational Stability 6.4.1.3.

It is not clear, whether the C 1 or the C s conformer is the most abundant and therefore energetically most favourable structure. Depending on the level of theory in use, the calculated energy orders change (see Figure 6.1), and under our measurement conditions described in Section 6.2.1., it is not possible to obtain reliable line intensities for a population ratio analysis. Dipole moment measurements were not performed. Hence, quantitative statements on the conformational stability are not attempted. Qualitatively, both conformers seem to be equally abundant in the spectrum.

"Chemical intuition" would suggest a preference for the C s structure. However, similar bent configurations have been observed for a number of molecules where an alkyl chain is attached to a carbonyl group such as n-aldehydes [124] [125] [126] [127] and esters like ethyl valerate [128]. In a study on methyl butyrate, Hernandez-Castillo et al. determined a population ratio of 59/41 for the (g±,a) conformer (C 1 conformer equivalent) vs. the (a,a) conformer (C s conformer equivalent) [20]. There, it has been proposed that the C 1 geometry is stabilised by two weak hydrogen bonds between the oxygen atom of the carbonyl group and (i) one hydrogen atom attached to the γ-carbon and (ii) one hydrogen atom attached to the βcarbon. Such weak hydrogen bonds are also conceivable for the C 1 conformers of the ketone series.

Acetates are molecules where the α-methylene group of methyl alkyl ketones is exchanged by an α-oxygen atom, and the carbon chain starts at the β-position. Here, the most abundant conformer shows a different C 1 structure, where the δ-carbon and not the γ-carbon is synclinal bent, and all other dihedral angles stay trans [7] [8] [9] [10]. It seems that a hydrogen bond between the α-oxygen and a hydrogen atom attached at the δ-carbon stabilises this conformation of acetates. It is noteworthy that even weak intramolecular interactions, like van der Waals forces, might be strong enough to switch the preference from an all-trans to a bent structure, as has been shown for stretched and double layered hairpin conformers of n-alkanes with a chain length of at least 16 to 18 carbons [129] [130]. However, the alkyl chains of methyl alkyl ketones studied so far are not long enough to experience this effect.

Only in hexan-2-one, a third conformer was observed which features the δ-carbon in a synclinal position, while the β-carbon is tilted out of the C-(C=O)-C plane by 10°, like it is the case for the C s conformer [2]. This structure, hereafter called C 1 -δ, is clearly less favourable than that of the C 1 and C s conformers. Torsional barriers of the acetyl methyl group in ketones can be categorised into two classes.

Acetyl Methyl

The first class contains all C s conformers of the methyl n-alkyl series [91] [1] [2] [3], and is therefore called the "C s class". As depicted in Figure 6.6, the barrier height is always about 180 cm -1 and firmly linked to the presence of a "pseudo-C s " structure (see Section 6.4.1.1.).

Other molecules belonging to this class are methyl neopentyl ketone (6) [27], cat ketone (7) [123], and the C 1 -δ conformer of hexan-2-one (3) [2] (for molecule numbering, see Figure 6.6). The second class encloses all C 1 conformers of the methyl alkyl ketone series [START_REF] Andresen | [END_REF] [2] [3], therefore called the "C 1 class", as well as allyl acetone (8) [31] and methyl isobutyl ketone ( 9) [26]. The barrier height is approximately 240 cm -1 , which connects to a structure with a synclinal γ-carbon. In summary, the barrier to internal rotation of the acetyl methyl group can be linked to structural characteristics of the alkyl chain, making the acetyl methyl group a spectroscopic "detector" of the molecular conformation.

In Table 6.3 a selection of ketones containing an acetyl methyl group is presented. These ketones neither fit in the C 1 nor in the C s class, because either the torsional barrier or the molecular structure does not match. Recently, Herbers et al. expanded the "two-class" concept of the acetyl methyl barriers in ketones to include a "phenyl class" [32]. There, a phenyl ring instead of an alkyl chain is attached on one side of the carbonyl group. The barrier heights are between 550 cm -1 and 630 cm -1 . Members of this class are acetophenone [33], 4methylacetophenone [32], acetovanillone [34], and 6-hydroxy-3-methoxyacetophenone [34].

A "mesomeric class" enclosing methyl vinyl ketone [30] and ionone [111] might also exist, since both molecules contain an unsaturated α,β-bond in their alkyl chains. This class needs a division in an antiperiplanar (ap) and a synperiplanar (sp) sub-class with respective barriers of approximately 430 cm -1 and 350 cm -1 . Acetone [87], 1,1-difluoroacetone [131], and 1,1,1trifluoroacetone [46] are candidates for an "acetone class" with barrier heights of about barrier by less than 40 cm -1 . Further systematic investigations will be needed to fully understand the acetyl methyl torsion in ketones and to propose new classifications (see the following chapters). (5) octan-2-one (this chapter), ( 6) methyl neopentyl ketone [27], (7) cat ketone [123], (8) allyl acetone [31], and (9) methyl isobutyl ketone [26] (Ref. [4], figure modified for consistent formatting).

Table 6.3:

A collection of ketones containing an acetyl methyl group and their respective barriers to internal rotation. All values are rounded to an accuracy of 1 cm -1 .

Acetone Class Mesomeric Class

Molecule Barrier Ref. Molecule Barrier Ref. Acetone 242 cm -1 [87] sp-β-Ionone [c] 341 -343 cm -1 [111] Trifluoroacetone 259 cm -1 [46]
sp-α-Ionone [c] 356 -360 cm -1

[111] Acetone + Ne [a] 259 cm -1 [132] sp-Methyl Vinyl Ketone 377 cm -1

[30] Acetone + Ar [a] 260 cm -1 [133] ap-β-Ionone [c] 427 -437 cm -1

[111] Difluoroacetone 261 cm -1 [131] ap-Methyl Vinyl Ketone 434 cm -1 [30] Trifluoroacetone + H 2 O [b] 275 cm -1 [44] ap-α-Ionone [c] 439 -455 cm Acetovanillone [c] 552 -622 cm -1

[34] Acetylacetone 57 cm -1

[45] 6-Hydroxy-3-methoxyacetophenone [c] 588

-612 cm -1 [34] Pinacolone 122 cm -1 [28] cis-2-Acetyl-5-methylfuran 213 cm -1 [48] Acetophenone + H 2 O [b] 589 cm -1 [33] Phenylacetone 238 cm -1 [35] 4-Methylacetophenone 594 cm -1 [32] trans-2-Acetyl-5-methylfuran 308 cm -1 [48] Acetophenone 627 cm -1 [33] Diacetyl 319 cm -1 [43] Diacetyl + H 2 O [b] 344 cm -1 [43] Cyclopropyl Methyl Ketone 413 cm -1
[40] [a] Barrier height of a noble gas complex. [b] Barrier height of a monohydrated water complex. [c] A range is given, since different orientations of functional groups other than the acetyl methyl group lead to different conformers with slightly different barrier heights.

Conformational Effects 6.4.2.2.

Steric or Electrostatic Effects?

As described in Section 6.4.2.1., the acetyl methyl group functioning as an internal rotor is a spectroscopic "detector" for the molecular structure. However, the essential questions remain: What exactly is detected by the internal rotation? Steric or electrostatic interactions? We assume that the impact of the latter is much greater, and that the acetyl methyl group can "read" the electrostatic environment on the other side of the carbonyl group. This hypothesis is based on a number of observations, where also substance classes other than ketones are taken into consideration:

(i) Methyl neopentyl ketone (molecule (6) in Figure 6.6) exhibits a "pseudo-C s " structure and a methyl group at the same position as the γ-carbon of a C 1 conformer. The steric hindrance of the γ-carbon should put the molecule in the "C 1 class", but the acetyl methyl barrier is 174.11(27) cm -1 [27], and methyl neopentyl ketone belongs to the "C s class". The electrostatic characteristic of the "pseudo-C s " geometry is the decisive factor.

(ii) Ketones of the "phenyl class" [32] show barrier heights of around 600 cm -1 (see Table 6.3), which is much higher than the values of 180 cm -1 and 230 cm -1 found for the C s and C 1 class, respectively. The reason is probably π-electron conjugation between the carbonyl group and the phenyl ring, indicating the important role of electrostatic interactions on the acetyl methyl torsion in ketones.

(iii) If the electrostatic environment in proximity to the carbonyl group is changed by the presence of an oxygen atom attached to the carbonyl group, as it is for example the case for methyl alkanoates and acetates, the barrier is almost unaffected by the molecular configuration and thereby steric hindrance of the alkyl chain. In all methyl alkanoates, the barrier to internal rotation of the methoxy methyl group is always around 400 cm -1 [5] [19] [20]. In most alkyl acetates, the barrier height of the acetyl methyl group is [10]. Nevertheless, in acetates where the electrostatic surrounding of the oxygen "buffer atom" is influenced by a double bond or a conjugated π-system, e.g. in vinyl acetate [14] and butadienyl acetate [17], the barrier height increases to 150 cm -1 .

approximately 100 cm -1 [5] [6] [7] [8] [9]
(iv) In amides, the carbonyl group is attached to a nitrogen atom and the barriers to internal rotation depend on the degree of substitution at that nitrogen. For acetamide (-NH 2 ), a remarkably low barrier of 24 cm -1 has been found for the acetyl methyl group [134]. If one of the hydrogen atoms attached to the nitrogen atom is substituted, secondary acetamides (-NHR) with acetyl methyl barriers of approximately 70 cm -1 are obtained. Examples are Nmethylacetamide (≈ 73 cm -1 ) [135], N-ethylacetamide (≈ 73 cm -1 ) [136], and N-tertbutylacetamide (≈ 66 cm -1 ) [137], as well as N-acetyl alanine methyl ester (≈ 65 cm -1 ) [119] and the two conformers of ethylacetamidoacetate (≈ 64 cm -1 and ≈ 65 cm -1 ) [138]. It is interesting that the substitution of one hydrogen atom leads to a difference of approximately 50 cm -1 in the barrier height between acetamide and the secondary acetamides. If both hydrogen atoms are substituted (-NR 2 ), the effect is even larger as the barrier height increases by an order of magnitude, e.g. to 677 cm -1 in N,N-dimethylacetamide [139] and to 517.04(13) cm -1 and 619.48(91) cm -1 in the two conformers of N,N-diethylacetamide [140].

Since the substituents are well-separated from the acetyl methyl group by the amide moiety (C=O)-N, the reasons can only be electrostatic and not steric effects.

(v) Finally, in acetyl halides the bond between the halide and the carbonyl group seems to possess a partially ionic character, causing a special electrostatic environment which induces acetyl methyl barriers of about 450 cm -1 [141] [142] [143] [144].

Chain Length Effects

Electrostatic and steric interactions are the main reasons behind the structural "detection" of the acetyl methyl rotation. The range of this detection probably extends up to the γ-carbon, since the C 1 -δ conformer of hexan-2-one belongs to the C s and not the C 1 class (see Section 6.4.2.1.) [2]. However, longer alkyl chains might affect the torsion of a methyl group as well. So far, no systematic investigations on chain length effects have been reported, but there are some two-point data sets hinting that a longer alkyl chain is responsible for a lower barrier to internal rotation. For example, the methoxy methyl barrier of methyl butyrate is 420.155(71) cm -1 for the (a,a) and 419.447(59) cm -1 for the (g±,a) conformer [20], clearly lower than the value of 429.324(23) cm -1 found for methyl propionate [19]. Similarly, the barrier of the propionyl methyl group of 9.46 cm -1 found for 3-pentyn-1-ol [145] is higher than that of 7.16 cm -1 found for 4-hexyn-3-ol [110].

In the C s class, the torsional barriers of pentan-2-one (188.3843(50) cm -1 ) [START_REF] Andresen | [END_REF], hexan-2-one (186.9198(50) cm -1 ) [2], heptan-2-one (185.469( 16) cm -1 ) [3], and octan-2-one (185.1442( 16) cm -1 ) (see Table 6.2) strongly support this assumption: The longer the alkyl chain, the lower the barrier. However, beyond a certain molecule length, chain length effects are no longer observed and a plateau of the values is reached. For methyl alkyl ketones, this limit seems to be at the ζ-carbon position, as the barrier height is almost unchanged in heptan-2-one and octan-2-one. It should be noted that the scale of these chain length effects is rather small, and that the barrier height is quite sensitive to the set of parameters used in the fitting process. Comparable sets of parameters are essential for a reasonable comparison. For this reason, butan-2-one (183.1702(82) cm -1 ) does not match the rest of the series [91]. The extraordinary low barrier of 764.8(16) cm -1 found for the ethyl methyl group requires a twotop model to reproduce the microwave spectrum, whereas for all other methyl n-alkyl ketones, a one-top model is sufficient.

For the C 1 conformer, the chain length detection is almost lost once the alkyl chain is bent at the γ-carbon position. The acetyl methyl barrier of 238.145(21) cm -1 observed for pentan-2one [START_REF] Andresen | [END_REF] decreases noticeably to 233.5913(97) cm -1 for hexan-2-one [2], and remains largely unchanged at a value of 233.380(28) cm -1 and 233.202(27) cm -1 for heptan-2-one [3] and octan-2-one (see Table 6.2), respectively.

Alkyl Methyl Internal Rotation 6.4.3.

The torsional barrier of the hexyl methyl group is about 1000 cm -1 for both conformers of octan-2-one (see Table 6.2). Similar values are found for the alkyl methyl groups in pentan-2one [START_REF] Andresen | [END_REF], hexan-2-one [2], and heptan-2-one [3]. In these cases, the splittings arising from the methyl group could be observed, leading to a precise determination of the barrier heights. It is noteworthy that barriers to internal rotation of methyl groups at the end of an alkyl chain are often higher than 1000 cm -1 , which usually inhibits the splittings to be resolved within the resolution of about 2 kHz of the spectrometer in use, as for example found in studies on triethyl amine [115] and diisopropyl ketone [29]. In contrast to methyl groups of longer alkyl chains, ethyl methyl groups show a more diverse range of barrier heights. In some cases, such as diethyl amine [146] and ethyl acetate [6], resolvable splittings have led to barrier heights of 1051.74(57) cm -1 and 1112.3(37) cm -1 , respectively. In other cases, like methyl ethyl ketone [91], diethyl ketone [103], and methyl propionate [19], the internal rotation of the ethyl methyl group possesses a smaller barrier height of about 800 cm -1 . Further conclusions cannot be drawn due to the small set of available data points.

Conclusions

Two conformers have been identified in the microwave spectrum of octan-2-one, one with a "pseudo-C s " symmetry and one with a C 1 structure where the γ-carbon is in a synclinal position. The barriers to the internal rotation of the acetyl methyl group are 185.3490(81) cm -1 and 233.340(28) cm -1 , respectively, confirming the link already established between the torsion of the acetyl methyl group and the conformational structure of methyl n-alkyl ketones. In general, the conformers of ketones exhibiting this specific C s or C 1 structure can respectively be categorised in a C s class with barrier heights of about 180 cm -1 and in a C 1 class with values of approximately 240 cm -1 . Electrostatic effects play a more decisive role for the acetyl methyl torsion than steric effects do. In addition, there is a small chain length effect observable within the methyl n-alkyl ketone series: Longer alkyl chains cause slightly smaller barriers, following the shape of a plateau curve, with the plateau being reached at the chain length of octan-2-one. Moreover, the barriers to the internal rotation of the hexyl methyl group are deduced to be 973.17(60) cm -1 for the C 1 and 979.62(69) cm -1 for the C s conformer. These values are in good agreement with other barriers found for methyl groups terminating various alkyl chains.

IV Ketones of the Mesomeric Class

As described in Part III of this work, there is a link between the molecular structure and the barrier to internal rotation of the acetyl methyl group in ketones. Different conformers of the methyl n-alkyl ketone series, and also some other ketones, either belong to the "C s class" with barrier heights of about 180 cm -1 or the "C 1 class", where the values are always approximately 240 cm -1 . Herbers et al. suggested an additional "phenyl class" comprised of acetophenone and its derivatives with barriers ranging from 550 cm -1 to 630 cm -1 , which can probably be traced back to the phenyl ring on the other side of the carbonyl group [32].

Methyl vinyl ketone [30] and ionone [111] are unsaturated molecules exhibiting a double bond in α,β-position. Hence, the double bond can form a π-conjugated system with the carbonyl group leading to a new class in terms of the acetyl methyl torsion. This class will be called "mesomeric class". If the double bond and the carbonyl group are in an antiperiplanar (ap) conformation, the barrier heights are about 430 cm -1 . If the conformers are synperiplanar (sp) the barriers are always approximately 350 cm -1 . However, so far, only two members of the "mesomeric class" seem to have been studied by microwave spectroscopy, the above mentioned methyl vinyl ketone [30] and ionone [111].

In the following chapters (Chapter 7 and Chapter 8), 3-penten-2-one and 3-methyl-3-buten-2one, also called methyl propenyl ketone and methyl isopropenyl ketone (see Figure 2), are studied to expand the available data and to gain a better understanding of the proposed "mesomeric class". Both molecules are derivatives of methyl vinyl ketone possessing an additional methyl group attached to either end of the double bond, respectively. This additional methyl group also shows internal rotation, and together with the torsion of the acetyl methyl group it leads to complicated splitting patterns, which are not easily analysed.

Due to the highly reactive double bond, both molecules can be polymerised [147] [148] [149]. 3-Penten-2-one is a small unsaturated ketone, which is also called methyl propenyl ketone. In this work, only the E isomers are investigated, since the Z isomers of the molecule are much higher in energy. Different conformers of E-3-Penten-2-one are created by rotating the dihedral angle φ = ∡(O 6 ,C 5 ,C 7 ,C 9 ), while changes of the dihedral angles

α 1 = ∡(H 2 ,C 1 ,C 5 ,C 7 )
and α 2 = ∡(C 7 ,C 9 ,C 11 ,H 12 ) refer to the internal rotations of the two terminal methyl groups (for atom numbering see Figure 7.1). Using the Gaussian09 package [62], geometry optimisations were performed at the MP2/6-311++G(d,p) level of theory, where starting geometries were generated by setting φ to 0°, ±60°, ±120° and 180°. As illustrated in Figure 7.1, two conformers are obtained and frequency calculations confirm them to be true minima rather than saddle points. Both conformers exhibit C s symmetry and all heavy atoms are located in the C-(C=O)-C plane. According to the notation used for the similar molecule methyl vinyl ketone [30], the two geometries will hereafter be called the antiperiplanar (ap) and the synperiplanar (sp) conformer with the φ values being 180° and 0°, respectively. The rotational constants and dipole moment components of both conformers are listed in Table 7.1, their nuclear coordinates in Table 17.1 in the Appendix. [a] 8.369 1.914 1.589 Exp. sp [a] 9.158 1.862 1.578 [a] Rotational constants of the respective conformer obtained from the 2Tops fit, see Table 7.4. To acquire a large data set which can be compared to the experimentally deduced parameters (see Section 7.2.2.), geometry optimisations were repeated for the ap and sp conformer using different combinations of methods and basis sets (for further information see Section 2.2.).

The rotational constants calculated this way are summarised in Table 17.2 to Table 17.5 in the Appendix.

It is noteworthy that depending on the level of theory in use, and whether zero-point correction was applied or not, the energetic order of the conformers changes. Some examples of this observation are given in Table 7.2. It is not clear, if the ap or the sp is the energetically more favourable conformer. In general, an energy difference of about 2 kJ mol -1 or significantly less can be found. Eventually, both conformers have been identified in the microwave spectrum (see Section 7.2.2.). Table 7.2: Absolute and relative energies of the two conformers of 3-penten-2-one without (E) and with zero-point corrections (E ZPE ) calculated with different methods using the 6-311++G(d,p) basis set.

Method

Absolute Energies

Relative Energies [ [a] Referring to the absolute energy of the respective energetically more favourable conformer without and with zero-point corrections (see columns to the left).

Internal Rotation 7.1.3.

3-Penten-2-one features two methyl groups functioning as internal rotors, the acetyl methyl group and the methyl group attached to the double bond, hereafter called propenyl methyl group. Due to the internal rotations each transition splits into five torsional species. The species are labelled as (σ 1 σ 2 ) = (00), ( 01), ( 10), ( 11) and ( 12), respectively [START_REF] Ferres | [END_REF], with the numbers 0, 1, 2 being equivalent to the three symmetry species A, E a , E b of the C 3 group [54]. σ 1 refers to the acetyl methyl group and σ 2 to the propenyl methyl group. To determine the barriers to internal rotation of the acetyl methyl group, the dihedral angle As expected, the potential energy curves of both conformers and both methyl groups show a threefold shape and only small higher order terms were necessary for the Fourier expansion.

α 1 = ∡(H 2 ,C 1 ,C 5 ,C 7 )
In all cases, the barriers to internal rotation are of a similar order of magnitude. They are between 300 cm -1 and 400 cm -1 for the acetyl methyl group and higher with values of about 600 cm -1 for the propenyl methyl group. If the barrier calculations are redone at different levels of theory (see Table 7.3), the barrier heights of the acetyl methyl group differ by up to approximately 45%, while for the propenyl methyl group a discrepancy of around 1% is observed. A list of all Fourier coefficients is given in Table 17.6 in the Appendix. [a] 434.1 581.9 358.1 595.3 [a] V 3 potential of the respective conformer and internal rotor obtained from the 2Tops fit, see Table 7.4.

Microwave Spectrum Experimental Setup 7.2.1.

The microwave spectrum of 3-penten-2-one was measured using a molecular jet Fourier transform microwave spectrometer operating in the frequency range from 2.0 to 26.5 GHz (for description see Ref. [60] and Section 2.1.). The substance was purchased from Sigma Aldrich, Merck KGaA, Darmstadt, Germany, with a stated purity of ≥ 95% and no further purification steps were carried out. 3-penten-2-one was placed on a piece of pipe cleaner and expanded in the Fabry-Pérot resonator via helium flow with a pressure of about 200 kPa. At first, a broadband scan of adjacent spectra was recorded from 9.0 GHz to 14.7 GHz. The step width was 0.25 MHz. After a first assignment, high resolution measurements within the whole frequency range were performed. The accuracy of the spectrometer under ideal conditions is about 2 kHz, as has for example been shown for the spectrum of carbonyl sulphide [109].

Spectral Assignment 7.2.2.

To predict the microwave spectrum, 3-penten-2-one was initially considered a rigid rotor and the rotational constants calculated at the MP2/6-311++G(d,p) level of theory (see Table 7.1) were inserted into the XIAM code [51]. Comparing the calculated and experimental spectra, transitions of both conformers could be assigned straight forwardly. However, the standard deviations of these first fits were very high with values between 300 kHz and 500 kHz, which is more than a hundred times the spectral resolution. Even the inclusion of centrifugal distortion constants did not improve the situation. The reason for this problem can be traced back to the splittings caused by the internal rotations of the acetyl methyl and propenyl methyl group. The barrier heights of both internal rotors feature values in the same order of magnitude (see Section 7.1.3.), resulting in splittings of the five torsional species on a scale ranging from a few MHz down to less than a few kHz. In some cases, the splittings are not resolvable at all. Moreover, each branch shows its own unique splitting pattern. An example is given in Figure 7.4 for the 4 13 ← 3 12 transition of the ap conformer of 3-penten-2-one.

Unfortunately, these patterns change significantly, if barrier heights calculated at different levels of theory (see Table 7.3) are used as initial values for the prediction. Hence, although the transitions were correctly identified in the first fitting attempts, the right species has not been assigned at that point. Due to a lack of reliable starting values for the barriers, multiple cycles of trial and error were necessary to recognise the proper species. It proved to be helpful to go back and forth between different XIAM fits floating various amounts of parameters. Fits only including the (00) species will hereafter be called 0Top fits. In case of the 1Top Acetyl and 1Top Propenyl fits either the (00) and (10) or the (00) and (01) species lines were assigned, respectively.

2Tops fits include all species lines and the internal rotation of both rotors. Eventually, standard deviations in agreement with the spectral resolution could be achieved for all fits and both conformers, proving the assignments to be correct. A summary of all fits is presented in Table 7.4 and frequency lists are given in Table 17.7 and Table 17.8 in the Appendix. In case of the ap conformer, the experimentally deduced barriers to internal rotation are 434.149(37) cm -1 for the acetyl methyl group and 581.903(45) cm -1 for the propenyl methyl group. For the sp conformer, they are 358.076(26) cm -1 and 595.271(71) cm -1 , respectively. Total number of lines. [b] Number of the (00)/(10)/(01) species transitions, respectively. [c] Number of the ( 11)/(12) species transitions, respectively. [d] Standard deviation of the fit. Two conformers with C s symmetry were assigned in the microwave spectrum of 3-penten-2one. As described in Section 7.1.2., it is not clear whether the ap or the sp conformer is the energetically more favourable structure, since the calculated order of energy changes with the level of theory in use. Moreover, the line intensities of the spectrum recorded under the experimental setup described in Section 7.2.1. are not suitable to obtain the population ratio.

Quantitative statements are not attempted, but qualitatively, both conformers seem to be equally present in the spectrum. In comparison, other molecules exhibiting a double bond in conjugated position to a C=O bond, such as acrolein [150], methacrolein [151] and crotonaldehyde [152] [153], show a clear preference for the equivalent of the ap conformer.

For methyl vinyl ketone, a population ratio N ap /N sp of 2.2 has been determined [154].

Nevertheless, in case of methyl methacrylate [24] the energetic difference between the two conformers is very small and for methacrylate [23] only the sp conformer has been assigned.

If the different fits of one conformer are compared (see Table 7.4), the parameters are in good agreement with each other, although they do not coincide within their respective errors.

Nevertheless, these small discrepancies are well within reasonable range when diverse numbers of lines and different sets of parameters are fitted. Comparing the experimentally deduced rotational constants with those calculated at different levels of theory (see Section 7.1.2.), deviations of about 1% or less are observed for both conformers, which are reliable enough results for a good prediction of the microwave spectrum. The same cannot be said for the calculations of the barriers to internal rotation of the two terminal methyl groups, where divergences of up to 45% are found (see Section 7.1.3.). However, measurement accuracy could finally be achieved with all fits.

Acetyl Methyl Internal Rotation 7.3.2.

The internal rotation of the acetyl methyl group can be linked to the molecular structure of the target ketone, as extensively described for the series of methyl n-alkyl ketones in Part III of this work (here also referred to as Ref. [START_REF] Andresen | [END_REF] [2] [3] and [4]). There, two classes have been proposed: The "C s class" with barrier heights of about 180 cm -1 , and the "C 1 class" exhibiting barrier values of approximately 240 cm -1 . Herbers et al. expanded this system by a third, so-called "phenyl class" with barriers of about 600 cm -1 [32]. Acetone [87], 1,1-difluoro -acetone [131] and 1,1,1-trifluoroacetone [46] might form an "acetone class" with barrier heights of about 250 cm -1 .

According to the 1Top Acetyl fits (see Table 7.4), the acetyl methyl barriers to internal rotation of 3-penten-2-one are 434.136(56) cm -1 and 357.278(40) cm -1 for the ap and sp conformer, respectively. Therefore, 3-penten-2-one can be placed in a fifth proposed class, called "mesomeric class". As illustrated in Figure 7.5, the "mesomeric class" also encloses methyl vinyl ketone [30] and ionone [111], both molecules with a double bond in a conjugated position to the carbonyl group. Moreover, a sub-classification in antiperiplanar (ap) conformers with barriers of about 430 cm -1 and synperiplanar (sp) conformers with barriers of approximately 350 cm -1 is reasonable. Steric hindrance is likely to explain the difference in the barrier values, since the propenyl methyl group in the ap conformer is located very close to the acetyl methyl group when compared to the sp conformer. While rotating, the acetyl methyl group seems to "read" the π-conjugated system on the other side of the carbonyl group. Interestingly, the structural detection appears to end with the end of this π-system, as can be seen for α-ionone and β-ionone where a huge six-membered ring structure is attached on the other side of the double bond [111]. Despite multiple different ring conformations, the barrier to internal rotation of the acetyl methyl group is only significantly dependent on the ap-sp conformerism of the double bond.

2-acetyl-5-methyl-furan [48] and diacetyl [43] are molecules also featuring double bonds in direct proximity to the carbonyl group, as well as containing additional oxygen atoms within the π-system. The barrier heights of the acetyl methyl group are 307.78(59) cm -1 and 212.71(30) cm -1 for the respective trans and cis conformer of 2-acetyl-5-methyl-furan, and 318.5(2) cm -1 and 343.6(2) cm -1 for the two acetyl methyl groups in diacetyl. These barriers are somewhat similar to those found in the "mesomeric class". However, their conformational structures do not coincide with the characteristics of the ap or sp conformers due to the additional oxygen. Hence, it is not likely that those two molecules are members of the "mesomeric class". Curiously, acetyl isocyanate [155] shows an acetyl methyl barrier of 356(5) cm -1 , and although the carbonyl group is attached to a nitrogen atom, the molecular structure is very similar to that of the sp conformers of the unsaturated ketones series. Indeed, acetyl isocyanate might belong to the "mesomeric sp sub-class". 3) acetyl isocyanate [155], (4) α-ionone [111] and (5) β-ionone [111]. For ionone multiple barrier values are given referring to different conformations of the ring, see Ref. [111].

Propenyl Methyl Internal Rotation 7.3.3.

The barrier to the internal rotation of the propenyl methyl group is 581.903(45) cm -1 and 595.271(71) cm -1 for the ap and sp conformer, respectively, which is the same order of magnitude as the barrier heights found for the propenyl methyl or isopropenyl methyl groups of propene (698.4 cm -1 ) [156], isopropenyl acetate (711.7(73) cm -1 ) [15], and crotonaldehyde (≈ 606 cm -1 ) [152] [153], as well as of methacrolein (491.574(24) cm -1 ) [151] and methyl methacrylate (632.5(73) cm -1 for the ap conformer and 761.7(87) cm -1 for the sp conformer) [24]. In general, methyl groups attached to double bonds show much smaller 3-Penten-2-one -104 -barriers (ranging from approximately 500 cm -1 to 750 cm -1 ) than for example methyl groups at the end of alkyl chain where the values is about 1000 cm -1 , as found for the series of methyl n-alkyl ketones (see Chapter 3 to Chapter 6 or Ref. [START_REF] Andresen | [END_REF], [2], [3] and [4]).

Conclusions

The antiperiplanar (ap) and the synperiplanar (sp) conformer were identified in the microwave spectrum of E-3-penten-2-one. The complicated splitting patterns arising due to the internal rotation of the acetyl methyl and propenyl methyl group could be resolved and fitted to measurement accuracy. The barrier heights of the acetyl methyl group are 434.149(37) cm -1 and 358.076(26) cm -1 for the ap and sp conformer, respectively, thereby expanding and verifying the "mesomeric class" as a new class connecting the internal rotation to structural aspects of the ketone molecules. In case of the propenyl methyl group, the respective barrier is 581.903(45) cm -1 for the ap conformer and 595.271(71) cm -1 for the sp conformer. To create different starting conformers, the dihedral angle φ = ∡(O 6 ,C 5 ,C 7 ,C 8 ) of 3-methyl-3buten-2-one or methyl isopropenyl ketone was varied in a grid of 30° (for atom numbering see Figure 8.1). Geometry optimisations were performed with the Gaussian16 package [63] using these initial conformations, and calculations at the MP2/6-311++G(d,p) level of theory yield two different conformers. Additional frequency calculations confirm them to be minima and not saddle points. According to the notation used for other α,β-unsaturated ketones, such as methyl vinyl ketone [30] and 3-penten-2-one (see Chapter 7), the two conformers will hereafter be called the antiperiplanar (ap) and the synperiplanar (sp) conformer. As depicted in Figure 8.1, all heavy atoms of the ap conformer lie in one plane and the defining dihedral angle is φ = 180.0°. However, planarity is not given for the sp conformer showing an optimised dihedral angle of φ = 21.0° instead of φ = 0.0°, which can be traced back to a large steric hindrance between the two methyl groups of the molecule. The acetyl methyl group, as well as the methyl group of the isopropenyl group, both undergo internal rotation, and since they are located relative close together in the sp conformer, these rotations are coupled with each other, as will be further explored in Section 8.1.3.1. This coupling also destroys the planarity of the conformer and the possibility of the carbonyl group and the double bond to form a π-conjugated system. Therefore, the sp conformer, or better distorted sp conformer, is calculated to be about 9 kJ mol -1 higher in energy than the ap conformer and not expected to be visible in the microwave spectrum under the experimental setup described in Section 8.2.1. The relative energies, rotational constants and dipole moment components of both molecules are listed in Table 8.1. Their nuclear coordinates are given in Table 18.1 in the Appendix.

3-Methyl-3-buten-2-one

Table 8.1: Relative energies without and with zero-point corrections (in kJ mol -1 ), as well as rotational constants (in GHz), dipole moment components (in Debye), and optimised dihedral angle φ = ∡(O 6 ,C 5 ,C 7 ,C 9 ) (in degree) of the antiperiplanar (ap) and synperiplanar (sp) conformer of 3-methyl-3-buten-2-one calculated at the MP2/6-311++G(d,p) level of theory. E [a] E 5.097 3.335 2.069 [a] Referring to the absolute energy of E = -269.833361 Hartree of the ap conformer. [b] Referring to the zero-point corrected energy of E = -269.715390 Hartree of the ap conformer. [c] Rotational constants of the ap conformer obtained from the 2Tops fit, see Table 8 [118] and provides good results in case of the similar structured molecule 3-penten-2-one (see Chapter 7). Nevertheless, for comparison, geometry optimisations of the ap conformer, which is the conformer eventually identified in the microwave spectrum of 3-methyl-3-buten-2-one (see Section 8.2.2.), were repeated at various levels of theory (for more information see Section 2.2.). The calculated rotational constants are summarised in Table 18.2 and Table 18.3 in the Appendix.

Internal Rotation 8.1.3.

The internal rotations of both methyl groups in the molecule cause each rotational transition in the microwave spectrum to split into five species, which are labelled (σ 1 σ 2 ) = (00), (01), (10), (11) and (12), respectively [START_REF] Ferres | [END_REF], with σ 1 referring to the acetyl methyl group and σ 2 to the methyl group of the isopropenyl group, or short the propenyl methyl group. The numbers 0, 1, 2 are equivalent to the three symmetry species A, E a , E b of the C 3 group [54].

To estimate the barriers to internal rotation, the dihedral angles α 1 = ∡(H 2 ,C 1 ,C 5 ,C 7 ) and α 2 = ∡(C 5 ,C 7 ,C 11 ,H 13 ) are fixed in a grid of 10° for the acetyl methyl and propenyl methyl group, respectively, with only a range of 120° being covered, due to the C 3 symmetry of a methyl group. All other geometry parameters were then optimised at the MP2/6-311++G(d,p) level of theory, and the ensuing energies were parametrised with a one-dimensional Fourier expansion. The Fourier coefficients are listed in Table 18.4 in the Appendix.

The Synperiplanar (sp) Conformer 8.1.3.1.

For the sp conformer of 3-methyl-3-buten-2-one, the potential energy curves of both methyl groups seem to show regular threefold shapes, as depicted in Figure 8.2 and Figure 8.3, but a closer look reveals that the curves are actually not symmetric and many higher order terms are applied in the one-dimensional Fourier expansion. These observations can be explained with a large steric hindrance between the two methyl groups within the sp conformer, leading to coupled internal rotations, as illustrated in the middle traces of Figure 8. the sp conformer are therefore not a one-dimensional, but a three-dimensional problem, and the one-dimensional Fourier coefficients determined here loose most of their physical meaning. The barrier heights can only roughly be estimated to be 499 cm -1 and 777 cm -1 for the acetyl methyl and propenyl methyl group, respectively. Further investigations of the complex interactions between α 1 , α 2 and φ were not performed, since for this work it is sufficient to know that the lack of planarity in the sp conformer causes a much higher energy than found for the ap conformer. In case of the ap conformer, the potential energy curves of both internal rotors show an expected threefold shape, as illustrated in Figure 8.4 and Figure 8.5. Only a few higher order parameters were necessary in the Fourier expansion and the calculated barrier heights are 452.1 cm -1 and 616.9 cm -1 for the acetyl methyl and propenyl methyl group, respectively.

Microwave Spectrum

Experimental Setup 8.2.1.

3-Methyl-3-buten-2-one with a stated purity of >95.0° and stabilised with hydroquinone was purchased from TCI Europe N. V., Zwijndrecht, Belgium. 1% substance was mixed with helium, and at a stagnation pressure of about 100°kPa, the mixture was expanded through a pulsed nozzle into the Fabry-Pérot resonator of the spectrometer. The spectrometer in use was a molecular jet Fourier transform microwave spectrometer as described in Ref. [60] working in a frequency range from 2.0 to 26.5 GHz (for more information see Section 2.1.).

Spectral Assignment 8.2.2.

Using the rotational constants calculated at the MP2/6-311++G(d,p) level of theory (see Table 8.1) in the XIAM code [51], branches were predicted in the microwave spectrum of 3-methyl-3-buten-2-one, which generally stretched over a range of some GHz. Hence, a whole survey spectrum was not recorded. Instead, single transitions were searched with miniscans covering about 100 MHz in a step width of 0.25 MHz. If a line was found it was remeasured at high resolution reaching an ideal accuracy of the spectrometer of about 2 kHz [109].

For the ap conformer, the line search was started with the three a-type transitions 2 02 ← 1 01 , 2 12 ← 1 11 and 2 11 ← 1 10 , which were eventually located at 10330.1066 MHz, 9542.0740 MHz and 12077.7002 MHz, respectively. Improving the prediction by fitting these first three lines, led to straight forward measurements and assignments of the (00) species. However, including the internal rotations of both methyl groups in the fit proved to be very difficult, since the splittings caused by the acetyl methyl group, as well as the splittings induced by the isopropenyl methyl group are of the same order of magnitude ranging from some MHz to less Complicated splitting patterns have also been observed in the microwave spectrum of the similar molecule 3-penten-2-one (see Chapter 7). Using the barrier heights of the ap conformer found there (434.149(37) cm -1 for the acetyl methyl group and 581.903(45) cm -1 for the propenyl methyl group) as initial values for the ap conformer of 3-methyl-3-buten-2-one led to a successful identification of the (01), (10), (11) and (12) species. To verify the correct assignment, different XIAM fits floating various numbers of parameters were created. In the 0Top fit the molecule is considered semi-rigid (including centrifugal distortion) and only the (00) species lines are fitted. The 1Top Acetyl and 1Top Propenyl fit either include the internal rotation of the acetyl methyl group ((00) and (10) species) or of the propenyl methyl group ((00) and (01) species). In the 2Tops fit both internal rotations are included and all lines are fitted. The standard deviations of all fits reached measurement accuracy. A summary is given in Table 8.2, a frequency list in Table 18.5 in the Appendix. The experimentally deduced barriers to internal rotation are 512.159(19) cm -1 and 600.254(59) cm -1 for the acetyl methyl and propenyl methyl group, respectively. Total number of lines. [b] Number of the (00)/(10)/(01) species transitions, respectively. [c] Number of the (11)/(12) species transitions, respectively. [d] Standard deviation of the fit.

Finally, although carefully searched for, the sp conformer was not detected in the microwave spectrum of 3-methyl-3-buten-2-one. This confirms the findings of the quantum chemical calculations that the sp conformer exhibits a significantly less favourable structure than the ap conformer due to a lack of planarity (see Section 8.1.1. and Section 8.1.3.1.).

Discussion

Geometry Parameters 8.3.1.

Usually, there are two different conformers with C s symmetry detected in the microwave spectrum of molecules containing a carbonyl group and an α,β-double bond, such as for example observed in studies on 3-penten-2-one (see Chapter 7) and methyl vinyl ketone [30], as well as in investigations of acrolein [150], methacrolein [151] and methyl methacrylate [24]. Here, the two conformers are called the antiperiplanar (ap) and the synperiplanar (sp) conformer (see Section 8.1.1.). In case of 3-methyl-3-buten-2-one only the ap conformer could be detected in the microwave spectrum, since for the sp conformer there is a steric hindrance between the two methyl groups, causing a non-planarity of the heavy atoms of the molecule and destroying the π-conjugated system normally formed by the carbonyl group and the double bond. Hence, the structure of the sp conformer is energetically too unfavourable (see Section 8.1.3.1.).

Comparing the molecular parameters obtained with the different XIAM fits of the ap conformer, no significant discrepancy beyond those expected when floating different sets of parameters are observed (see Table 8.2). Moreover, the experimentally deduced rotational constants and the ones calculated at different levels of theory (see Section 8.1.2.) agree within 1% or less, which are good results.

Acetyl Methyl Internal Rotation 8.3.2.

The internal rotations of acetyl methyl groups in ketones are strongly connected to the molecular structures on the other side of the carbonyl group. The corresponding barrier heights can be categorised in a class system. Conformers of aliphatic ketones, such as for example found for pentan-2-one (see Chapter 3 or Ref. [START_REF] Andresen | [END_REF]), hexan-2-one (see Chapter 4 or Ref. [2]), heptan-2-one (see Chapter 5 or Ref. [3]) and octan-2-one (see Chapter 6 or Ref. [4]), either belong to the "C s class" with barriers of around 180 cm -1 or the "C 1 class" with barrier heights of approximately 240 cm -1 (see Part III). Acetone [87], 1,1-difluoroacetone [131] and 1,1,1-trifluoroacetone [46] constitute an "acetone class" with acetyl methyl barriers of around 250 cm -1 . α,β-unsaturated ketones, like methyl vinyl ketone [30], 3-penten-2-one (see Chapter 7) and ionone [111] form the "mesomeric class" with a sub-classification in ap conformers with barriers of approximately 430 cm -1 and sp conformers with values of around 350 cm -1 . Herbers et al. expanded the system by a "phenyl class" containing ketones with phenyl rings attached to a carbonyl group, as can be observed for acetophenone and its derivatives [32] [33] [34]. The barriers to the internal rotation of the acetyl methyl group range from 550 cm -1 to 630 cm -1 .

Due to its double bond, the ap conformer of 3-methyl-3-buten-2-one shares many structural and steric characteristics with other members of the "mesomeric ap sub-class" and was hence expected to exhibit an acetyl methyl barrier of about 430 cm -1 . However, according to the XIAM 1Top Acetyl fit (see Table 8.2), the actual barrier values is 512.130(28) cm -1 , much too high for the "mesomeric ap sub-class". Interestingly, the barrier height is also too small to match the "phenyl class". The acetyl methyl group as an internal rotor seems to "read" the structural environment in direct proximity to the carbonyl group. If the structural aspects of 3-methyl-3-buten-2-one are considered in detail, it becomes clear that this molecule needs its own barrier class somewhere in-between the "mesomeric class" and the "phenyl class", which is accurately mirrored by the value of the acetyl methyl barrier. In comparison to the molecules of the "mesomeric ap sub-class", there is a carbon atom instead of a hydrogen atom attached at the α-end of the double bond. In contrast to the big π-conjugated system of the "phenyl class", which is formed by the carbonyl group and the entire phenyl ring, there is only a fraction of this π-system, constituted of the carbonyl and the isopropenyl group, present in 3-methyl-3-buten-2-one. The new class will be called "branched mesomeric class", and because only one example of this class could be identified, it will be considered a sub-class of the "mesomeric class".

Propenyl Methyl Internal Rotation 8.3.3.

Concerning the internal rotation of the isopropenyl methyl group of the ap conformer, a barrier height of 600.254(59) cm -1 was obtained. This value is very similar to the barriers of 581.903(45) cm -1 and 595.271(71) cm -1 found for the ap and sp conformer of 3-penten-2-

3-Methyl-3-buten-2-one

-114 -one, respectively (see Chapter 7). Overall, it agrees well with the barrier range of about 500 cm -1 to 750 cm -1 frequently observed for propenyl methyl or isopropenyl methyl groups in molecules like propene [156], isopropenyl acetate [15], and crotonaldehyde [152] [153], as well as in studies on methacrolein [151] and methyl methacrylate [24].

Conclusions

The microwave spectrum of the ap conformer of 3-methyl-3-buten-2-one was recorded and splittings caused by the internal rotations of the acetyl methyl and isopropenyl methyl group could be resolved. The barrier heights are 512.159(19) cm -1 and 600.254(59) cm -1 for the acetyl methyl and propenyl methyl group, respectively. Similar to other ketones, the torsion of the acetyl methyl group can be linked to the structural aspects on the other side of the carbonyl group, and the "barrier class" system needs to be expanded by a "branched mesomeric sub-class", as part of the "mesomeric class". The barrier of the isopropenyl methyl group agrees well with the values found for other propenyl methyl and isopropenyl methyl groups undergoing internal rotation.

V Ketones of the Tunnelling Class

In Part III and Part IV of this work, the internal rotations of saturated and unsaturated ketones were thoroughly investigated and could be categorised in different classes linking the barrier to internal rotation of the acetyl methyl group to the respective conformational structure of the molecule. The question remains how branched structures influence the internal rotation of the acetyl methyl group. Here, two main cases should be differentiated. If the branching of the carbon chain in any given molecule is at the β-carbon position or further along the carbon chain, there seems to be only a minor impact on the barrier heights, as can be seen for methyl isobutyl ketone [26] and methyl neopentyl ketone [27], which belong to the "C 1 " or "C s class", respectively. If there is a branching at the α-carbon position, which is in direct proximity to the carbonyl group, the second case is obtained and a very unique behaviour for each single molecule can be observed. One example for this second case is found in 3-methyl-3-buten-2-one where the barrier height of the acetyl methyl group with a value of 512.130(28) cm -1 neither fits the "ap mesomeric sub-class" nor the "phenyl class" (see Chapter 8). Another example is pinacolone [28] which is a ketone containing an acetyl methyl group and a tert-butyl group. There, the detected conformer possesses a conformational structure similar to the "pseudo-C s " structure of the "C s class". However, additional splittings, besides those arising from the internal rotation of the acetyl methyl group, are visible in the microwave spectrum. These additional splittings are caused by a tunnelling between the two enantiomeric versions of the conformer, as also observed in form of the proton tunnelling in molecules like methyl ethyl amine [157], dimethyl amine [158], diethyl amine [146] and methyl-3-mercaptopropionate [22]. For further information on this kind of tunnelling see Section 1.5.

3-Methylbutan-2-one, also called methyl isopropyl ketone, is a solvent comparable to the more prominent substance methyl isobutyl ketone. Among others, it shows good properties extracting cresols [159] or phenols [160], and in reactions with borohydrides [161]. From a structural point of view, 3-methylbutan-2-one is very similar to both, pinacolone and 3-methyl-3-buten-2-one (see Figure 3). Instead of the tert-butyl group of pinacolone, it possesses an isopropyl group in direct proximity to the carbonyl group. This isopropyl group features two single carbon-carbon bonds, instead of one single and one double bond as it is the case for the isopropenyl group in 3-methyl-3-buten-2-one. It was interesting to see, as will be presented in the following chapter, if the internal rotation of the acetyl methyl group in 3-methylbutan-2-one rather acts like it does in "tunnelling molecules" such as pinacolone or if 3-methylbutan-2-one should be grouped together with its unsaturated counterpart 3-methyl-3buten-2-one in the "branched mesomeric sub-class" (see Chapter 8). As already revealed in the title of this part, 3-methylbutan-2-one is a member of the "tunnelling class", which leads to complex effects in the microwave spectrum.

3-Methylbutan-2-one

Chapter 9 is based on the measurements and quantum chemical calculations performed by Kenneth Koziol during his research project at RWTH Aachen University. Maike Andresen supervised the project.

Quantum Chemical Calculations

Geometry Optimisations 9.1.1.

Different starting geometries of 3-methylbutan-2-one or methyl isopropyl ketone are created by setting the dihedral angle φ = ∡(O 6 ,C 5 ,C 7 ,H 8 ) to 0°, ±30°, ±60°, ±90°, ±120°, ±150° and 180°, respectively (for atom numbering see Figure 9.1). Geometry optimisations at the MP2/6-311++G(d,p) level of theory conducted with the Gaussian09 package [62] yield three conformers, and additional frequency calculations confirm them to be stable minima rather than saddle points. The rotational constants, dipole moment components and relative energies of all three conformers are listed in Table 9.1, while the nuclear coordinates are given in 0.00 [a] 0.00 [b] 0.84 [a] 0.96 [b] 2.93 [a] 3.61 [b] E / cm -1 0.00 [a] 0.00 [b] 70.60 [a] 79.89 [b] 244.76 [a] 302.06 [b] E ZPE / kJ mol -1 0.00 [c] 0.00 [d] 1.00 [c] 0.75 [d] 3.36 [c] 3.71 [d] E ZPE / cm -1 0.00 [c] 0.00 [d] 83.99 [c] 62.77 [d] 280.53 [c] 309.74 [d] [a] Relative to the absolute energy of E = -271.049700 Hartree of conformer I. [b] Relative to the absolute energy of E = -271.866283 Hartree of conformer I. [c] Relative to the zero-point corrected energy of E ZPE = -270.907457 Hartree of conformer I. [d] Relative to the zero-point corrected energy of E ZPE = -271.726177 Hartree of conformer I. Conformer I of 3-methylbutan-2-one shows the hydrogen atom of the isopropyl group more or less in eclipsed position to the acetyl methyl group, in conformer II the carbonyl group and one methyl group of the isopropyl group are eclipsing each other, and for conformer III the isopropyl hydrogen is in eclipsed position to the carbonyl group (see Figure 9.1). However, all structures are bent out of the perfect symmetry plane by about 5 to 30°, with the respective value of the dihedral angle φ = ∡(O 6 ,C 5 ,C 7 ,H 8 ) being -155.0°, -126.3° and 15.1°, instead of 180.0°, -120.0° and 0.0°. Hence, every conformer exists as an enantiomeric pair of image and mirror image. Conformer I is the energetically most favourable conformer with conformer II being about 1 kJ mol -1 higher in energy, and conformer III about 3 kJ mol -1 higher. All conformers might be visible in the microwave spectrum under the experimental conditions described in Section 9.2.1., with conformer I and conformer II being more likely than conformer III. To obtain alternative molecular parameters for the analysis of the spectrum, the geometry optimisation was repeated at the B3LYP/6-311++G(d,p) level of theory. The results are also given in Table 9.1.

Internal Rotation 9.1.2.

Three different methyl groups in 3-methylbutan-2-one are undergoing internal rotation, the acetyl methyl group and the two methyl groups of the isopropyl group. The methyl group rotating around the C 7 -C 9 bond will be called first isopropyl methyl group and the one rotating around the C 7 -C 13 bond second isopropyl methyl group. To calculate the corresponding torsional barriers, the dihedral angles

α 1 = ∡(H 2 ,C 1 ,C 5 ,C 7 ), α 2 =
∡(C 5 ,C 7 ,C 9 ,H 10 ), and α 3 = ∡(C 5 ,C 7 ,C 13 ,H 14 ) were fixed in a grid of 10°, respectively, while all other parameters were allowed to relax during geometry optimisation. These scan calculations were performed at the MP2/6-311++G(d,p) level of theory and the resulting energies were then parametrised with a one-dimensional Fourier expansion. A list of all Fourier coefficients is given in Table 19.4 in the Appendix.

Acetyl Methyl Group 9.1.2.1.

The internal rotation of the acetyl group is very complex for all three conformers. As depicted in Figure 9.2, the potential energy curves of conformer I and conformer II show rather unusual behaviours. Sometimes the data points of the two different scan calculations align, and there are multiple global and multiple local minima. The global minima refer to the structure of conformer I. The local minima are about 70 cm -1 higher in energy and refer to conformer II. The barrier heights of the acetyl methyl groups of both conformers are approximately 150 cm -1 , which is very close to the energy difference of conformer I and II of 70.60 cm -1 (0.84 kJ mol -1 ), and upon the rotation of the acetyl methyl group the dihedral angle φ changes as well (lower trace of Figure 9.2). Hence, scan calculations are not possible without switching between the two conformers. This problem will hereafter be called the "conformer-switch problem", and although the measured data points can be fitted with a Fourier Expansion, the coefficients would lose all physical meaning. In consequence, the barrier height of either conformer cannot be reliably calculated with a one-dimensional approach. In addition, scan calculations of conformer I and conformer II also exhibit changes between different enantiomeric versions of the respective conformer, here called I a and I b or In an attempt to still calculate the barrier height of conformer I, all data points clearly belonging to conformer II were neglected and an interpolated Fourier expansion was performed. The result is an energy curve with three double minima and a global barrier height of 161.0 cm -1 (see black line in Figure 9.3). The two pits of one double minimum refer to I a and I b , respectively, and they are separated by a local barrier of 24.4 cm -1 . The double minima are very similar to those observed in the series of methyl n-alkyl ketones for the "pseudo-C s " conformers (see Part III or Ref. [START_REF] Andresen | [END_REF], [2], [3] and [4]). The question remains if the ground state of conformer I of 3-methylbutan-2-one lies above or below the value of the local barrier. In the former case, the structure would act as "effective C s " in the microwave spectrum, as was found for the methyl alkyl ketone series [START_REF] Andresen | [END_REF] [2] [3] [4]. In the latter case, there would be an additional splitting of the energy levels in symmetric (+) and asymmetric (-) sub-levels, such as has been observed in the study on pinacolone [28]. This effect will hereafter be called "enantiomer tunnelling". Unfortunately, the local barrier of 24.4 cm -1 is a rather unreliable value due to the "conformer-switch problem". Hence, it is unclear which of these two cases applies for conformer I. The potential energy curve of conformer III is illustrated in Figure 9.4. Here, a double minima shape is clearly shown. The global barrier height is 181.2 cm -1 , the local barrier height 51.3 cm -1 . The two pits of a double minimum refer to the two enantiomers of the conformer, as depicted with the changes of the dihedral angle φ (see lower trace of Figure 9.4). For conformer III, it is possible to calculate the tunnelling ground state, which is found at about 42.0 cm -1 , clearly a value below that of the local barrier. Additional splittings arising from the "enantiomer tunnelling" are hence expected to be visible in the microwave spectrum of conformer III. Since structure-wise conformer III and conformer I are very similar, conformer I is consequently more likely to show "enantiomer tunnelling" as well.

Isopropyl Methyl Groups 9.1.2.2.

In Figure 9.5 and Figure 9.6 the potential energy curves of both isopropyl methyl groups for all three conformers are depicted, and as expected for internal rotors with C 3 symmetry, they exhibit a threefold shape. Consequently, it was sufficient to cover only a range of 120° with the scan calculations. However, some higher order coefficients were necessary for the Fourier expansion due to some degree of steric repulsion between the hydrogen atoms of the two different methyl groups forming the isopropyl group. All barriers show values of about 1000 cm -1 . Small differences between conformers and first and second isopropyl methyl group can be explained with the different orientation of the respective methyl group within the conformers. For conformer I the barriers to internal rotation of the first and second group are 1087.1 cm -1 and 1066.0 cm -1 , respectively. For conformer II the values are 1061.2 cm -1 and 1048.9 cm -1 , while they are 1057.2 cm -1 and 1053.9 cm -1 in case of conformer III.

Microwave Spectrum Experimental Setup 9.2.1.

The microwave spectrum of 3-methylbutan-2-one was recorded using a molecular jet Fourier transform microwave spectrometer operating in the frequency range from 2.0 to 26.5 GHz (for description see Ref. [60], for more information see Section 2.1.). The substance was purchased from TCI Europe N. V., Zwijndrecht, Belgium. The stated purity was > 99.0% and no further purification steps were carried out. A substance-helium mixture of 1% was expanded through a pulsed nozzle into the cavity. The stagnation pressure of the flow was about 100 kPa. A series of adjacent spectra was measured from 8.0 to 16.0 GHz in a step width of 0.25 MHz. The survey spectrum is given in Figure 9.7. Moreover, recordings of the signals at higher resolution were also performed.

Only a few high resolution measurements show splittings of the lines in the order of a few kHz. These splittings are caused by the internal rotations of the two isopropyl methyl groups with barrier heights of about 1000 cm -1 (see Section 9.1.2.2.). Nevertheless, the quantity of these splittings is low and quite often the signals are slightly broadened instead. Hence, these splittings are neglected and 3-methylbutan-2-one is considered a one-rotor problem for the assignment process. Examples of other microwave spectroscopic studies where the internal rotations of branched alkyl methyl groups are not resolvable due to high barriers of more than

3-Methylbutan-2-one

-124 -1000 cm -1 are the investigations of methyl isobutyl ketone [26], methyl neopentyl ketone [27], and diisopropyl ketone [29], as well as studies on isopropyl acetate [11] and tertbutyl acetate [12].

Spectral Assignment Attempts 9.2.2.

Predicted spectra of all three conformers were determined with the XIAM code [51] using the parameters calculated at the MP2/6-311++G(d,p) level of theory as initial values (see Table 9.1). A successful assignment however was not achieved, although there are always lines experimentally detectable in proximity to the predicted frequency of any given transition. The problem is that a single line is seldom observed. Instead, bundles of several lines are found, with the lines in one bundle being only some MHz apart (see Figure 9.6). These line bundles are very difficult to analyse, which can be traced back to three main reasons: (i) three conformers with similar rotational constants and similar spectra, (ii) splittings in the (0) and (1) species due to the internal rotation of the acetyl methyl group, and (iii) additional splitting effects caused by the "enantiomer tunnelling". In the following paragraphs each of these problems will be explained in detail.

Firstly, there are three conformers calculated for 3-methylbutan-2-one, all of which might be detectable in the microwave spectrum. As listed in Table 9.1, the respective rotational constants A, B and C of the three conformers are very similar, if compared to each other. This leads to similar predicted spectra, while the conformer difference between the frequencies of a specific transition is in the order of some MHz. The line bundles of the experimental spectrum may very well be constituted of lines of all three conformers. Changing the level of theory to calculate the spectrum, for example to the B3LYP/6-311++G(d,p) level, alters the absolute predicted frequency of the transition but not the frequency positions of the different conformers relative to each other. Still, it is too difficult to assign all three conformers at the same time. Furthermore, the "conformer-switch problem" may not only be an anomaly of the calculations (see Section 9.1.2.1.), but a real occurring problem due to a low activation energy separating conformer I and conformer III. The two conformers may hence constantly convert from one form to the other and may be undistinguishable in the gas phase.

Secondly, there is also the splitting of every transition into the (0) and the (1) species due to the internal rotation of the acetyl methyl group. The barrier heights of the different conformers are about 150 cm -1 (see Section 9.1.2.1.). Comparing these to other barrier heights of about 100 cm -1 to 250 cm -1 , for example found for the series of methyl alkyl ketones [START_REF] Andresen | [END_REF] [2] [3] [4] (see Part III), the splittings are expected to be in the order of several MHz up to some GHz. Consequently, the line bundles of the experimental spectrum may also be formed by lines of different species. Unfortunately, due to the "conformer-switch problem" of conformer I and conformer II (see Section 9.1.2.1.), there are no reliable barrier values available which could serve as initial parameters for a prediction. In case of conformer III the barrier height could be calculated, but this conformer is much higher in energy than the other two. It may or may not be visible in the spectrum. If it is detectable, the intensities of conformer III are expected to be lower than those of the other two conformers, making it a difficult candidate to start the assignment with. Lastly, there is the "enantiomer tunnelling" effect. If it is indeed the case that there is a tunnelling motion between the two enantiomeric versions of a conformer, as at least suggested for conformer III and very likely for conformer I (see Section 9.1.2.1.), there might be additional splittings and also problems with the programs used for the assignment. The "enantiomer tunnelling" is a phenomenon similar to the proton inversion tunnelling observed in amines [157] [158] [146], or the hydrogen wagging in molecules like methyl-3mercaptopropionate [22] or the pyruvic acid-water complex [105]. The tunnelling motion causes each energy level to split up in a symmetric (+) and an asymmetric (-) sub-level. The Another problem with the "enantiomer tunnelling" is that there are no suitable fitting programs to deal with this type of tunnelling and internal rotation at the same time. Normally, either the (+) and the (-) state are separately fitted and internal rotation can be included, or the (0) and ( 1) species are separately dealt with and the tunnelling motion can be analysed, as has been done in studies on diethyl amine [146], methyl-3-mercaptopropionate [22] or the pyruvic acid-water complex [105]. The investigation of pinacolone, a molecule showing "enantiomer tunnelling" as well as internal rotation, revealed that the programs XIAM [51], ERHAM [58],

BELGI [52] [53] and RAM36 [59] are all unsuited to provide global fits dealing with both effects [28]. There, the fits showed standard deviations of up to about 1 MHz. For the microwave spectrum of 3-methylbutan-2-one, this may mean that a correct assignment is not recognised as such, due to very high standard deviations of the first fitting attempts. In the future, promising assignments will be tested via closed loops of four transitions, which are called Ritz cycles. Ritz proposed that there is a clearly defined relation between series of lines in a spectrum [162]. For microwave spectroscopy, that means that if there are four energy levels i,j = 1, 2, 3, 4, the following relation must be true: υ 2←1 + υ 4←2 = υ 3←1 + υ 4←3 , where υ i←j is the frequency of the transition i ← j. However, such an analysis is time consuming and has not been performed yet.

Discussion

Of the three conformers calculated for 3-methylbutan-2-one none could be identified in the microwave spectrum. Therefore, each statement concerning the molecule is of a theoretical nature and could not be experimentally verified. Nevertheless, the aim of this work was to learn more about the acetyl methyl group and how it may connect to the general molecular structure. In this regard, the scan calculations to determine the barrier heights (see Section 9.1.2.) as well as the problems fitting the conformers (see Section 9.2.2.) still give a lot of insight. 3-Methylbutan-2-one is most likely a molecule with "enantiomer tunnelling".

Moreover, this tunnelling effect makes the treatment of the acetyl methyl torsion much more complicated, probably due to interactions of these two large amplitude motions which cannot be sufficiently reproduced by any established fitting formalism yet. As a result, 3-methylbutan-2-one acts very similar to pinacolone, a molecule for which the exact same problems have been reported [28]. Both molecules exhibit branched alkyl groups in direct proximity to the carbonyl group.

As has been thoroughly described in Part III and Part IV of this work, the link between the barrier to internal rotation of the acetyl methyl group and the structural aspect of a ketone can be categorised. Methyl n-alkyl ketones either belong to the "C s class" with barriers of roughly 180 cm -1 and "pseudo-C s " geometries or the "C 1 class" showing a bent structure and barrier heights of approximately 240 cm -1 [91] [1] [2] [3] [4]. Branched alkyl ketones where the branching is not in direct proximity to the carbonyl group, such as methyl isobutyl ketone [26] or methyl neopentyl ketone [27], are also members of either of the two classes. Ketones with phenyl rings and barriers of about 600 cm -1 constitute the "phenyl class" [32] [33] [34], and α,β-unsaturated ketones are enclosed by the "mesomeric class" showing barriers values of about 430 cm -1 or 350 cm -1 (see Chapter 7 and Ref. [30], [111] and [155]). The "acetone class" contains molecules like acetone [87], 1,1-difluoroacetone [131] and 1,1,1trifluoroacetone [46] and exhibits barriers to internal rotation of around 250 cm -1 . With 3-methylbutan-2-one and pinacolone [28] the class system can be expanded by a "tunnelling class". The barrier of 121.532(57) cm -1 observed for pinacolone [28] fits with the calculated values of approximately 150 cm -1 found for 3-methylbutan-2-one (see Section 9.1.2.1.). The characteristics of the "tunnelling class" should however be clearly differentiated from the traits of the "branched mesomeric sub-class" formed by 3-methyl-3-buten-2-one, a molecule also featuring a branching directly attached to the carbonyl group. Due to its α,β-double bond, the barrier height is much larger with a value of 512.130(28) cm -1 (see Chapter 8).

The biggest common feature of molecules of the "tunnelling class" is a tunnelling motion causing additional splittings. Are there thus more possible candidates for this class?

Acetylacetone is a molecule exhibiting an enolic structure with C 2v symmetry [45]. This structure shows a hydrogen atom in the middle between the two carbonyl groups, not unlike a transition state between the two enol versions of the molecule. The question is whether the structure is indeed a "stable transition state" or if there rather is hydrogen tunnelling between the two enols. Moreover, can the rather low acetyl methyl barrier of 57.0 cm -1 then be explained with tunnelling effects? Instead, the barrier height might also be caused by strong hydrogen bond interactions, which are likewise observed for hydroxyacetone [163] and peroxyacetic acid [164]. There, the barrier to internal rotation of the acetyl methyl group are 65.3560( 22) cm -1 and 76.70(45) cm -1 , much more similar to the value of 57.0 cm -1 and hinting at the possibility of a "hydrogen bond class". From the data available the situation in acetylacetone is simply not clear. Other ketones exhibiting acetyl methyl internal rotation and tunnel motions seem to not have been studied, yet.

Conclusions

The microwave spectrum of 3-methylbutan-2-one was recorded and detailed quantum chemical calculations to analyse the molecule were performed. However, none of the three possible conformers was identified in the microwave spectrum. Nevertheless, it became clear that 3-methylbutan-2-one probably shows an "enantiomer tunnelling" motion besides the internal rotation of the acetyl methyl group similar to the one observed in pinacolone [28].

The classification system linking the acetyl methyl torsion to the structure of a ketone could thus be expanded by a "tunnelling class".

VI General Discussion

Internal Rotation of the Acetyl Methyl Group

To summarise the results of the previous chapters, here an overview of all observations concerning the internal rotation of the acetyl methyl group is given. The main aim of this dissertation is to figure out whether the barrier height of an acetyl methyl group in a ketone is linked to the overall structure of the molecule or not. This question can be answered with a firm yes. So far, six different "barrier classes" could be identified, where the barrier to internal rotation of the acetyl methyl group acts as a "detector" for the molecular structure of the ketone.

Starting with relatively simple, saturated ketones, three "barrier classes" can be differentiated (see Table 10.1):

"C s Class": All members of the methyl n-alkyl ketone series exhibit one conformer with a "straight" carbon chain belonging to this class, where the barrier height of approximately 180 cm -1 is linked to the existence of a "pseudo-C s " or "effective C s "

symmetry [91] [1] [2] [3] [4]
. In such a "pseudo-C s " structure, all heavy atoms seem to lie in one C s mirror plane, but the entire alkyl chain is actually slightly tilted out of plane, according to calculations at the MP2/6-311++G(d,p) level of theory by about 10°. However, this kind of structure acts like a "true C s " structure in the microwave spectrum, making the symmetry "effective C s ". It is noteworthy that the electrostatic environment of a "pseudo-C s " structure seems to have a bigger influence on the internal rotation of the acetyl methyl group than steric effects do. For this reason branched molecules, like methyl neopentyl ketone [27] and cat ketone [123],

belong to this class as well. Moreover, the interaction between the acetyl methyl group and the rest of the molecule only ranges up to the γ-carbon of the alkyl chain, as can be seen for the C 1 -δ conformer of hexan-2-one, which features a barrier of 182 cm -1 although the δ-carbon is bent to a synclinal position, thereby breaking the C s symmetry [2].

"C 1 Class": This class encloses all the conformers of the methyl n-alkyl ketone series where the γ-carbon of the alkyl chain is bent to a synclinal position [START_REF] Andresen | [END_REF] [2] [3] [4]. To distinguish this conformer from other structures with C 1 symmetry, it shall be called the C 1 -γ conformer. As long as the a γ-carbon is in this particular bent position, the barrier is always about 240 cm -1 , even if specific branched chain elements or double bonds exist within the molecule, as is the case in methyl isobutyl ketone [26] and allyl acetone [31]. The C 1 -γ conformation might be stabilised by weak hydrogen interactions of the carbonyl group with one of the hydrogens at the γ-carbon and with one of the hydrogens at the β-carbon.

"Acetone Class": In acetone, as well as in 1,1-difluoroacetone and 1,1,1trifluoroacetone, the barrier height of the acetyl methyl group is approximately 250 cm -1 [87] [131] [46]. This value is very similar to that of the "C 1 class". However, all three molecules are not long enough to support a C 1 -γ structure. A better explanation for the barrier value might be that there is only a relative small group on the other side of the carbonyl group of all molecules and that the acetyl methyl torsion is hence not significantly influenced by it.

As illustrated in Table 10.2, there exist two more "barrier classes", if the carbonyl group of the ketone can be part of a conjugated π-system. Depending on the type of π-system, the barrier heights range from 340 cm -1 to 630 cm -1 . The classes are defined as follows:

"Mesomeric Class": Ketones exhibiting a double bond in a conjugated position to the carbonyl group constitute this class (see Chapter 7 and Ref. [30], [111] and [155]).

Here, sub-classes must be defined. Conformers where the carbonyl group and the double bond are synperiplanar (sp) to each other always show barriers to internal rotation of about 350 cm -1 . If the structure is antiperiplanar (ap), the value is approximately 430 cm -1 . The much higher barrier heights of the ap conformers are probably caused by a steric hindrance between the acetyl methyl group and the double bond. Interestingly, supplementary structural aspects beyond the double bond do not significantly influence the barrier values of the acetyl methyl group, as can be seen for αand β-ionone [111], where a large ring showing different conformational structures is attached to the double bond. As known so far, only 3-methyl-3-buten-2-one shows a barrier height of 512 cm -1 , probably due to an additional branching at the α-position (see Chapter 8). Hence, 3-methyl-3-buten-2-one is sorted in the "branched mesomeric sub-class". Structure-wise, this molecule is somewhere in-between the double bond structure of a ketone of the "mesomeric class" and the full aromatic phenyl ring of the "phenyl class" ketones, which will be discussed in the next paragraph. This inbetween-structure is nicely reflected by the value of the barrier height.

"Phenyl Class": This class encloses acetophenone and its derivatives with barriers of the acetyl methyl group ranging from 550 cm -1 to 630 cm -1 [32] [33] [34]. Here, the structural characteristic is the phenyl ring attached to the carbonyl group. The rather large difference in barrier heights between different members of this class is probably caused by diverse substituents at the ring. Nevertheless, there are no apparent trends visible and the detailed interactions should be further investigated in the future.

In addition, there are also ketones containing an acetyl methyl group where the classification is rather difficult (see Table 10.3), either because the effects influencing the internal rotation of the acetyl methyl group are not as obvious as for the other classes, or because there is no sufficient modell describing these effects. For treating members of the following "tunnelling class", such a problem is encountered.

"Tunnelling Class": Pinacolone and 3-methylbutan-2-one are molecules which show additional splittings in the microwave spectrum, besides those due to the internal rotation of the acetyl methyl group (see Chapter 9 and Ref. [28]). These splittings are caused by a tunnelling between the two enantiomeric configurations of the molecule.

Unfortunately, there is no suitable fitting program to treat such an inversion tunnelling coupled with effects of internal rotation, yet. In the case of pinacolone, the standard deviation of different fits is up to 1 MHz, which is approximately a thousand times higher than the measurement accuracy of the spectrometer. For 3-methylbutan-2-one, this problem altogether prevented a successful assignment. Quantitatively, a statement about the internal rotation of the acetyl methyl group cannot be made. Qualitatively, it is clear that a branched structure in direct proximity to the carbonyl group has a high impact on the internal rotation of the acetyl methyl group.

Table 10.1: Ketones categorised in the "C s ", "C 1 " and "acetone class", as well as their barriers to the internal rotation of the acetyl methyl group. If several fits are available, the barrier heights are those obtained from a XIAM or XIAM(1Top) fit. All values are rounded to an accuracy of 1 cm -1 . The molecules studied in this work are marked grey.

C s Class

butan-2-one [91] 183 cm -1

pentan-2-one [a] C s : 188 cm -1

hexan-2-one [b] C s : 187 cm -1

heptan-2-one [c] C s : 185 cm -1

octan-2-one [d] C s : 185 cm -1 methyl neopentyl ketone [27] 174 cm -1

cat ketone [123] 179 cm -1

hexan-2-one [b] C 1 -δ: 182 cm -1

C 1 Class

pentan-2-one [a] C 1 -γ:

238 cm -1 hexan-2-one [b] C 1 -γ: 234 cm -1 heptan-2-one [c] C 1 -γ: 233 cm -1
octan-2-one [d] C 1 -γ: 233 cm -1 methyl isobutyl ketone [26] 250 cm -1

allyl acetone [31] 225 cm -1

Acetone Class

acetone [87] 242 cm -1 +Ne [e] : 259 cm -1 [132] +Ar [e] : 260 cm -1 [133] difluoroacetone [131] 261 cm -1 trifluoroacetone [46] 259 cm -1 13 C(CH 3 ) [f] : 259 cm -1 13 C(CF 3 ) [f : 259 cm -1 13 C(CO) [f] : 259 cm -1

18

O [f] : 260 cm -1 +H 2 O [g] : 275 cm -1 [44] [a]
This work, see Chapter 3. [b] This work, see Chapter 4. [c] This work, see Chapter 5. [d] This work, see Chapter 6. [e] Referring to an acetone noble gas complex. [f] Referring to different 13 C and 18 O isotopologues, see Ref. [46]. [g] Referring to a monohydrated water complex, see Ref. [44].

Table 10.2: Ketones containing a conjugated π-system categorised in the "mesomeric" and "phenyl class", as well as their barriers to the internal rotation of the acetyl methyl group. If several fits are available, the barrier heights are those obtained from a XIAM or XIAM(1Top) fit. All values are rounded to an accuracy of 1 cm -1 . The molecules studied in this work are marked grey.

Mesomeric Classsynperiplanar (sp) sub-class

methyl vinyl ketone [30] sp: 377 cm -1 3-penten-2-one [a] sp: 357 cm -1 α-ionone [111] sp/-ac 6 HC 5 [b] : 360 cm -1 sp/sp 6 HC 5 [b] : 360 cm -1 sp/-ac 5 HC 6 [b] : 356 cm -1 β-ionone [111] sp/-sc [b] : 343 cm -1 sp/+sc [b] : 341 cm -1 acetyl isocyanate

[155] 356 cm -1

Mesomeric Classantiperiplanar (ap) sub-class

methyl vinyl ketone [30] ap: 434 cm -1 3-penten-2-one [a] ap: 434 cm -1 α-ionone [111] ap/-ac 6 HC 5 [b] : 439 cm -1 ap/sp 6 HC 5 [b] : 455 cm -1 ap/-ac 5 HC 6 [b] : 441 cm -1 β-ionone [111] ap/-sc [b] : 427 cm -1 ap/+sc [b] : 437 cm -1

Mesomeric Classbranched mesomeric sub-class

3-methyl-3-buten -2-one [c] 512 cm -1

Phenyl Class

acetophenone [33] 627 cm -1 +H 2 O [d] : 589 cm -1 4-methylacetophenone [32] 594 cm -1 acetovanillone [34] s-cis [e] : 552 cm -1 s-trans [e] : 622 cm -1 6-hydroxy-3methoxyacetophenone [34] s-trans [e] : 612 cm -1 t-trans [e] : 588 cm -1 [a] This work, see Chapter 7. [b] The notations -ac, -sc, +sc, 6 HC 5 and 5 HC 6 refer to different conformations of the ring in ionone, see Ref. [111]. [c] This work, see Chapter 8. [d] Referring to a monohydrated water complex, see Ref. [33]. [e] The notations s-cis, s-trans and t-trans refer to different conformations of the substituents at the phenyl ring, see Ref. [34].

Table 10.3:

Ketones containing an acetyl methyl group, which are difficult to categorise in different classes, as well as their barriers to the internal rotation of the acetyl methyl group. If several fits are available, the barrier heights are those obtained from a XIAM or XIAM(1Top) fit. All values are rounded to an accuracy of 1 cm -1 . The molecules studied in this work are marked grey.

Tunnelling Class

pinacolone [28] 122 cm -1 [a] 3-methylbutan -2-one [b] barrier not determined Other Ketones acetylacetone [45] 57 cm -1 hydroxyacetone [163] 65 cm -1

phenyl acetone [35] 238 cm -1 2-acetyl-5-methylfuran [48] cis [c] : 213 cm -1 trans [c] : 308 cm -1 methylglyoxal [165] 272 cm -1 diacetyl [43] 319 cm -1 +H 2 O [d] : 344 cm -1 cyclopropyl methyl ketone [40] 413 cm -1 [a] Barrier determined with low accuracy, see Ref. [28]. [b] This work, see Chapter 9. [c] The notations cis and trans refer to different conformations of the furan ring, see Ref. [48]. [d] Referring to a monohydrated water complex, see Ref. [43].

Finally, there are ketones containing an acetyl methyl group which are quite unique in terms of structure and barrier to internal rotation. For example, studies on acetylacetone have shown that the most stable conformer is not the keto but an enolic form with C 2v symmetry, resembling a transition state [45]. Maybe there is even a proton tunnelling between the two enol structures of the molecule. This might explain its relatively low barrier height of 57 cm -1 .

However, the barrier value might also be connected to a strong hydrogen bond with the carbonyl group, which is observed for hydroxyacetone, as well [163], where the barrier is 65 cm -1 . Phenyl acetone shows a barrier value of 238 cm -1 for its gauche conformer [35],

which seems to fit very well in the "C 1 class". However, the gauche conformer of phenyl acetone is not a C 1 -γ conformer, since here the βand not the γ-carbon is bent to a synclinal position. 2-acetyl-5-methylfuran, methylglyoxal and diacetyl might be candidates for the "mesomeric class". Nevertheless, their conformers and barriers of the acetyl methyl group do not actually align with the characteristics of this mesomeric class [48] [165] [43]. Lastly, cyclopropyl methyl ketone exhibits a unique ring structure, as well as a barrier of 413 cm -1 [40].

Regarding the dependence of the barrier heights on the molecular conformation, it is also interesting to consider molecules of other substance classes, which contain an acetyl methyl group undergoing internal rotation. In general, each substance class can be categorised in its own "barrier class", including sub-classes:

Acetates: In case of the acetates, a class system similar to that established for ketones can be observed. However, for acetates there are only three classes [17] [16]. The third class is the equivalent of the "branched mesomeric sub-class", as seen for isopropenyl acetate with a barrier height of 135 cm -1 [15].

Acetyl Halides: This class encloses acetyl fluoride (364 cm -1 ) [166], acetyl chloride (453 cm -1 ) [141], acetyl bromide (457 cm -1 for 79 Br and 456 cm -1 for 81 Br) [142] and acetyl iodide (455 cm -1 ) [143], as well as acetyl cyanide (444 cm -1 ) [144]. The barrier to internal rotation of the acetyl methyl group is about 450 cm -1 , probably due to a partly ionic character of the halide-carbonyl bond. Only the barrier value of acetyl fluoride is smaller for unknown reasons.

Acids: There are some acids containing an acetyl methyl group undergoing internal rotation, such as acetic acid (170 cm -1 ) [167], pyruvic acid (339 cm -1 ) [168] and thioacetic acid (76 cm -1 and 358 cm -1 for the syn and anti conformer, respectively) [169]. To fully understand the reasons behind the respective acetyl methyl barrier values, an additional systematic investigation of acids would most likely be necessary. Nevertheless, it is interesting to see that peroxyacetic acid [164], a molecule exhibiting a hydrogen bond within its structure, shows a rather low barrier of 77 cm -1 . Low barriers of 57 cm -1 and 65 cm -1 have also been found for acetyl acetone [45] and hydroxyacetone [163], respectively. These low barriers might be connected to the presence of a hydrogen bond, since studies on acetic acid water complexes demonstrated that an increasing number of hydrogen bonds leads to a decrease in barrier height values [170]. A "hydrogen bond class" might exist, but it would neither be a "ketone barrier class" nor an "acid barrier class", if it includes molecules of both substance classes.

Aldehydes: By definition, aldehydes are molecules where a carbonyl group is attached to a hydrogen atom and an alkyl rest. Consequently, they usually do not contain an acetyl methyl group. An exception is acetaldehyde with an acetyl methyl torsional barrier of 408 cm -1 [171]. However, there are many structural similarities between aldehydes and ketones, e.g. there are two conformers detected in the microwave spectra of all n-alkyl aldehydes, one with C s and one with C 1 symmetry [124] [125]

[126] [127]. Interestingly, the C 1 conformers exhibit the exact same C 1 -γ structure as the ketones of the "C 1 class" do, probably because they are also able to form a weak hydrogen bond between the carbonyl group and one of the γ-hydrogens, as well as one of the β-hydrogens.

Amides:

In amides, molecules with a nitrogen atom attached to the carbonyl group, the barrier to internal rotation of the acetyl methyl group depends on the other substituents at the nitrogen. Acetamide (-NH 2 ) possesses a barrier of 24 cm -1 [134]. In monosubstituted amides (-NHR) the value is about 70 cm -1 . Examples are N-methylacetamide (≈ 73 cm -1 ) [135], N-ethylacetamide (≈ 73 cm -1 ) [136], and N-tert-butylacetamide (≈ 66 cm -1 ) [137], as well as ethylacetamidoacetate (≈ 64 cm -1 and ≈ 65 cm -1 ) [138], and N-acetyl alanine metyhl ester (≈ 65 cm -1 ) [119].

Disubstituted amides (-NR 2 ) like N,N-dimethylacetamide (≈ 677 cm -1 ) [139] and N,Ndiethylacetamide (≈ 517 cm -1 and ≈ 619 cm -1 ) [140] show barrier heights in the range of 500 cm -1 to 700 cm -1 .

Although there are not many studies providing barriers to internal rotation of the acetyl methyl group in different isotopologues or complexes of a molecule, the effects on the acetyl methyl torsion, which are known, should be mentioned here, as well:

Complexes: As can be seen for trifluoroacetone [44], acetophenone [33], and diacetyl [43], the barrier height in monohydrated water complexes changes by 10-40 cm -1 compared to the single substance (see Table 10.1, Table 10.2 and Table 10.3). If the complex is formed with a noble gas, as found in studies on acetoneneon [132] and acetone-argon [133], the differences are of the same order of magnitude (see Table 10.1). This is a relatively small variance, which does not change the overall categorisation system presented here.

Isotopologues:

The influence of isotopic substitution on the internal rotation of the acetyl methyl group is rather small as well. In trifluoroacetone and diverse acetyl halides the barrier height only changes by a few wavenumbers or not at all [46] [166]

[141] [142]. If a hydrogen of the acetyl methyl group itself is exchanged with deuterium, the impact is slightly higher, and the barrier changes in the order of 10 cm -1 , as has for example been reported for acetone by Vacherand et al. [84] [172].

The barrier values found there are 266 cm -1 for the main isotopologue CH 3 COCH 3 , and 264 cm -1 , 251 cm -1 and 251 cm -1 for CH 3 COCH 2 D, CD 3 COCHD 2 and CD 3 COCD 3 , respectively.

In conclusion, a broad overview of the internal rotation of the acetyl methyl group in ketones and other molecules is listed in this chapter. Moreover, attempts are made to explain differences of the barriers to internal rotation. In general, it seems that the acetyl methyl group "reads" the electrostatic environment on the other side of the carbonyl, whereas steric effects only have a minor impact on the internal rotation. The closer specific structural elements like branchings, double bonds or bent configurations are to the carbonyl group, the larger is the influence on the barrier height. Beyond the δ-carbon, there is no influence, but it should be noted that there is a rather soft transition for the end of the interaction range. Investigations of the methyl n-alkyl series have shown that the barrier values asymptotically reach a plateau the longer the alkyl chain becomes (see Chapter 6 or Ref. [4]). It can be argued that the structure at the α-position determines the value of the acetyl methyl group barrier, and structural aspects at the βand γ-position only indirectly change the structure at the α-position. As illustrated in Figure 10.1, the "detection active" range can hence be further separated in a "highly active" and an "indirect active" zone. Microwave spectroscopy alone does not provide sufficient data to fully understand all effects observed. For example, the nature of the interactions in a molecular bond cannot be determined from the spectrum. Nevertheless, the results of this work might function as helpful guidelines for further microwave spectroscopic studies dealing with the phenomenon of internal rotation.

Methods of Parameter Prediction

As has been shown throughout this work, precise predictions of the rotational constants A, B and C are essential for a successful assignment of a microwave spectrum. But, choosing the most suitable calculation method for such a prediction can be a challenging task, since so far, there is no "golden method" capable to predict reasonable parameters for every problem which might occur in the spectroscopic investigations of very different target molecules. The approach used in this dissertation was that of doing quantum chemical calculations either For hexan-2-one (see Chapter 4), a third kind of conformer was assigned. This conformer features C 1 symmetry, but in comparison to the other C 1 -γ conformers the δand not the γ-carbon is bent to a synclinal position. In this case, the A rotational constants behave like those of the C s conformers in terms of calculation-experiment deviation, but the deviations of the B rotational constants rather resemble those of the C 1 -γ conformers. For the C constants, mostly ΔX values between 0.5% and 1% are found.

utilizing
Consequently, every type of molecule symmetry (C s structure, or diverse C 1 structures) seems to cause different systematic errors in each level of theory, but similar errors, if conformers with the same symmetry and structure are compared. For a successful use of the "calibration method", each set of level of theory, symmetry type and rotational constant needs its own calibration graph.

Finally, the calculations of the barriers to internal rotations should be briefly mentioned as well. As demonstrated throughout this dissertation, it is possible to obtain calculated values of the barrier heights. But, while the deviations from the experimental parameters are only up to 5% in case of the rotational constants, it varies in a range up to 80% for the barrier values, rendering the results of the calculation not very reliable. Examples are given in Table 7.3 in Chapter 7 and also in Ref. [48], [119], and [140]. Further studies to understand and improve the calculation method were not attempted here, since such investigations are far beyond the scope of this thesis.

VII Final Conclusion

The microwave spectra of pentan-2-one (Chapter 3), hexan-2-one (Chapter 4), heptan-2-one Additionally, the splittings caused by the internal rotation of the methyl group at the end of the respective alkyl chain could be resolved and the barrier was determined to be about 1000 cm -1 for each conformer.

(
In the spectrum of E-3-penten-2-one, two conformers were assigned, one with an antiperiplanar (ap) and one with a synperiplanar (sp) structure. For 3-methyl-3-buten-2-one, only the ap conformer could be identified. Complicated splitting patterns arose due to the internal rotations of both, the acetyl methyl group and the methyl group of the propenyl or isopropenyl group, respectively. They were eventually resolved to yield acetyl methyl barriers of 434.149(37) cm -1 (ap-3-penten-2-one), 358.076(26) cm -1 (sp-3-penten-2-one) and 512.159(19) cm -1 (ap-3-metyhl-3-buten-2-one). For the propenyl methyl groups the barrier values are 581.903(45) cm -1 , 595.271(71) cm -1 and 600.254(59) cm -1 , respectively.

The microwave spectrum of 3-methylbutan-2-one could not be assigned to any of its three predicted conformers due to additional splittings beside those caused by internal rotation.

These splittings were suspected to arise from a tunnelling between two enantiomeric versions of the molecule.

Based on the results provided in this dissertation and on other acetyl methyl barriers found in the literature, a barrier class system for ketones was proposed linking the barrier height of the acetyl methyl group to the geometry of the molecule on the other side of the carbonyl group (Chapter 10). The classes identified so far are:

 "C s class": ketones with "pseudo-C s " structure and barriers of about 180 cm -1

 "C 1 class": ketones with a γ-carbon bent to a synclinal position and barriers of about 240 cm -1

 "acetone class": acetone-like ketones such as acetone [87], 1,1-difluoroacetone [131] and 1,1,1-trifluoroacetone [46] with barriers of about 250 cm -1

 "mesomeric class": α,β-unsaturated ketones sub-classified in ap conformers with barriers of about 430 cm -1 and sp conformers with barriers of about 350 cm -1 , while the ap conformer of 3-methyl-3-buten-2-one with a barrier value of 512 cm -1 needs its own sub-class, due to a branching at the α-positon, called the "branched mesomeric sub-class"

 "phenyl class": ketones with a phenyl ring and barriers from about 550 cm -1 to 630 cm -1 [32]  "tunnelling class": ketones exhibiting an additional tunnelling motion which strongly influences the internal rotation of the acetyl methyl group

The acetyl methyl group seems to "read" the electrostatic environment on the other side of the carbonyl group with the barrier value functioning as a reliable detector for structural aspects.

Steric effects only show a minor impact on the barrier and the range of the interactions ends at the δ-carbon position, with the barrier heights asymptotically reaching a plateau value.

Furthermore, it should be noted that precise calculations of the rotational constants were difficult to obtain for the ketones of the "C 1 class" (Chapter 11). The characteristic C 1 structure of this class is probably stabilised by weak hydrogen bonds, which might be the reason for deviations between the experimentally deduced and calculated rotational constants of up to 5%. [a] 6.554 2.148 1.927 [a] Rotational constants of conformer I obtained from the XIAM(1Top) fit, see Table 3.2. [a] 6.554 2.148 1.927 [a] Rotational constants of conformer I obtained from the XIAM(1Top) fit, see Table 3.2. [a] 8.336 1.795 1.534 [a] Rotational constants of conformer II obtained from the XIAM(1Top) fit, see Table 3.2. [a] 8.336 1.795 1.534 [a] Rotational constants of conformer II obtained from the XIAM(1Top) fit, see Table 3.2.

Basis Set Variation

Fourier Coefficients and Potential Energy Curves

Additional Fits

Table 13.7: Spectroscopic constants of conformer I of methyl propyl ketone in the rho axis system obtained with the BELGI-C 1 program [53] and spectroscopic constants of conformer II obtained with the BELGI-C s program [52].

Operator [a] Parameter [ P a , P b , P c are the components of the overall rotation angular momentum P, P α is the angular momentum of the internal rotor rotating around the internal rotor axis by an angle α. [b] The product of the parameter and operator from any given row yields the term used in the vibration-rotation-torsion Hamiltonian, except for F, ρ and A, which occur in the form F(P α -ρP a ) 2 +AP a 2 . [c] Fixed to a value obtained from a previous XIAM fit. [d] Total number of lines. [e] Number of the (00)/(10) torsional transitions, respectively. [f] Root-mean-square deviation of the fit.

Frequency Lists

Table 13.8: Observed frequencies υ obs of 174 rotational transitions of conformer II of methyl propyl ketone. 120 additional frequencies of the (01), ( 11) and ( 12) species are marked grey, with υ obs -υ cal referring to the respective BELGI-C s and XIAM(1Top) fit, as well as to the respective absolute and relative XIAM(2Tops) fit. Angles experimentally deduced from the XIAM(2Tops) fits, see Table 4.2. [b] Fixed due to symmetry. [c] Fixed in the XIAM(2Tops) fits to the values obtained from the MP2 calculations. [a] 7.511 1.041 0.941 [a] Rotational constants of conformer I obtained from the XIAM(1Top) fit, see Table 4 [a] 7.511 1.041 0.941 [a] Rotational constants of conformer I obtained from the XIAM(1Top) fit, see Table 4 [a] 5.865 1.244 1.153 [a] Rotational constants of conformer II obtained from the XIAM(1Top) fit, see Table 4 [a] 5.865 1.244 1.153 [a] Rotational constants of conformer II obtained from the XIAM(1Top) fit, see Table 4.2 Table 14.9: Rotational constants of conformer III of methyl butyl ketone calculated with the Gaussian09 package [62] at various levels of theory. ΔA, ΔB and ΔC are the deviations of the calculated values from the experimental ones. [a] 5.848 1.174 1.052 [a] Rotational constants of conformer III obtained from the XIAM(1Top) fit, see Table 4 [a] 5.848 1.174 1.052 [a] Rotational constants of conformer III obtained from the XIAM(1Top) fit, see Table 4.2

J' K

Method/Basis Set

Fourier Coefficients and Potential Energy Curves

+ ∑ b m sin (3mα) 5 m=1
) for the potential energy curves of the acetyl methyl group of the three assigned conformers of methyl butyl ketone calculated at the MP2/6-311++G(d,p) and B3LYP/6-311++G(d,p) level of theory.

Conformer

+ ∑ b m sin (3mα) 5 m=1
) for the potential energy curves of the butyl methyl group of the three assigned conformers of methyl butyl ketone calculated at the MP2/6-311++G(d,p) and B3LYP/6-311++G(d,p) level of theory. 311++G(d,p

Conformer I Conformer II MP2/6-

Additional Fits

Table 14.13: Molecular parameters in the rho axis system of the three assigned conformers of methyl butyl ketone. For conformer I, they were obtained with the BELGI-C s program [52]. For conformer II and III the BELGI-C 1 code [53] was used.

Operator [a] Parameter P a , P b , P c are the components of the overall rotation angular momentum P, P α is the angular momentum of the internal rotor rotating around the internal rotor axis by an angle α. [b] The product of the parameter and operator from any given row yields the term used in the vibration-rotation-torsion Hamiltonian, except for F, ρ and A, which occur in the form F(P α -ρP a ) 2 +AP a 2 . [c] Fixed to a value obtained from the XIAM(1Top) fit, see Table 4.2.

[d]

Total number of lines. [e] Number of the (00)/(10) torsional transitions, respectively. [f] Root-mean-square deviation of the fit. 01), ( 11) and ( 12) species are marked grey, with υ obs -υ cal referring to the respective BELGI-C s and XIAM(1Top) fit, as well as to the respective absolute and relative XIAM(2Tops) fit.

Frequency Lists

J'

Basis Set Variation

Table 15.2: Rotational constants of conformer I of heptan-2-one calculated at different levels of theory using the Gaussian09 package [62], as well as their relative deviations from the respective experimentally deduced values. [a] 6.964 0.650 0.608 [a] Rotational constants of conformer I obtained from the XIAM(1Top) fit, see Table 5.2.

Method/Basis

Table 15.3:

Rotational constants of conformer I of heptan-2-one calculated at different levels of theory using the Gaussian16 package [63], as well as their relative deviations from the respective experimentally deduced values. [a] 6.964 0.650 0.608 [a] Rotational constants of conformer I obtained from the XIAM(1Top) fit, see Table 5.2.

Method/Basis

Table 15.4:

Rotational constants of conformer II of heptan-2-one calculated at different levels of theory using the Gaussian09 package [62], as well as their relative deviations from the respective experimentally deduced values. [a] 4.465 0.808 0.766 [a] Rotational constants of conformer II obtained from the XIAM(1Top) fit, see Table 5.2.

Method/Basis

Table 15.5: Rotational constants of conformer II of heptan-2-one calculated at different levels of theory using the Gaussian16 package [63], as well as their relative deviations from the respective experimentally deduced values. [a] 4.465 0.808 0.766 [a] Rotational constants of conformer II obtained from the XIAM(1Top) fit, see Table 5.2.

Method/Basis

Fourier Coefficients and Potential Energy Curves

Table 15.6: Fourier coefficients (in Hartree) of the acetyl methyl group and the pentyl methyl group of the two assigned conformers of heptan-2-one calculated at the MP2/6-311++G(d,p) and B3LYP/6-311++G(d,p) level of theory. The potential was expanded in a one-dimensional Fourier expansion as V(α) = a 0 + ∑ a n cos (3nα) [52] and BELGI-C 1 [53] code, respectively. All parameters refer to the rho axis system.

Operator [a] Parameter [ P a , P b , P c are the components of the overall rotation angular momentum P, P α is the angular momentum of the internal rotor rotating around the internal rotor axis by an angle α. [b] The product of the parameter and operator from any given row yields the term used in the vibration-rotation-torsion Hamiltonian, except for F, ρ and A, which occur in the form F(P α -ρP a ) 2 +AP a 2 . [c] Fixed to a value obtained from the XIAM(1Top) fit. [d] Total number of lines. [e] Number of the respective torsional species. [f] Root-mean-square deviation of the fit. 4.184 0.528 0.508 [a] Rotational constants of the C 1 conformer obtained from the XIAM(1Top) fit, see Table 6.2. 4.184 0.528 0.508 [a] Rotational constants of the C 1 conformer obtained from the XIAM(1Top) fit, see Table 6.2. 6.308 0.438 0.417 [a] Rotational constants of the C s conformer obtained from the XIAM(1Top) fit, see Table 6.2. 6.308 0.438 0.417 [a] Rotational constants of the C s conformer obtained from the XIAM(1Top) fit, see Table 6.2.

Frequency Lists

Fourier Coefficients and Potential Energy Curves

Additional Fits

Table 16.7: Molecular parameters in the rho axis system of the two assigned conformers of octan-2-one deduced with the BELGI-C 1 [53] and BELGI-C s [52] code, respectively.

Operator [a] Parameter P a , P b , P c are the components of the overall rotation angular momentum P, P α is the angular momentum of the internal rotor rotating around the internal rotor axis by an angle α. [b] The product of the parameter and operator from any given row yields the term used in the vibration-rotation-torsion Hamiltonian, except for F, ρ and A, which occur in the form F(P α -ρP a ) 2 +AP a 2 . [c] Fixed to a value obtained from the XIAM(1Top) fit. [d] Total line number. [e] Line number of the respective species. [f] Root-mean-square deviation of the fit. [a] 8.369 1.914 1.589 [a] Rotational constants of the ap conformer obtained from the 2Tops fit, see Table 7.4. [a] 8.369 1.914 1.589 [a] Rotational constants of the ap conformer obtained from the 2Tops fit, see Table 7.4 [a] 9.158 1.862 1.578 [a] Rotational constants of the sp conformer obtained from the 2Tops fit, see Table 7.4

Frequency Lists

Table 17.5: Rotational constants of the sp conformer of 3-penten-2-one calculated with the Gaussian16 package [63] at different levels of theory. ΔA, ΔB and ΔC are the deviations of calculated values from the experimental ones. [a] 9.158 1.862 1.578 [a] Rotational constants of the sp conformer obtained from the 2Tops fit, see Table 7.4

Method/Basis

Fourier Coefficients

Table 17.6: Fourier coefficients (in Hartree) of the acetyl methyl group and the propenyl methyl group of the two assigned conformers of 3-penten-2-one calculated at different levels of theory. The potential was expanded in a one-dimensional Fourier expansion as V(α) = a 0 + ∑ a n cos (3nα) The potential was expanded in an one-dimensional Fourier expansion as V(α) = a 0 + ∑ a n cos (3nα)

5 n=1
+ ∑ b m sin (3mα) m=1

.

Acetyl Methyl Group Conformer I [a] Conformer II [b] Conformer III [a] Referring to the interpolated Fourier expansion of conformer I by neglecting conformer II, see Section 9.1.2.1.

[b]

The potential energy curve of conformer II was not obtainable, due to the "conformer switch problem", see Section 9.1.2.1.

(1. 2 )

 2 However, choosing the right Hamiltonian operator H and finding solutions for the equation follows different approaches for different molecules. Based on the symmetry of the molecule, diverse cases can be distinguished, such as: I a = I b = I c : spherical top I a < I b = I c : prolate symmetric top I a = I b < I c : oblate symmetric top I a < I b < I c : asymmetric top With I a , I b , I c being the principal moments of inertia in a principal axis system referring to the principal axes a, b and c. For n atoms i with the respective mass m i , they are defined as: I a = ∑ m i (b 2 + c 2 )

  Considering the inertia ellipsoids of the asymmetric molecule leads to special selection rules, which are dependent on the respective dipole moment component of the molecule, and a differentiation in three branches (a-, b-, c-type) can be made. The selection rules of a transition J' K' a K' c ← J K a K c are: ΔJ = 0, ±1 a-type: μ a ≠ 0 ΔK a = 0, ±2, ... ΔK c = ±1, ±3, ... b-type: μ b ≠ 0 ΔK a = ±1, ±3, ... ΔK c = ±1, ±3, ... c-type: μ c ≠ 0 ΔK a = ±1, ±3, ... ΔK c = 0, ±2, ...

2 +H

 2 Z ab (P a P b + P b P a ) + Z bc (P b P c + P c P b ) + Z ac (P a P c + P c P a ) RT = -2Q a P a P α -2Q b P b P α -2Q c P c P α (1.45)

Figure 1

 1 Figure 1.2.

Figure 1 . 3 :

 13 Figure 1.3: Schematic depiction of a rotational transition and the splittings of the rotational energy levels caused by inversion tunnelling and internal rotation effects, respectively.

Figure 2 . 1 :

 21 Figure 2.1: General procedure of a microwave spectroscopic analysis.

  converted twice: First, to an intermediate frequency (IF) of 160 MHz + δ; second, to an IF of 2.5 MHz + δ. Finally, the signal is send to an A/D (analog/digital) converter and the data is Fourier transformed (FT) into a spectrum. Specific details on sample preparation and operation modes are given in the respective molecule chapters (Chapter 3 to Chapter 9).

( 2 . 3 )ε = |λ y | λ x √λ x 2 + λ y 2 ( 2 . 4 )

 23224 cos δ = cos ∡(i,z) = λ z cos Detailed information and the code of the program are given on the PROSPE (Programs for ROtational SPEctroscopy) website [79].

Figure 1 :

 1 Figure 1: Molecules of the methyl n-alkyl ketones series investigated in this dissertation. The carbon atoms of the alkyl chain are numbered with Greek letters as shown for octan-2-one.

Figure 3 . 1 :

 31 Figure 3.1: Atom numbering of methyl propyl ketone in a C s reference configuration. The hydrogen atoms are in white, the carbon atoms in grey, and the oxygen atom is in red (Ref. [1], figure modified for consistent formatting).

Figure 3 . 2 :

 32 Figure 3.2: Geometries of the four conformers of methyl propyl ketone calculated at the MP2/6-311++G(d,p) level of theory. Left hand side: view on the C-(C=O)-C plane. Right hand side: view along the O=C bond. The relative energies refer to the absolute energy of conformer I with E = -271.047861 Hartree (Ref. [1], figure modified for consistent formatting).

Figure 3 . 3 :

 33 Figure 3.3: Upper figure: Potential energy curve of the acetyl methyl group of conformer I of methyl propyl ketone obtained by varying the dihedral angle α 1 = ∡(H 2 ,C 1 ,C 5 ,C 7 ) with a step width of 10° and parametrising the resulting energies with a Fourier expansion. The energies are calculated at the MP2/6-311++G(d,p) and B3LYP/6-311++G(d,p) levels of theory and are given relative to that of the lowest energy conformations. Lower figure: Deviation of the dihedral angle θ 1 = ∡(C 1 ,C 5 ,C 7 ,C 10 ) depending on the position of the acetyl methyl group. Δθ 1 is given relative to values of θ 1 = 161.4° (MP2) and 165.9° (B3LYP) (Ref. [1], figure modified for consistent formatting).

Figure 3 . 4 :

 34 Figure 3.4: Upper figure: Potential energy curve of the acetyl methyl group of conformer II of methyl propyl ketone obtained by varying the dihedral angle α 1 = ∡(H 2 ,C 1 ,C 5 ,C 7 ) with a step width of 10° and parametrising the resulting energies with a Fourier expansion. The energies are calculated at the MP2/6-311++G(d,p) and B3LYP/6-311++G(d,p) levels of theory and are given relative to that of the lowest energy conformations. Inset: The double minimum located between α 1 = 40° and 80° is depicted in an enlarged scale, where α 1 was varied in a step width of 1°. Lower figure: Deviation of the dihedral angle θ 1 = ∡(C 1 ,C 5 ,C 7 ,C 10 ) depending on the position of the acetyl methyl group. Δθ 1 is given relative to values of θ 1 = 170.1°(MP2) and 174.0° (B3LYP) (Ref. [1], figure modified for consistent formatting).

Figure 3 .

 3 5 and Figure 3.6 illustrate a typical spectrum of the 4 13 ← 3 12 rotational transition of conformer II. Some transitions exhibit further additional splittings, which might be caused by spin-spin or spinrotation coupling of the hydrogen atoms. All of these effects result in significant enlargement of the line widths. The average line width is 45 kHz (fwhh), but the variation for individual lines is large. Consequently, the measurement accuracy of the line position is only approximately 7-8 kHz for some lines, while other lines have a much better accuracy. For the whole data set, we use a measurement accuracy of 4.5 kHz, which corresponds to 1/10 of the average line width.

Figure 3 . 5 :

 35 Figure 3.5: High resolution measurement of the (00) species of the 4 13 ← 3 12 transition of conformer II found at 13826.9668 MHz. The splitting indicated by the brackets is caused by the Doppler effect. The splitting in (00) and (10) species is not resolvable (Ref.[START_REF] Andresen | [END_REF], figure modified for consistent formatting).

Figure 3 . 6 :

 36 Figure 3.6: High resolution measurement of the (10) (13795.5167 MHz), (11) (13795.5239 MHz), and (12) (13795.5082 MHz) species of the 4 13 ← 3 12 transition of conformer II. The splittings indicated by the brackets are caused by the Doppler effect (Ref. [1], figure modified for consistent formatting).

Figure 4 . 1 :

 41 Figure 4.1: Atom numbering of methyl butyl ketone. The hydrogen atoms are colour coded in white, the carbon atoms in grey and the oxygen atom in red (Ref. [2], figure modified for consistent formatting).

Figure 4 . 2 :

 42 Figure 4.2: Geometries of the three energetically most favourable conformers of methyl butyl ketone optimised at the B3LYP/6-311++G(d,p) level of theory. Left hand side: view on the C-(C=O)-C plane. Right hand side: view along the O=C bond (Ref. [2], figure modified for consistent formatting).

Figure 4 . 3 )

 43 Figure 4.3). The MP2 and B3LYP methods yield quite different barrier heights of 230.1 cm -1 and 168.7 cm -1 , respectively.

Figure 4 . 3 :

 43 Figure 4.3: Upper trace: Potential energy curve calculated at the MP2/6-311++G(d,p) and B3LYP/6-311++G(d,p) levels of theory obtained by rotating the acetyl methyl group of conformer II of methyl butyl ketone. The energies are given relative to the lowest energy conformations. Lower trace: Oscillation of the butyl group visualised by changes in the dihedral angle θ 1 = ∡(C 1 ,C 5 ,C 7 ,C 10 ) relative to the values θ 1 = 161.2° (MP2) and θ 1 = 166.2° (B3LYP) of the fully optimised structures (Ref. [2], figure modified for consistent formatting).

Figure 4 . 4 and

 44 Figure 4.4 and Figure 4.5 depict the potential energy curves obtained for conformer I and III, all of which show three double minima. These double minima are also caused by the coupling between the motions of the whole butyl chain and the acetyl methyl group. To look closer at the minima, the dihedral angle α 1 = ∡(H 2 ,C 1 ,C 5 ,C 7 ) was varied in finer steps of 1° in the range

Figure 4 . 4 :

 44 Figure 4.4: Upper trace: Potential energy curve calculated at the MP2/6-311++G(d,p) and B3LYP/6-311++G(d,p) levels of theory obtained by rotating the acetyl methyl group of conformer I of methyl butyl ketone. The energies are given relative to the lowest energy conformations. Inset: Enlarged scale for the region between α 1 = 40° and 80°. Lower trace: Oscillation of the butyl group visualised by changes in the dihedral angle θ 1 = ∡(C 1 ,C 5 ,C 7 ,C 10 ) relative to the values θ 1 = 169.4° (MP2) and θ 1 = 174.5° (B3LYP) of the fully optimised structures (Ref. [2], figure modified for consistent formatting).

Figure 4 . 5 :

 45 Figure 4.5: Upper trace: Potential energy curve calculated at the MP2/6-311++G(d,p) and B3LYP/6-311++G(d,p) levels of theory obtained by rotating the acetyl methyl group of conformer III of methyl butyl ketone. The energies are given relative to the lowest energy conformations. Inset: Enlarged scale for the region between α 1 = 40° and 80°. Lower trace: Oscillation of the butyl group visualised by changes in the dihedral angle θ 1 = ∡(C 1 ,C 5 ,C 7 ,C 10 ) relative to the values θ 1 =171.1° (MP2) and θ 1 = 173.1°(B3LYP) of the fully optimised structures (Ref. [2], figure modified for consistent formatting).

Figure 4 .

 4 Figure 4.5). It is difficult to decide which geometry corresponds to the real global energy minimum, because the results calculated with the MP2 and B3LYP methods are

Figure 4 . 6 :

 46 Figure 4.6: A high resolution measurement of the 5 14 ← 4 13 transition of conformer I. The (10), (11), and (12) species are found at 10122.2444 MHz, 10122.2530 MHz and 10122.2353 MHz, respectively. The splittings indicated by the brackets are caused by the Doppler effect (Ref. [2], figure modified for consistent formatting).

Figure 4 . 7 :

 47 Figure 4.7: A high resolution measurement of the 5 14 ← 4 13 transition of conformer I. The (00) species is found at 10154.5331 MHz, while the splitting in the (00) and (01) species is not resolvable. The splitting indicated by the bracket is caused by the Doppler effect (Ref. [2], figure modified for consistent formatting).

13 C

 13 isotopologues. There are five major results: (i) Three conformers of MBK can be identified in the jet-cooled microwave spectrum. (ii) Conformer I possesses a straight butyl chain. (iii) Conformer II shows a C 1 structure with the γ-carbon of the butyl group bent to a nearly synclinal position. (iv) In conformer III, the methyl group at the end of the butyl chain is bent to a synclinal position. (v) The barrier heights of the acetyl methyl group deduced from the torsional splittings in the spectrum are 186.9198(50) cm -1 , 233.5913(97) cm -1 , and 182.2481(

  because they are quite different for the two conformers (∡(i 1 ,a) = 44.78°, ∡(i 1 ,b) = 45.54° and ∡(i 1 ,c) = 85.78° in the case of conformer III and ∡(i 1 ,a) = 155.92°, ∡(i 1 ,b) = 100.18° and ∡(i 1 ,c) = 68.42° for conformer II).

Figure 4 . 8 .

 48 The first class comprises molecules with a C 1 structure similar to that of conformer II of MBK, where the γ-carbon of the alkyl chain is tilted out of the C-(C=O)-C plane to a nearly synclinal position (called the "C 1 class"). The torsional barrier of the acetyl methyl group is always Hexan-2-one -54 -around 240 cm -1 . Examples of this class are conformer II of MBK (233.5913(97) cm -1 ), the C 1 conformer of methyl propyl ketone (238.145(21) cm -1 ) [1], allyl acetone (224.95(

Figure 4 . 8 :

 48 Figure 4.8: Experimental torsional barriers of the acetyl methyl group in different ketones: (1) methyl propyl ketone [1], (2) MBK (this chapter), (3) allyl acetone[31], (4) methyl isobutyl ketone[26], (5) methyl ethyl ketone[91], and (6) methyl neopentyl ketone[27] (Ref.[2], figure modified for consistent formatting).

Figure 4 . 5 ,

 45 Figure 4.5, there are double minimum potentials similar to those in the curves of conformer I in Figure 4.4 (see Section 4.1.3.1). This kind of double minimum potentials has been reported

Maike Andresen ,

 Andresen Isabelle Kleiner, Martin Schwell, Wolfgang Stahl, Ha Vinh Lam Nguyen Microwave Spectrum and Internal Rotations of Heptan-2-one: A Pheromone in the Gas Phase J. Phys. Chem. A 2020, 124, 1353-1361

Figure 5 . 1 :

 51 Figure 5.1: Atom numbering of heptan-2-one. The hydrogen atoms are white, the carbon atoms are grey, and the oxygen atom is red (Ref. [3], figure modified for consistent formatting).

Figure 5 . 2 :

 52 Figure 5.2: Geometries of the two assigned conformers of heptan-2-one optimised at the B3LYP/6-311++G(d,p) level of theory. Left hand side: view on the C-(C=O)-C plane. Right hand side: view along the O=C bond (Ref. [3], figure modified for consistent formatting).

trace of Figure 5 . 4 )

 54 , which indicates a certain degree of flexibility of the alkyl chain about the C 5 -C 7 bond. The barriers to internal rotation predicted at the MP2 and B3LYP level are 228.3 cm -1 and 162.7 cm -1 , respectively.

Figure 5 . 3 :

 53 Figure 5.3: Upper trace: Potential energy curves obtained by rotating the acetyl methyl group of conformer I of heptan-2-one. The energies are calculated at the MP2/6-311++G(d,p) and B3LYP/6-311++G(d,p) level of theory and given relative to the lowest energy conformations with E = -349.438905 and -350.515894 Hartree, respectively. Inset: The double minimum between α 1 = 40° and 80° depicted at an enlarged scale. Lower trace: Oscillation of the entire pentyl group upon the rotation of the acetyl methyl group. The deviations of the dihedral angle θ 1 = ∡(C 1 ,C 5 ,C 7 ,C 10 ) are given relative to the values θ 1 = 169.4° (MP2) and θ 1 = 174.9° (B3LYP) of the fully optimised geometries (Ref. [3], figure modified for consistent formatting).

Figure 5 . 4 :

 54 Figure 5.4: Upper trace: Potential energy curves obtained by rotating the acetyl methyl group of conformer II of heptan-2-one. The energies are calculated at the MP2/6-311++G(d,p) and B3LYP/6-311++G(d,p) level of theory and given relative to the lowest energy conformations with E = -349.439836 and -350.515618 Hartree, respectively. Lower trace: Oscillation of the entire pentyl group upon the rotation of the acetyl methyl group. The deviations of the dihedral angle θ 1 = ∡(C 1 ,C 5 ,C 7 ,C 10 ) are given relative to the values θ 1 = 161.5°(MP2) and θ 1 = 165.9° (B3LYP) of the fully optimised geometries (Ref. [3], figure modified for consistent formatting).

Figure 5 . 5 :

 55 Figure 5.5: Two typical high resolution measurements of the 4 22 ← 3 13 transition of conformer II of heptan-2-one. The frequencies are in MHz. The (00), (10), (11), and (12) species are found at 17470.9960 MHz, 17670.3342 MHz, 17670.2907 MHz, and 17670.3867 MHz, respectively. The splitting between the (00) and (01) species is not resolvable. The brackets indicate the Doppler doublets (Ref. [3], figure modified for consistent formatting).

  [c] For conformer I, the internal rotation parameters of the second rotor are fixed to F 0,2 = 158.0 GHz, ∡(i 2 ,a) = 150.52°, ∡(i 2 ,b) = 119.48°, and ∡(i 2 ,c) = 90.00°. [d] For conformer II, they are F 0,2 = 158.0 GHz, ∡(i 2 ,a) = 128.17°, ∡(i 2 ,b) = 128.59°, and ∡(i 2 ,c) = 118.60°. [e] Total number of lines. [f] Number of the respective torsional species. [g] Root-mean-square deviation of the fit.

Maike Andresen ,

 Andresen Damian Schöngen, Isabelle Kleiner, Martin Schwell, Wolfgang Stahl, Ha Vinh Lam Nguyen Internal Rotation of the Acetyl Methyl Group in Methyl Alkyl Ketones: The Microwave Spectrum of Octan-2-one ChemPhysChem 2020, 21, 2206-2216

Figure 6 . 1 :

 61 Figure 6.1: Atom numbering of octan-2-one. The hydrogen atoms are white, carbon atoms grey, and the oxygen atom is red. The carbon atom position of the hexyl chain is labelled with Greek letters (see Section 6.4.) (Ref. [4], figure modified for consistent formatting).

Figure 6 . 2 :

 62 Figure 6.2: Geometries of the two conformers of octan-2-one optimised at the MP2/6-311++G(d,p) level of theory. Left hand side: View on the C-(C=O)-C plane. Right hand side: View along the O=C bond (Ref. [4], figure modified for consistent formatting).

Figure 6 . 3 :

 63 Figure 6.3: Upper diagram: Potential energy curves of the acetyl methyl rotation of the C 1 conformer of octan-2-one obtained by varying the dihedral angle α 1 in a step width of 10°. The energies are calculated at different levels of theory and given relative to the lowest energy conformation. Lower diagram: Changes of the dihedral angle θ 1 upon the rotation of the acetyl methyl group. The values are given relative to 161.6° (MP2) and 165.9° (B3LYP) (Ref. [4], figure modified for consistent formatting).

Figure 6 . 4 :

 64 Figure 6.4: Upper diagram: Potential energy curves of the acetyl methyl rotation of the C s conformer of octan-2-one obtained by varying the dihedral angle α 1 in a step width of 10°. The energies are calculated at different levels of theory and given relative to the lowest energy conformation. Inset: The double minimum between α 1 = 40° and 80°, where α 1 was varied in a step width of 1°, is depicted in an enlarged scale. Lower diagram: Changes of the dihedral angle θ 1 upon the rotation of the acetyl methyl group. The values are given relative to 169.3° (MP2) and 174.9° (B3LYP) (Ref. [4], figure modified for consistent formatting).

Figure 6 . 5 :

 65 Figure 6.5: Typical high resolution measurements of the 7 26 ← 6 15 transition of the C 1 conformer of octan-2-one. The frequencies are given in MHz showing the (00), (10), (11), and (12) species at 18049.6607 MHz, 18188.4716 MHz, 18188.4181 MHz, and 18188.5113 MHz, respectively. The splitting between the (00) and (01) species is not resolved. The brackets indicate splittings caused by the Doppler effect (Ref. [4], figure modified for consistent formatting).

  ) transitions were fitted with the program XIAM, yielding an rms deviation of 3.8 kHz and a V 3 potential of 185.1442(79) cm -1 . The respective values obtained with the program BELGI are 3.5 kHz and 185.126(

Figure 6 . 6 :

 66 Figure 6.6: Conformational structures of ketones in the "C s " and "C 1 class", as well as their respective barrier to internal rotation of the acetyl methyl group (rounded to an accuracy of 1 cm -1 ): (1) butan-2-one [91], (2) pentan-2-one [1], (3) hexan-2-one [2], (4) heptan-2-one [3],(5) octan-2-one (this chapter), (6) methyl neopentyl ketone[27],(7) cat ketone[123], (8) allyl acetone[31], and (9) methyl isobutyl ketone[26] (Ref.[4], figure modified for consistent formatting).

Figure 2 :

 2 Figure 2: The derivatives of methyl vinyl ketone investigated in this dissertation.

Figure 7 . 1 :

 71 Figure 7.1: The two conformers of 3-penten-2-one as calculated at the MP2/6-311++G(d,p) level of theory. The atoms are labelled. Hydrogens are colour-coded white, carbons grey and oxygens red

Figure 7 . 2 :

 72 Figure 7.2: Potential energy curve calculated at the MP2/6-311++G(d,p) level of theory by rotating the acetyl methyl group of the antiperiplanar (ap) and synperiplanar (sp) conformer of 3-penten-2-one, respectively. The energies are given relative to the respective lowest energy conformation with E = -269.832894 Hartree and E = -269.832273 Hartree.

Figure 7 . 3 :

 73 Figure 7.3: Potential energy curve calculated at the MP2/6-311++G(d,p) level of theory by rotating the propenyl methyl group of the antiperiplanar (ap) and synperiplanar (sp) conformer of 3-penten-2-one, respectively. The energies are given relative to the respective lowest energy conformation with E = -269.832894 Hartree and E = -269.832273 Hartree.

  was fixed in a step width of 10° (for atom numbering see Figure7.1), while a range of 120° was sufficient due to the symmetry of the methyl group. All other geometry parameters were optimised at the MP2/6-311++G(d,p) level of theory and the resulting energies were parametrised with a one-dimensional Fourier expansion. The potential energy curves of both conformers are depicted in Figure7.2. For the internal rotation of the propenyl methyl group the same procedure was applied to the dihedral angle α 2 = ∡(C 7 ,C 9 ,C 11 ,H 12 ) with the respective potential energy curves being illustrated in Figure7.3.

Figure 7 . 4 :

 74 Figure 7.4: A typical high resolution measurement of the 4 13 ← 3 12 transition of the antiperiplanar (ap) conformer of 3-penten-2-one. The frequencies are given in MHz, with the (00), (01), (10), (11) and (12) species found at 14637.1844 MHz, 14637.1719 MHz, 14636.8355 MHz, 14636.8291 MHz and 14636.8172 MHz, respectively. The splittings indicated with the brackets are caused by the Doppler effect.

Figure 7 . 5 :

 75 Figure 7.5: Ketones of the "mesomeric class" and the respective barrier height of the acetyl methyl group: (1) methyl vinyl ketone [30], (2) 3-penten-2-one (this chapter), (3) acetyl isocyanate[155], (4) α-ionone[111] and (5) β-ionone[111]. For ionone multiple barrier values are given referring to different conformations of the ring, see Ref.[111].

Figure 8 . 1 :

 81 Figure 8.1: The two conformers of 3-methyl-3-buten-2-one, as calculated at the MP2/6-311++G(d,p) level of theory. Left hand side: view on the C-(C=O)-C plane. Right hand side: view along the C 5 -C 7 bond. The atoms are labelled and hydrogens are colour-coded white, carbons grey and oxygens red.

  2 and Figure 8.3. In addition, the coupling of the acetyl methyl and the propenyl methyl group forces the double bond of the isopropenyl group to bend out of the C-(C=O)-C plane by about ±40° as visualised in the lower traces of Figure 8.2 and Figure 8.3. The internal rotation motions in

Figure 8 . 2 :Figure 8 . 3 :

 8283 Figure 8.2: Upper diagram: Potential energy curve determined by rotating the acetyl methyl group of the synperiplanar (sp) conformer of 3-methyl-3-buten-2-one. The energies are calculated at the MP2/6-311++G(d,p) level of theory and given relative to the lowest energy conformation with E = -269.830195 Hartree. Middle diagram: Data points visualising the changes of the isopropenyl methyl group upon the rotation of the acetyl methyl group. The angles are given relative to the value α 2 = 60°. Lower diagram: Data points visualising the changes of the dihedral angle φ = ∡(O 6 ,C 5 ,C 7 ,C 9 ) upon the rotation of the acetyl methyl group. The angles are given relative to the value φ = 0°

Figure 8 . 4 :

 84 Figure 8.4: Potential energy curve determined by rotating the acetyl methyl group of the antiperiplanar (ap) conformer of 3-methyl-3buten-2-one. The energies are calculated at the MP2/6-311++G(d,p) level of theory and given relative to the lowest energy conformation with E = -269.833361 Hartree.

Figure 8 . 5 :

 85 Figure 8.5: Potential energy curve determined by rotating the isopropenyl methyl group of the antiperiplanar (ap) conformer of 3-methyl-3buten-2-one. The energies are calculated at the MP2/6-311++G(d,p) level of theory and given relative to the lowest energy conformation with E = -269.833361 Hartree.

  than a few kHz. Complicated splitting patterns are visible in the spectrum and in some cases the splittings are not resolvable at all. An example high resolution measurement of the 4 22 ← 3 21 transition of the ap conformer is given in Figure 8.6.

Figure 8 . 6 :

 86 Figure 8.6: A typical high resolution measurement of the 4 22 ← 3 21 transition of the antiperiplanar (ap) conformer of 3-methyl-3-buten-2-one. The frequencies are given in MHz, with the (00), (01), (10), (11) and (12) species found at 24168.4958 MHz, 24168.3857 MHz, 24168.2949 MHz, 24168.1921 MHz and 24168.1783 MHz, respectively. The brackets indicate the Doppler doublets.

Figure 3 :

 3 Figure 3: Structure of 3-methylbutan-2-one, also called methyl isopropyl ketone.

Figure 9 . 1 :

 91 Figure 9.1: The three conformers of 3-methylbutan-2-one calculated at the MP2/6-311++G(d,p) level of theory. Left hand side: view on the C-(C=O)-C plane. Right hand side: view along the C 5 -C 7 bond. The atoms are labelled and hydrogens are colour-coded white, carbons grey and oxygens red.

  II a and II b . Depending on the initial structure, scan calculations yield slightly different results. Starting the scan calculation with conformer I a (see minimum at α 1 = 167.9° and green triangles in Figure 9.2), the minima refer to I a → I b → II b → I b → II b → I b → II b , ending with the II b and not the I a structure. If the scan is started with conformer II a (see minimum at α 1 = 327.2° and red dots in Figure 9.2) the sequence is II a → I a → I b → II b → I b → II b → I b ending with I b and not II a .

Figure 9 . 2 :

 92 Figure 9.2: Upper diagram: Potential energy of the acetyl methyl torsion calculated at the MP2/6-311++G(d,p) level of theory by rotating the dihedral angle α 1 = ∡(H 2 ,C 1 ,C 5 ,C 7 ) in a step width of 10°. The energy points calculated by starting the scan calculations with conformer I of 3methylbutan-2-one are marked with green triangles, those started with conformer II with red dots. All energies are given relative to the lowest energy conformation. Lower diagram: Change of the dihedral angle φ = ∡(O 6 ,C 5 ,C 7 ,H 8 ) upon rotation of the acetyl methyl group. See text for further explanation.

Figure 9 . 3 :

 93 Figure 9.3: Same diagram as Figure 9.2. The black line and black data points indicate the potential energy curve of conformer I of 3-methylbutan-2-one, interpolated by excluding data points referring to a conformer II configuration (pink data points). See text for further explanation.

Figure 9 . 4 :

 94 Figure 9.4: Upper diagram: Potential energy curve of the acetyl methyl group calculated at the MP2/6-311++G(d,p) level of theory by rotating the dihedral angle α 1 = ∡(H 2 ,C 1 ,C 5 ,C 7 ) in a step width of 10°. The energies of conformer III of 3-methylbutan-2-one are given relative to the lowest energy conformation. Lower diagram: Change of the dihedral angle φ = ∡(O 6 ,C 5 ,C 7 ,H 8 ) upon rotation of the acetyl methyl group. See text for further explanation.

Figure 9 . 5 :

 95 Figure 9.5: Potential energy curve of the first isopropyl methyl group calculated at the MP2/6-311++G(d,p) level of theory by rotating the dihedral angle α 2 = ∡(C 5 ,C 7 ,C 9 ,H 10 ) in a step width of 10°. The energies of conformer I, conformer II and conformer III of 3-methylbutan-2-one are given relative to the lowest energy conformation, respectively.

Figure 9 . 6 :

 96 Figure 9.6: Potential energy curve of the second isopropyl methyl group calculated at the MP2/6-311++G(d,p) level of theory by rotating the dihedral angle α 3 = ∡(C 5 ,C 7 ,C 13 ,H 14 ) in a step width of 10°. The energies of conformer I, conformer II and conformer III of 3-methylbutan-2-one are given relative to the lowest energy conformation, respectively.

Figure 9 . 7 :

 97 Figure 9.7: Survey spectrum of 3-methylbutan-2-one recorded in the frequency range from 8 to 16 GHz.

  specific selection rules are depending on the dipole moment components μ a , μ b and μ c , especially whether or not their signs change during the tunnelling. If the sign of the dipole moment component stays the same, the selection rules are (+) ↔ (+) and (-) ↔ (-). The frequencies should be the same as those predicted with a rigid-rotor model. If however the sign of the dipole moment component changes, the selection rules are (+) ↔ (-) and (-) ↔ (+) and the splittings will be 2ΔE t , with ΔE t being the energy difference of the two sublevels. Further information is given in Section 1.5. In case of all three conformers of 3-methlbutan-2-one, |μ a | changes to -|μ a | meaning that the a-type transitions should show the large tunnel splittings. Unfortunately, ΔE t is unknown.

Figure 10 . 1 :

 101 Figure 10.1: Schematic depiction of the range of interactions between the internal rotation of the acetyl methyl group and the molecular structure on the other side of the carbonyl group in a ketone. The position where a characteristic structure element like a branching or a double bond, etc. might be present is marked with a *. R stands for any structural rest.

Figure 11 . 1 :

 111 Figure 11.1: The rotational constants A, B and C calculated at the MP2/6-311++G(d,p), B3LYP/6-311++G(d,p), B3LYP-D3BJ/6-311G(df,pd) and B3LYP-D3BJ/cc-pVDZ level of theory given as deviations from the experimental constants. The values are depicted for the unsaturated ketones (1) 3-methyl-3-buten-2-one (ap conformer), (2) 3-penten-2-one (ap conformer), and (3) penten-3-one (sp conformer), the C s conformers of (4) pentan-2-one, (5) hexan-2-one, (6) heptan-2-one and (7) octan-2one, as well as for (8) the C 1 -δ conformer of hexan-2-one and the C 1 -γ conformers of (9) pentan-2-one, (10) hexan-2-one, (11) heptan-2-one and (12) octan-2-one. See text for information.

  Chapter 5) and octan-2-one (Chapter 6), as well as of E-3-penten-2-one (Chapter 7), 3-methyl-3-buten-2-one (Chapter 8) and 3-methylbutan-2-one (Chapter 9) were recorded and thoroughly investigated using quantum chemical calculations. All molecules show splittings in multiple species in their respective spectrum due to the internal rotations of at least two methyl groups. This dissertation is especially focused on the barrier to internal rotation of the acetyl methyl group and how it connects to the structural aspects of the molecule.Two conformers could be identified in the microwave spectrum of each methyl n-alkyl ketone. The first conformer type with C 1 symmetry always shows a bent alkyl chain with the γ-carbon located in a synclinal position. For the second conformers, the symmetry seems to be C s and all heavy atoms should lie in one plane. Effectively, these conformers behaved like C s conformers in the microwave spectra. However, calculations showed that the entire alkyl chain is bent out of the C-(C=O)-C plane by approximately 10°, which was called a "pseudo-C s " structure. For the C 1 conformers the barriers to internal rotation of the acetyl methyl group are 238.192(22) cm -1 , 233.911(12) cm -1 , 233.418(32) cm -1 and 233.340(28) cm -1 for pentan-2-one, hexanon-2-one, heptan-2-one and octan-2-one, respectively. For the C s conformer, the respective barrier heights are 188.6959(59) cm -1 , 187.2303(49) cm -1 , 185.666(14) cm -1 and 185.3490(81) cm -1 . Only in the spectrum of hexan-2-one, a third conformer was assigned. This conformer exhibits the δ-carbon bent to a synclinal position, while the acetyl methyl torsional barrier is 182.2581(27) cm -1 .

Figure 13 . 1 :

 131 Figure 13.1: Potential energy curves of the propyl methyl group of conformer I and conformer II of methyl propyl ketone obtained by varying the dihedral angle α 2 = ∡(C 7 ,C 10 ,C 13 ,H 15 ) with a step width of 10° and parametrising the resulting energies with a Fourier expansion. The energies are calculated at the MP2/6-311++G(d,p) level of theory and are given relative to the lowest energy conformations of the respective conformer.

Figure 13 . 2 :

 132 Figure 13.2: Potential energy curves of the propyl methyl group of conformer I and conformer II of methyl propyl ketone obtained by varying the dihedral angle α 2 = ∡(C 7 ,C 10 ,C 13 ,H 15 ) with a step width of 10° and parametrising the resulting energies with a Fourier expansion. The energies are calculated at the B3LYP/6-311++G(d,p) level of theory and are given relative to the lowest energy conformations of the respective conformer.

Figure 15 . 1 :

 151 Figure 15.1: Potential energy curves obtained by rotating the pentyl methyl group of conformer I of heptan-2-one. The energies are calculated at the MP2/6-311++G(d,p) and B3LYP/6-311++G(d,p) level of theory and given relative to the lowest energy conformations.

Figure 15 . 2 :Figure 15 . 3 :

 152153 Figure 15.2: Potential energy curves obtained by rotating the pentyl methyl group of conformer II of heptan-2-one. The energies are calculated at the MP2/6-311++G(d,p) and B3LYP/6-311++ G(d,p) level of theory and given relative to the lowest energy conformations.

Figure 16 . 1 :

 161 Figure 16.1: Potential energy curves of the hexyl methyl group rotation of the C 1 conformer of octan-2-one obtained by varying the dihedral angle α 2 in a step width of 10°. The energies are calculated at different levels of theory and given relative to the respective energy of the lowest energy conformation.

Figure 16 . 2 :

 162 Figure 16.2: Potential energy curves of the hexyl methyl group rotation of the C s conformer of octan-2-one obtained by varying the dihedral angle α 2 in a step width of 10°. The energies are calculated at different levels of theory and given relative to the respective energy of the lowest energy conformation.

  and parts of the publication are reproduced (adapted) with permission from ChemPhysChem 2019, 20, 2063-2073; Copyright 2019, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim. The measurements, quantum chemical calculations and spectral assignments, as well as the writing of the manuscript were mainly performed by Maike Andresen. Ha Vinh Lam Nguyen co-wrote the manuscript.

Isabelle Kleiner, Martin Schwell, Wolfgang Stahl and Ha Vinh Lam Nguyen discussed and corrected the contents of the manuscript. Chloé Quignot is thankfully acknowledged for the measurements, calculations and preliminary assignments she carried out during her research project at the Université Paris-Est Créteil to contribute to this work. Dr. Halima Mouhib is thanked for her help with the DFT-D3 calculations. Preliminary studies on this chapter's topic were performed within the Master thesis titled "Microwave Spectroscopic and Quantum Chemical Investigations on Methyl Alkyl Ketones" by Maike Andresen presented to the RWTH Aachen University.

Table 14 .

 14 2, Table 14.3 and Table 14.4 in the Appendix.

Table 4 . 1 :

 41 Relative energies with (E ZPE ) and without (E) zero-point corrections (in kJ mol -1 ), rotational constants (in GHz), dipole moment components (in Debye), and dihedral angles (in degree) of the eleven stable conformers of methyl butyl ketone calculated at the MP2/6-311++G(d,p) and B3LYP/6-311++G(d,p) level of theory. The assigned conformers are marked grey.

	MP2/6-311++G(d,p)

/ kJ mol -1

							a]
	A / GHz	6.915	6.983	6.964	4.217	4.433	4.465
	B / GHz	0.650	0.643	0.650	0.822	0.790	0.808
	C / GHz	0.608	0.602	0.608	0.784	0.755	0.766
	|μ a | / D	0.43	0.44		0.80	0.67
	|μ b | / D	3.19	2.81		2.05	2.04
	|μ c | / D	0.10	0.05		2.29	1.81
	θ 1 / °	169.4	-174.9		161.5	165.9
	θ 2 / °	178.8	-179.2		-70.3	-73.0
	θ 3 / °	179.7	179.8		179.0	-180.0
	θ 4 / °	179.9	-180.0		179.5	179.7
	E

Conformer I Conformer II BELGI-C 1 [b] XIAM(1Top) XIAM(2Tops) [c] BELGI-C s [b] XIAM(1Top) XIAM(2Tops) [d]

	A		GHz	6.95042(13)	6.9638384(29)	6.9638442(26)	4.40251(56)	4.4652469(10)	4.4652475(12)
	B		GHz	0.650203(39)	0.65009654(12)	0.65009790(12)	0.81073(15)	0.80820856(15)	0.80820880(18)
	C		GHz	0.6086448(25)	0.608408524(68)	0.608406889(69)	0.76739(24)	0.766226397(75)	0.766226085(87)
	Δ J		kHz	0.0142(02)	0.01363(30)	0.01336(29)		0.16654(22)	0.16655(25)
	Δ JK		kHz		0.2863(23)	0.2829(23)		-2.6595(21)	-2.6605(23)
	Δ K		kHz		4.301(36)	4.346(32)		28.047(24)	28.083(25)
	δ J		kHz		0.00087(11)	0.00070(11)		0.012423(62)	0.012438(73)
	δ K		kHz					0.943(17)	0.935(20)
	F 0,1 V 3,1		GHz cm -1	158.578(40) 185.275(11)	158.0(fixed) 185.469(16)	158.0(fixed) 185.666(14)	166.40(43) 229.14(16)	158.0(fixed) 233.380(28)	158.0(fixed) 233.418(32)
	∡(i 1 ,a)		°	34.551(15)	34.770(18)	34.820(15)	29.714(96)	29.739(37)	29.764(42)
	∡(i 1 ,b)		°	124.551(15)	124.770(18)	124.820(15)	97.514(56)	97.62(24)	97.78(27)
	∡(i 1 ,c)		°	90.00(fixed)	90.00(fixed)	90.00(fixed)	118.56(10)	118.55(11)	118.53(12)
	D pi2J,1		MHz		0.01728(23)	0.01774(22)		0.16066(41)	0.16085(46)
	D pi2K,1		MHz		-0.976(12)	-1.010(12)		-3.8902(78)	-3.8979(88)
	D pi2-,1 V 3,2 N [e]		MHz cm -1 -	285	0.003681(93) 285	0.003820(88) 982.22(86) 406	448	0.03973(17) 448	0.03958(20) 979.2(21) 545
	[f] N (01)/(11)/(12) N (00)/(10) σ rms [g]	[f]	--kHz	145/140 3.5	145/140 6.5	145/140 22/47/52 7.1	262/186 2.3	262/186 5.9	262/186 15/41/41 7.0
	[a]

  C 10 ,C 13 ,C 16 ), θ 4 = ∡(C 10 ,C 13 ,C 16 ,C 19 ), and θ 5 = ∡(C 13 ,C 16 ,C 19 ,C 22

Table 6 .1: Rotational

 6 constants, dipole moment components, optimised dihedral angles and relative energies without (E) and with zero-point (E ZPE ) corrections of the two assigned conformers of octan-2-one calculated at different levels of theory.

	Parameter	MP2	C 1 Conformer B3LYP	Exp. [a]	MP2	C s Conformer B3LYP	Exp. [a]
	A / GHz	3.962	4.147	4.184	6.261	6.332	6.308
	B / GHz	0.536	0.518	0.528	0.438	0.433	0.438
	C / GHz	0.517	0.500	0.508	0.417	0.412	0.417
	|μ a | / D	1.00	0.85		0.28	0.28
	|μ b | / D	2.05	2.01		3.28	3.28
	|μ c | / D	2.23	1.78		0.14	0.15
	θ 1 / °	161.6	165.9		169.3	174.9
	θ 2 / °	-70.2	-72.9		178.8	179.2
	θ 3 / °	178.9	179.7		179.7	-179.8
	θ 4 / °	179.4	179.7		179.8	180.0
	θ 5 / °	179.8	179.6		179.9	-179.9
	E

/ kJ mol -1

Table 7 . 1 :

 71 Rotational constants, dipole moment components, and optimised dihedral angle φ = ∡(O 6 ,C 5 ,C 7 ,C 9 ) of the antiperiplanar (ap) and synperiplanar (sp) conformer of 3-penten-2-one calculated at the MP2/6-311++G(d,p) level of theory.

		A / GHz	B / GHz	C / GHz	|μ a | / D	|μ b | / D	|μ c | / D	φ / °
	ap	8.328	1.910	1.584	3.47	2.90	0.00	180.0
	sp	9.070	1.857	1.571	1.80	3.01	0.00	0.0
	Exp. ap

a] E / Hartree E ZPE / Hartree E / kJ mol -1 E ZPE / kJ mol -1

		ap	sp	ap	sp	ap	sp	ap	sp
	MP2	-269.832894 -269.832273 -269.714657 -269.714356	0.00	1.63	0.00	0.79
	B3LYP	-270.639032 -270.639295 -270.521963 -270.522418	0.69	0.00	1.19	0.00
	B3PW91	-270.528391 -270.528689 -270.411131 -270.411609	0.78	0.00	1.25	0.00
	B3LYP-D3	-270.646706 -270.646682 -270.529477 -270.529745	0.00	0.06	0.70	0.00
	B3LYP-D3BJ -270.656589 -270.656383 -270.539441 -270.539470	0.00	0.54	0.08	0.00
	M06-2X	-270.503615 -270.503436 -270.385100 -270.385196	0.00	0.47	0.25	0.00

Table 7 . 3 :

 73 Barriers to internal rotation (in cm -1 ) of the acetyl methyl and the propenyl methyl group of the two conformers of 3-penten-2-one calculated at different levels of theory.

Method/Basis Set Antiperiplanar (ap) Conformer Synperiplanar (sp) Conformer Acetyl Group Propenyl Group Acetyl Group Propenyl Group

	MP2/6-311++G(d,p)	379.9	621.5	325.8	644.2
	B3LYP/6-311++G(d,p)	241.6	620.3	255.9	647.8
	B3PW91/6-311++G(d,p)	255.2	619.6	261.3	645.5
	B3LYP-D3/6-311++G(d,p)	302.7	614.8	280.7	644.0
	B3LYP-D3BJ/6-311++G(d,p)	282.2	618.8	270.1	647.5
	M06-2X/6-311++G(d,p)	431.1	619.5	325.1	648.5
	Exp.

Table 7 . 4 :

 74 Molecular parameters of the two assigned conformers of 3-penten-2-one obtained from the XIAM code. The fits differ by including the internal rotation of neither (0Top), either (1Top Acetyl or 1Top Propenyl), and both (2Tops) methyl groups of the molecule. Watson's A reduction and I r representation were used. All parameters refer to the principal axis system.

	Parameter	0 Top	Antiperiplanar (ap) Conformer 1 Top Acetyl 1 Top Propenyl	2 Tops	0 Top	Synperiplanar (sp) Conformer 1 Top Acetyl 1 Top Propenyl	2 Tops
	A / GHz		8.36881945(36)	8.36873666(25)	8.36863701(25)	8.36855439(16)	9.16024109(48)	9.15839633(88)	9.16004917(34)	9.15820427(56)
	B / GHz		1.914141708(77) 1.914108065(63) 1.914170024(60) 1.914136437(43) 1.86241765(16)	1.86239767(15)	1.86244624(12)	1.862426431(94)
	C / GHz		1.58862570(11)	1.588620400(80) 1.588596450(77) 1.588591079(54) 1.57825363(22)	1.57822604(18)	1.57822407(16)	1.57819645(11)
	Δ J / kHz		0.13255(74)	0.13226(56)	0.13282(52)	0.13212(36)	0.1282(12)	0.12686(90)	0.12843(85)	0.12783(56)
	Δ JK / kHz		1.9029(49)	1.8962(39)	1.8980(34)	1.8898(26)	1.813(12)	1.7015(86)	1.8016(84)	1.6903(53)
	Δ K / kHz		2.789(30)	2.805(22)	2.607(21)	2.642(14)	9.394(68)	8.207(65)	9.227(51)	8.070(43)
	δ J / kHz		0.02447(23)	0.02426(17)	0.02405(16)	0.02414(11)	0.02144(25)	0.02144(19)	0.02144(18)	0.02158(12)
	δ K / kHz		1.044(16)	1.020(12)	1.0430(11)	1.0245(75)	0.890(70)	0.842(58)	0.893(51)	0.851(37)
	F 0,1 / GHz V 3,1 / cm -1			158.0(fixed) 434.136(56)		158.0(fixed) 434.149(37)		158.0(fixed) 357.278(40)		158.0(fixed) 358.076(26)
	∡(i 1 ,a) / °			108.445(12)		108.4486(80)		141.732(28)		141.749(17)
	∡(i 1 ,b) / °			18.445(12)		18.4486(80)		128.268(28)		128.252(17)
	∡(i 1 ,c) / °			90.00(fixed)		90.00(fixed)		90.00(fixed)		90.00(fixed)
	D pi2-,1 / MHz		-0.0749(22)		-0.0741(15)		-0.0302(15)		-0.03052(95)
	D pi2K,1 / MHz						-0.644(30)		-0.635(19)
	F 0,2 / GHz V 3,2 / cm -1				158.0(fixed) 581.875(67)	158.0(fixed) 581.903(45)			158.0(fixed) 593.89(11)	158.0(fixed) 595.271(71)
	∡(i 2 ,a) / °				17.986(78)	17.951(53)			20.30(11)	20.152(69)
	∡(i 2 ,b) / °				107.986(78)	107.951(53)			110.30(11)	110.152(69)
	∡(i 2 ,c) / ° N [a]		97	200	90.00(fixed) 200	90.00(fixed) 505	72	159	90.00(fixed) 150	90.00(fixed) 410
	N (00)/(10)/(01) [c] N (11)/(12) σ [d]	[b]	97/0/0 0/0 2.6	97/103/0 0/0 2.7	97/0/103 0/0 2.6	97/103/103 99/103 2.7	72/0/0 0/0 2.6	72/87/0 0/0 2.8	72/0/78 0/0 2.7	72/87/78 86/87 2.7
	[a]

. ap [c]

			ZPE [b]	A	B	C	|μ a |	|μ b |	|μ c |	φ
	ap	0.00	0.00	5.061	3.341	2.064	1.04	3.24	0.00	180.0
	sp	8.31	8.94	4.904	3.338	2.090	2.10	2.77	0.59	-21.0
	Exp

  .2.

	8.1.2.	Basis Set Variation
	The MP2/6-311++G(d,p) level of theory was chosen for the geometry optimisation (see
	Section 8.1.1.), because it is an often used combination throughout the microwave
	spectroscopic community [21] [105] [106] [107] [116] [117]

Table 8 . 2 :

 82 Molecular parameters of the ap conformer of 3-methyl-3-buten-2-one obtained from the XIAM code. The fits differ by including the internal rotation of neither (0Top), either (1Top Acetyl or 1Top Propenyl), and both (2Tops) methyl groups of the molecule. Watson's A reduction and I r representation were used. All parameters refer to the principal axis system.

	Parameter	0 Top	Antiperiplanar (ap) Conformer 1 Top Acetyl 1 Top Propenyl	2 Tops
	A / GHz		5.09708214(22)	5.09700038(15)	5.09705839(15)	5.096976683(96)
	B / GHz		3.33526004(17)	3.33527517(11)	3.33527932(12)	3.335294579(74)
	C / GHz		2.06894124(17)	2.06890330(11)	2.06891007(11)	2.068872088(72)
	Δ J / kHz		0.4994(43)	0.4972(29)	0.4982(29)	0.4957(19)
	Δ JK / kHz		-0.4109(36)	-0.4226(24)	-0.4147(25)	-0.4251(16)
	Δ K / kHz		1.1032(66)	1.1029(44)	1.1071(45)	1.1059(28)
	δ J / kHz		0.18867(48)	0.18828(32)	0.18857(33)	0.18849(21)
	δ K / kHz		0.4762(28)	0.4669(19)	0.4713(19)	0.4613(12)
	F 0,1 / GHz V 3,1 / cm -1			158.0(fixed) 512.130(28)		158.0(fixed) 512.159(19)
	∡(i 1 ,a) / °			39.015(19)		38.997(13)
	∡(i 1 ,b) / °			50.985(19)		51.003(13)
	∡(i 1 ,c) / °			90.00(fixed)		90.00(fixed)
	F 0,2 / GHz V 3,2 / cm -1				158.0(fixed) 600.199(92)	158.0(fixed) 600.254(59)
	∡(i 2 ,a) / °				132.733(44)	132.776(29)
	∡(i 2 ,b) / °				137.267(44)	137.224(29)
	∡(i 2 ,c) / ° N [a]		93	187	90.00(fixed) 186	90.00(fixed) 465
	N (00)/(10)/(01) [c] N (11)/(12) σ [d]	[b]	93/0/0 0/0 2.4	93/94/0 0/0 2.3	93/0/93 0/0 2.3	93/94/93 92/93 2.3
	[a]

Table 19 .

 19 1, Table 19.2 and Table 19.3 in the Appendix. The conformational structures are illustrated in Figure 9.1.

Table 9 . 1 :

 91 Rotational constants, dipole moment components and optimised dihedral angle φ = ∡(O 6 ,C 5 ,C 7 ,H 8 ), as well as the relative energies without and with zero-point corrections of the three conformers of 3-methylbutan-2-one calculated at the MP2/6-311++G(d,p) and B3LYP/6-311++G(d,p) level of theory.

	Parameter	Conformer I MP2	B3LYP	Conformer II MP2	B3LYP	Conformer III MP2	B3LYP
	A / GHz	4.751	4.738	4.686	4.681	4.540	4.526
	B / GHz	2.776	2.775	3.060	3.019	2.718	2.678
	C / GHz	2.285	2.241	2.116	2.092	2.400	2.384
	|μ a | / D	0.66	0.64	0.81	0.77	2.63	2.28
	|μ b | / D	2.65	2.37	3.08	2.70	1.94	1.69
	|μ c | / D	1.96	1.68	1.20	1.05	1.42	1.31
	φ / °	-155.0	-152.0	-126.3	-125.8	15.1	14.0
	E / kJ mol -1

  the MP2 method or different DFT functionals (see Section 2.2.). One of the biggest problems of these calculation methods in this context is that they yield equilibrium parameters, while the experimental ones obtained with microwave spectroscopy are parameters of the vibrational ground state. Nevertheless, due to error compensation relative cost-efficient MP2 and DFT levels of theory quite often deliver values in good agreement with the experimental data, making them computation time saving alternatives to more Lists of the ΔX values are given in the Appendix in Table13.2 to Table 13.5, Table 14.5 to Table 14.10, Table 15.2 to Table 15.5, and Table 16.2 to Table 16.5, as well as in Table 17.2 to Table 17.5, and Table 18.2 to Table 18.3. A good or very good agreement is achieved, if ΔX shows values clearly below 0.5%. If the deviationvalues are much higher than about 1%, the spectral assignment becomes difficult, because discrepancies between predicted and observed lines in the microwave spectrum can be of the order of several MHz or even some GHz, while the accuracy of the spectrometers is only a few kHz. damping (B3LYP-D3BJ), and the best agreements are obtained if basis sets without diffuse functions (e.g. 6-311G(d,p), 6-311G(df,pd) and 6-311G(3df,3pd)) are applied. One example is the B3LYP-D3BJ/6-311G(df,pd) level of theory (see Figure11.1). B3LYP-D3BJ/cc-pVDZ is also a very good combination. Both these levels yield judicious results for the C s conformers as well.

elaborate methods. If no sufficiently accurate predictions could be achieved this way, preexisting data of other, similar molecules were applied to calibrate the errors of a certain level of theory, as explained in Section 4.2.2.1., Section 5.2.3.2. and Section 6.2.2.1. for the C 1 conformers of the linear aliphatic ketone series. Such a "calibration approach", however, requires reliable empirical data.

To increase the pool of data available for future studies, in this chapter, it is summarised how different combinations of calculation methods and basis sets compare to the experimentally deduced parameters of the assigned ketones investigated in this dissertation (see Chapter 3 to Chapter 8). The parameter to consider is the relative deviation ΔX (with X = A, B, C) between the calculated rotational constants X cal and the experimental ones X exp (in percent), which is defined in Eq. (11.1).

13. Pentan-2-one 13.1. Nuclear CoordinatesTable 13 . 1 :

 131 Nuclear coordinates in the principal axis system of the four conformers of methyl propyl ketone calculated at the MP2/6-311++G(d,p) level of theory. The atoms are numbered according to Figure3.1.

Table 13 . 2 :

 132 Rotational constants of conformer I of methyl propyl ketone calculated with the Gaussian09 package[62] using various methods and basis sets. ΔA, ΔB and ΔC are the deviations of the calculated values from the experimental ones.

	Method/Basis Set	A / GHz	ΔA / %	B / GHz	ΔB / %	C / GHz	ΔC / %
	MP2/6-311G(d,p)	6.401	-2.34	2.171	1.07	1.960	1.70
	MP2/6-311+G(d,p)	6.300	-3.88	2.169	0.98	1.975	2.49
	MP2/6-311++G(d,p)	6.301	-3.86	2.169	0.99	1.975	2.50
	MP2/6-311G(df,pd)	6.439	-1.76	2.186	1.74	1.973	2.39
	MP2/6-311+G(df,pd)	6.328	-3.45	2.184	1.68	1.990	3.27
	MP2/6-311++G(df,pd)	6.330	-3.42	2.184	1.64	1.989	3.24
	MP2/6-311G(3df,3pd)	6.519	-0.53	2.193	2.08	1.968	2.12
	MP2/6-311G+(3df,3pd)	6.446	-1.65	2.189	1.91	1.976	2.55
	MP2/6-311G++(3df,3pd)	6.445	-1.66	2.189	1.91	1.976	2.56
	MP2/cc-pVDZ	6.480	-1.13	2.156	0.38	1.925	-0.10
	MP2/cc-pVTZ	6.493	-0.94	2.185	1.71	1.964	1.93
	B3LYP/6-311G(d,p)	6.596	0.64	2.117	-1.45	1.898	-1.49
	B3LYP/6-311+G(d,p)	6.497	-0.88	2.109	-1.81	1.908	-0.98
	B3LYP/6-311++G(d,p)	6.501	-0.81	2.110	-1.80	1.907	-1.02
	B3LYP/6-311G(df,pd)	6.603	0.75	2.123	-1.18	1.905	-1.16
	B3LYP/6-311+G(df,pd)	6.502	-0.80	2.116	-1.51	1.915	-0.61
	B3LYP/6-311++G(df,pd)	6.501	-0.82	2.117	-1.47	1.916	-0.58
	B3LYP/6-311G(3df,3pd)	6.611	0.87	2.124	-1.14	1.908	-0.97
	B3LYP/6-311G+(3df,3pd)	6.545	-0.14	2.118	-1.43	1.913	-0.72
	B3LYP/6-311G++(3df,3pd)	6.545	-0.14	2.117	-1.43	1.913	-0.73
	B3LYP/cc-pVDZ	6.590	0.54	2.115	-1.53	1.892	-1.84
	B3LYP/cc-pVTZ	6.592	0.58	2.118	-1.41	1.905	-1.11
	B3PW91/6-311G(d,p)	6.589	0.54	2.134	-0.68	1.918	-0.46
	B3PW91/6-311+G(d,p)	6.509	-0.69	2.128	-0.95	1.926	-0.03
	B3PW91/6-311++G(d,p)	6.514	-0.62	2.128	-0.95	1.925	-0.08
	B3PW91/6-311G(df,pd)	6.597	0.65	2.139	-0.41	1.924	-0.16
	B3PW91/6-311+G(df,pd)	6.512	-0.65	2.134	-0.65	1.933	0.32
	B3PW91/6-311++G(df,pd)	6.514	-0.62	2.135	-0.63	1.933	0.31
	B3PW91/6-311G(3df,3pd)	6.617	0.96	2.140	-0.37	1.925	-0.09
	B3PW91/6-311G+(3df,3pd)	6.559	0.07	2.135	-0.63	1.929	0.12
	B3PW91/6-311G++(3df,3pd)	6.559	0.08	2.135	-0.64	1.929	0.11
	B3PW91/cc-pVDZ	6.589	0.53	2.128	-0.94	1.908	-0.96
	B3PW91/cc-pVTZ	6.598	0.66	2.133	-0.73	1.921	-0.30
	Exp. I

Table 13 . 3 :

 133 Rotational constants of conformer I of methyl propyl ketone calculated with the Gaussian16 package[63] using various methods and basis sets. ΔA, ΔB and ΔC are the deviations of the calculated values from the experimental ones.

	Method/Basis Set	A / GHz	ΔA / %	B / GHz	ΔB / %	C / GHz	ΔC / %
	B3LYP-D3/6-311G(d,p)	6.575	0.32	2.146	-0.09	1.916	-0.56
	B3LYP-D3/6-311+G(d,p)	6.475	-1.20	2.139	-0.41	1.928	0.05
	B3LYP-D3/6-311++G(d,p)	6.479	-1.15	2.140	-0.40	1.927	0.02
	B3LYP-D3/6-311G(df,pd)	6.582	0.42	2.152	0.17	1.923	-0.22
	B3LYP-D3/6-311+G(df,pd)	6.480	-1.13	2.146	-0.12	1.935	0.44
	B3LYP-D3/6-311++G(df,pd)	6.480	-1.14	2.146	-0.10	1.935	0.43
	B3LYP-D3/6-311G(3df,3pd)	6.585	0.47	2.153	0.21	1.927	0.01
	B3LYP-D3/6-311+G(3df,3pd)	6.519	-0.54	2.147	-0.05	1.933	0.33
	B3LYP-D3/6-311++G(3df,3pd)	6.519	-0.54	2.147	-0.05	1.933	0.33
	B3LYP-D3/cc-pVDZ	6.573	0.29	2.143	-0.26	1.908	-0.99
	B3LYP-D3/cc-pVTZ	6.570	0.24	2.147	-0.06	1.924	-0.14
	B3LYP-D3/aug-cc-pVDZ	6.447	-1.64	2.138	-0.48	1.928	0.03
	B3LYP-D3/aug-cc-pVTZ	6.524	-0.46	2.146	-0.12	1.930	0.18
	B3LYP-D3BJ/6-311G(d,p)	6.551	-0.05	2.144	-0.19	1.922	-0.23
	B3LYP-D3BJ/6-311+G(d,p)	6.450	-1.59	2.137	-0.52	1.934	0.36
	B3LYP-D3BJ/6-311++G(d,p)	6.454	-1.53	2.137	-0.51	1.933	0.34
	B3LYP-D3BJ/6-311G(df,pd)	6.557	0.04	2.150	0.09	1.929	0.11
	B3LYP-D3BJ/6-311+G(df,pd)	6.454	-1.54	2.144	-0.21	1.942	0.77
	B3LYP-D3BJ/6-311++G(df,pd)	6.454	-1.53	2.144	-0.19	1.942	0.78
	B3LYP-D3BJ/6-311G(3df,3pd)	6.561	0.11	2.151	0.13	1.934	0.35
	B3LYP-D3BJ/6-311+G(3df,3pd)	6.493	-0.93	2.145	-0.14	1.939	0.65
	B3LYP-D3BJ/6-311++G(3df,3pd)	6.493	-0.94	2.145	-0.15	1.939	0.65
	B3LYP-D3BJ/cc-pVDZ	6.547	-0.11	2.141	-0.35	1.915	-0.64
	B3LYP-D3BJ/cc-pVTZ	6.544	-0.15	2.145	-0.16	1.931	0.19
	B3LYP-D3BJ/aug-cc-pVDZ	6.422	-2.02	2.136	-0.58	1.934	0.35
	B3LYP-D3BJ/aug-cc-pVTZ	6.498	-0.85	2.144	-0.22	1.937	0.50
	M06-2X/6-311G(d,p)	6.591	0.56	2.179	1.44	1.948	1.08
	M06-2X/6-311+G(d,p)	6.512	-0.64	2.175	1.26	1.958	1.59
	M06-2X/6-311++G(d,p)	6.516	-0.58	2.175	1.26	1.957	1.55
	M06-2X/6-311G(df,pd)	6.594	0.61	2.184	1.65	1.952	1.31
	M06-2X/6-311+G(df,pd)	6.515	-0.60	2.180	1.49	1.963	1.88
	M06-2X/6-311++G(df,pd)	6.516	-0.59	2.181	1.51	1.963	1.88
	M06-2X/6-311G(3df,3pd)	6.614	0.91	2.184	1.67	1.954	1.42
	M06-2X/6-311+G(3df,3pd)	6.565	0.16	2.180	1.49	1.959	1.66
	M06-2X/6-311++G(3df,3pd)	6.566	0.18	2.180	1.48	1.959	1.64
	M06-2X/cc-pVDZ	6.618	0.97	2.177	1.31	1.938	0.57
	M06-2X/cc-pVTZ	6.601	0.71	2.179	1.45	1.952	1.31
	M06-2X/aug-cc-pVDZ	6.490	-0.98	2.175	1.26	1.959	1.67
	M06-2X/aug-cc-pVTZ	6.571	0.25	2.179	1.43	1.957	1.54
	Exp. I

Table 13 . 4 :

 134 Rotational constants of conformer II of methyl propyl ketone calculated with the Gaussian09 package[62] using various methods and basis sets. ΔA, ΔB and ΔC are the deviations of the calculated values from the experimental ones.

	Method/Basis Set	A / GHz	ΔA / %	B / GHz	ΔB / %	C / GHz	ΔC / %
	MP2/6-311G(d,p)	8.297	-0.47	1.798	0.12	1.535	0.09
	MP2/6-311+G(d,p)	8.267	-0.82	1.797	0.07	1.534	0.02
	MP2/6-311++G(d,p)	8.264	-0.86	1.797	0.08	1.534	0.02
	MP2/6-311G(df,pd)	8.344	0.10	1.809	0.75	1.545	0.73
	MP2/6-311+G(df,pd)	8.313	-0.27	1.808	0.68	1.544	0.65
	MP2/6-311++G(df,pd)	8.312	-0.29	1.808	0.69	1.544	0.66
	MP2/6-311G(3df,3pd)	8.388	0.63	1.814	1.05	1.548	0.91
	MP2/6-311G+(3df,3pd)	8.354	0.21	1.813	0.99	1.546	0.78
	MP2/6-311G++(3df,3pd)	8.354	0.22	1.813	0.99	1.546	0.78
	MP2/cc-pVDZ	8.256	-0.96	1.790	-0.28	1.527	-0.44
	MP2/cc-pVTZ	8.345	0.11	1.813	0.97	1.546	0.77
	B3LYP/6-311G(d,p)	8.374	0.46	1.779	-0.92	1.522	-0.77
	B3LYP/6-311+G(d,p)	8.342	0.07	1.777	-1.01	1.521	-0.86
	B3LYP/6-311++G(d,p)	8.343	0.08	1.777	-1.00	1.521	-0.87
	B3LYP/6-311G(df,pd)	8.388	0.63	1.784	-0.63	1.527	-0.49
	B3LYP/6-311+G(df,pd)	8.357	0.26	1.782	-0.72	1.525	-0.57
	B3LYP/6-311++G(df,pd)	8.357	0.26	1.783	-0.71	1.525	-0.57
	B3LYP/6-311G(3df,3pd)	8.419	1.00	1.787	-0.47	1.529	-0.33
	B3LYP/6-311G+(3df,3pd)	8.386	0.60	1.786	-0.53	1.527	-0.44
	B3LYP/6-311G++(3df,3pd)	8.386	0.60	1.786	-0.53	1.527	-0.44
	B3LYP/cc-pVDZ	8.331	-0.06	1.778	-0.95	1.521	-0.87
	B3LYP/cc-pVTZ	8.391	0.66	1.786	-0.52	1.527	-0.44
	B3PW91/6-311G(d,p)	8.397	0.74	1.792	-0.18	1.533	-0.06
	B3PW91/6-311+G(d,p)	8.371	0.43	1.791	-0.26	1.532	-0.14
	B3PW91/6-311++G(d,p)	8.371	0.43	1.791	-0.25	1.532	-0.14
	B3PW91/6-311G(df,pd)	8.407	0.85	1.797	0.09	1.537	0.19
	B3PW91/6-311+G(df,pd)	8.383	0.57	1.795	0.00	1.536	0.12
	B3PW91/6-311++G(df,pd)	8.383	0.57	1.796	0.01	1.536	0.12
	B3PW91/6-311G(3df,3pd)	8.440	1.25	1.800	0.26	1.539	0.34
	B3PW91/6-311G+(3df,3pd)	8.410	0.89	1.799	0.20	1.538	0.25
	B3PW91/6-311G++(3df,3pd)	8.410	0.89	1.799	0.20	1.538	0.24
	B3PW91/cc-pVDZ	8.365	0.35	1.790	-0.32	1.530	-0.25
	B3PW91/cc-pVTZ	8.413	0.92	1.798	0.18	1.537	0.21
	Exp. II

Table 13 . 5 :

 135 Rotational constants of conformer II of methyl propyl ketone calculated with the Gaussian16 package[63] using various methods and basis sets. ΔA, ΔB and ΔC are the deviations of the calculated values from the experimental ones.

	Method/Basis Set	A / GHz	ΔA / %	B / GHz	ΔB / %	C / GHz	ΔC / %
	B3LYP-D3/6-311G(d,p)	8.365	0.35	1.785	-0.56	1.526	-0.50
	B3LYP-D3/6-311+G(d,p)	8.333	-0.03	1.784	-0.65	1.525	-0.57
	B3LYP-D3/6-311++G(d,p)	8.334	-0.02	1.784	-0.64	1.525	-0.58
	B3LYP-D3/6-311G(df,pd)	8.378	0.51	1.790	-0.28	1.531	-0.21
	B3LYP-D3/6-311+G(df,pd)	8.349	0.16	1.789	-0.37	1.530	-0.28
	B3LYP-D3/6-311++G(df,pd)	8.349	0.16	1.789	-0.36	1.530	-0.29
	B3LYP-D3/6-311G(3df,3pd)	8.409	0.88	1.793	-0.12	1.533	-0.06
	B3LYP-D3/6-311+G(3df,3pd)	8.379	0.52	1.792	-0.18	1.531	-0.17
	B3LYP-D3/6-311++G(3df,3pd)	8.379	0.52	1.792	-0.18	1.531	-0.17
	B3LYP-D3/cc-pVDZ	8.320	-0.19	1.785	-0.60	1.525	-0.59
	B3LYP-D3/cc-pVTZ	8.382	0.55	1.792	-0.17	1.532	-0.16
	B3LYP-D3/aug-cc-pVDZ	8.302	-0.40	1.782	-0.72	1.524	-0.68
	B3LYP-D3/aug-cc-pVTZ	8.372	0.43	1.792	-0.20	1.531	-0.20
	B3LYP-D3BJ/6-311G(d,p)	8.367	0.38	1.788	-0.43	1.529	-0.35
	B3LYP-D3BJ/6-311+G(d,p)	8.335	0.00	1.786	-0.51	1.527	-0.43
	B3LYP-D3BJ/6-311++G(d,p)	8.336	0.00	1.786	-0.51	1.527	-0.44
	B3LYP-D3BJ/6-311G(df,pd)	8.380	0.54	1.793	-0.14	1.533	-0.06
	B3LYP-D3BJ/6-311+G(df,pd)	8.350	0.18	1.791	-0.23	1.532	-0.14
	B3LYP-D3BJ/6-311++G(df,pd)	8.351	0.18	1.791	-0.22	1.532	-0.14
	B3LYP-D3BJ/6-311G(3df,3pd)	8.414	0.94	1.796	0.02	1.535	0.08
	B3LYP-D3BJ/6-311+G(3df,3pd)	8.379	0.52	1.795	-0.04	1.534	-0.02
	B3LYP-D3BJ/6-311++G(3df,3pd)	8.379	0.53	1.795	-0.04	1.534	-0.02
	B3LYP-D3BJ/cc-pVDZ	8.326	-0.12	1.787	-0.47	1.527	-0.47
	B3LYP-D3BJ/cc-pVTZ	8.386	0.60	1.795	-0.02	1.534	-0.02
	B3LYP-D3BJ/aug-cc-pVDZ	8.304	-0.38	1.785	-0.59	1.526	-0.54
	B3LYP-D3BJ/aug-cc-pVTZ	8.372	0.44	1.794	-0.06	1.533	-0.06
	M06-2X/6-311G(d,p)	8.423	1.05	1.804	0.48	1.542	0.55
	M06-2X/6-311+G(d,p)	8.399	0.76	1.803	0.42	1.541	0.48
	M06-2X/6-311++G(d,p)	8.400	0.77	1.803	0.42	1.541	0.47
	M06-2X/6-311G(df,pd)	8.429	1.12	1.808	0.69	1.545	0.74
	M06-2X/6-311+G(df,pd)	8.407	0.85	1.807	0.62	1.545	0.68
	M06-2X/6-311++G(df,pd)	8.407	0.86	1.807	0.63	1.544	0.67
	M06-2X/6-311G(3df,3pd)	8.465	1.55	1.810	0.83	1.548	0.89
	M06-2X/6-311+G(3df,3pd)	8.438	1.23	1.810	0.79	1.546	0.80
	M06-2X/6-311++G(3df,3pd)	8.439	1.24	1.810	0.79	1.546	0.80
	M06-2X/cc-pVDZ	8.404	0.83	1.804	0.47	1.542	0.51
	M06-2X/cc-pVTZ	8.437	1.21	1.811	0.87	1.547	0.85
	M06-2X/aug-cc-pVDZ	8.383	0.57	1.802	0.37	1.540	0.41
	M06-2X/aug-cc-pVTZ	8.428	1.11	1.811	0.85	1.547	0.82
	Exp. II

Table 13 . 6 :

 136 Coefficients in Hartree of the one-dimensional Fourier expansion for the energy potential curves of conformer I and II of methyl propyl ketone calculated at the MP2/6-311++G(d,p) and B3LYP/6-311++G(d,p) levels of theory, obtained by varying the dihedral angle α 1 = ∡(H 2 ,C 1 ,C 5 ,C 7 ) for the acetyl methyl group, and the dihedral angle α 2 = ∡(C 7 ,C 10 ,C 13 ,H 15 ) for the propyl methyl group. The potential is expanded as V(α) = a 0 + ∑ a n cos (3nα)

		5 n=1	+ ∑ b m sin (3mα) 5 m=1	.
			Acetyl Methyl Group
		Conformer I	Conformer II
		MP2/6-311++G(d,p)	B3LYP/6-311++G(d,p)	MP2/6-311++G(d,p)	B3LYP/6-311++G(d,p)
	a 0	-271.047280358	-271.866379183	-271.047064990	-271.866931352
	a 1	0.000410056	0.000314648	0.000330228	0.000272911
	a 2	0.000049127	0.000044898	0.000089828	0.000054816
	a 3	-0.000010045	-0.000009234	-0.000028187	-0.000015738
	a 4			0.000013571	0.000003642
	b 1	-0.000262288	-0.000185230
	b 2	0.000078986	0.000045244
			Propyl Methyl Group
		Conformer I	Conformer II
		MP2/6-311++G(d,p)	B3LYP/6-311++G(d,p)	MP2/6-311++G(d,p)	B3LYP/6-311++G(d,p)
	a 0	-271.045628175	-271.864608092	-271.044864500	-271.864825717
	a 1	0.002257381	0.002230208	0.002531202	0.002364704
	a 2	0.000022731	0.000041524	0.000064933	0.000046458

Table 13 . 9 :

 139 Observed frequencies υ obs of 264 rotational transitions of conformer I of methyl propyl ketone. 124 additional frequencies of the (01),(11) and(12) species are marked grey, with υ obs -υ cal referring to the respective BELGI-C 1 and XIAM(1Top) fit, as well as to the respective absolute and relative XIAM(2Tops) fit.

				J	K a	K c				υ obs -υ cal / kHz
	upper level		lower level	Species	υ obs / GHz	BELGI-C s	XIAM (1Top)	XIAM (absolute)	XIAM (relative)
	2	0	2	1	0	1	(00)	6.6520616	1	-0.4	-1.2
	2	0	2	1	0	1	(10)	6.6499023	0	1.0	1.4
	2	1	1	1	1	0	(00)	6.9213897	0	-1.1	-1.9
	3	0	3	2	0	2	(00)	9.9589390	0	-0.9	-2.0
	3	0	3	2	0	2	(10)	9.9558994	0	1.5	1.9
	3	1	3	2	1	2	(00)	9.5923665	1	-0.3	-1.3
	3	1	3	2	1	2	(10)	9.6498492	1	5.8	5.7
	3	1	3	2	1	2	(11)	9.6498343			2.6	-3.0
	3	1	3	2	1	2	(12)	9.6498645			9.3	-3.5
	3	1	2	2	1	1	(00)	10.3772055	0	-1.3	-2.5
	3	1	2	2	1	1	(10)	10.3164823	-1	-5.1	-6.0
	3	1	2	2	1	1	(11)	10.3164950			-5.0	1.0
	3	1	2	2	1	1	(12)	10.3164693			-6.9	-0.8
	3	2	2	2	2	1	(00)	9.9895510	2	1.2	0.2
	3	2	2	2	2	1	(10)	10.0034271	-1	2.6	2.3
	3	2	1	2	2	0	(00)	10.0202100	4	2.5	1.6
	3	2	1	2	2	0	(10)	10.0027060	-1	-4.1	-4.3
	4	0	4	3	0	3	(00)	13.2430880	0	-1.2	-2.7
	4	0	4	3	0	3	(10)	13.2393627	0	1.9	2.3
	4	1	4	3	1	3	(00)	12.7811774	1	-0.1	-1.5
	4	1	4	3	1	3	(10)	12.8079974	1	4.0	3.9
	4	1	4	3	1	3	(11)	12.8079898			3.2	-0.7
	4	1	4	3	1	3	(12)	12.8080056			5.4	1.5
	4	1	3	3	1	2	(00)	13.8269668	0	-2.2	-3.7
	4	1	3	3	1	2	(10)	13.7955167	0	-2.6	-3.5
	4	1	3	3	1	2	(11)	13.7955239			-2.9	0.6
	4	1	3	3	1	2	(12)	13.7955082			-4.9	-1.3
	4	2	3	3	2	2	(00)	13.3134126	1	-1.0	-2.3
	4	2	3	3	2	2	(10)	13.3483018	1	5.0	4.6
	4	2	2	3	2	1	(00)	13.3897683	0	-1.1	-2.4
	4	2	2	3	2	1	(10)	13.3500647	0	-3.5	-3.7
	4	3	2	3	3	1	(10)	13.3328300	1	6.8	6.6
	4	3	1	3	3	0	(10)	13.3315843	-2	-8.2	-8.1
	5	0	5	4	0	4	(00)	16.4977370	0	-1.3	-3.2
	5	0	5	4	0	4	(10)	16.4935241	1	2.1	2.3
	5	1	5	4	1	4	(00)	15.9629896	1	-0.7	-2.4
	5	1	5	4	1	4	(10)	15.9761000	1	3.2	3.0
	5	1	4	4	1	3	(00)	17.2683220	-1	-2.8	-4.7
	5	1	4	4	1	3	(10)	17.2490106	-1	-1.5	-2.2
	5	1	4	4	1	3	(11)	17.2490140			-2.3	-0.1
	5	1	4	4	1	3	(12)	17.2490057			-2.9	-0.7
	5	2	4	4	2	3	(00)	16.6321475	-2	-3.8	-5.5
	5	2	4	4	2	3	(10)	16.6967160	0	4.8	4.3
	5	2	3	4	2	2	(00)	16.7836827	6	4.0	2.4
	5	2	3	4	2	2	(10)	16.7131085	0	-5.2	-5.5
	5	3	3	4	3	2	(00)	16.6740494	13	11.5	10.2
	5	3	3	4	3	2	(10)	16.6733586	1	8.4	8.2
	5	3	2	4	3	1	(00)	16.6769961	8	6.8	5.5
	5	3	2	4	3	1	(10)	16.6715236	0	-7.5	-7.4
	6	0	6	5	0	5	(00)	19.7174781	0	-1.9	-4.1
	6	0	6	5	0	5	(10)	19.7129497	1	2.1	2.0
	6	1	6	5	1	5	(00)	19.1365537	1	-1.0	-3.1
	6	1	6	5	1	5	(10)	19.1431186	1	3.0	2.6

a ' K c '

-one 14.1. Nuclear Coordinates and Additional Geometry InformationTable 14 . 1 :

 141 Angles (in degree) between the internal rotor axes and the principal axes of the 11 conformers of methyl butyl ketone. i 1 refers to the acetyl methyl group, i 2 to the butyl methyl group. The three assigned conformers are marked in grey.

				MP2/6-311++G(d,p)
		∡(i 1 ,a)	∡(i 1 ,b)	∡(i 1 ,c)	∡(i 2 ,a)	∡(i 2 ,b)	∡(i 2 ,c)
	I	146.02	123.59	85.46	35.81	54.75	84.53
	II	148.10	78.55	60.67	20.61	105.90	102.77
	III	48.52	41.54	88.05	112.58	39.82	120.83
	IV	77.54	12.75	87.35	139.81	64.43	118.66
	V	48.09	41.92	90.66	109.24	19.63	86.23
	VI	81.99	8.03	90.64	157.96	68.20	93.06
	VII	118.18	151.77	91.58	63.97	26.03	89.88
	VIII	105.30	16.79	83.24	63.92	68.39	145.01
	IX	136.09	74.33	129.70	110.05	20.13	88.19
	X	123.46	127.59	124.68	63.09	37.35	66.17
	XI	104.12	93.56	14.58	106.38	157.39	74.86
				B3LYP/6-311++G(d,p)
		∡(i 1 ,a)	∡(i 1 ,b)	∡(i 1 c)	∡(i 2 ,a)	∡(i 2 ,b)	∡(i 2 ,c)
	I	146.27	123.63	87.77	35.14	54.99	87.33
	II	150.94	77.11	64.45	20.57	104.86	103.89
	III	47.74	42.37	87.43	114.25	43.66	123.70
	IV	76.32	13.98	87.17	140.77	65.39	118.42
	V	44.83	45.96	96.73	118.31	28.57	93.58
	VI	81.05	9.01	91.00	157.59	67.71	92.24
	VII	126.91	143.00	87.80	61.12	36.51	69.67
	VIII	105.07	17.80	80.75	63.33	60.84	138.51
	IX	138.54	79.51	129.54	103.41	13.57	92.07
	X	124.59	129.96	121.00	58.81	40.55	66.86
	XI	105.04	94.08	15.61	103.77	159.89	75.64
	Exp. I [a]	148.25	121.75	90.00 [b]	35.81 [c]	54.19 [c]	90.00 [b]

Exp. II [a] 155.92 100.18 68.42 20.61 [c] 105.90 [c] 102.77 [c] Exp. III [a] 44.78 45.54 85.78 112.58 [c] 39.82 [c] 120.8 [c]

	[a]

Table 14 . 2 :

 142 Nuclear coordinates in the principal axis system of conformer I of methyl butyl ketone calculated at the MP2/6-311++G(d,p) and the B3LYP/6-311++G(d,p) level of theory (for atom numbering see Figure4.1).

				Conformer I
		MP2/6-311++G(d,p)		B3LYP/6-311++G(d,p)
		a / Å	b / Å	c / Å	a / Å	b / Å	c / Å
	C 1	-2.905794	-0.733805	0.099134	-2.920066	-0.734878	0.047553
	H 2	-2.872750	-1.584482	-0.588065	-2.901757	-1.527417	-0.706131
	H 3	-3.786188	-0.120508	-0.096842	-3.795478	-0.102658	-0.096243
	H 4	-2.966216	-1.135894	1.116691	-2.987878	-1.223896	1.025311
	C 5	-1.648442	0.105106	-0.020947	-1.657403	0.106012	-0.011542
	O 6	-1.685068	1.324445	-0.046670	-1.702981	1.317085	-0.024397
	C 7	-0.338864	-0.663532	-0.096153	-0.339923	-0.656959	-0.046172
	H 8	-0.355578	-1.449335	0.671862	-0.353720	-1.392504	0.769430
	H 9	-0.331389	-1.193210	-1.060472	-0.338542	-1.257715	-0.966674
	C 10	0.901170	0.211439	0.042039	0.908959	0.219681	0.026820
	H 11	0.868327	0.732309	1.006672	0.882055	0.808595	0.949845
	H 12	0.876698	0.991365	-0.726985	0.883595	0.948035	-0.789736
	C 13	2.199494	-0.587966	-0.067954	2.210531	-0.587640	-0.035151
	H 14	2.224990	-1.102814	-1.037051	2.230430	-1.175527	-0.961354
	H 15	2.210762	-1.369746	0.702454	2.228899	-1.314885	0.786127
	C 16	3.439637	0.294680	0.077896	3.462809	0.291026	0.036284
	H 17	3.443305	0.798025	1.050120	3.490179	0.864387	0.968084
	H 18	4.360354	-0.290635	-0.003864	4.375314	-0.309573	-0.011719
	H 19	3.457988	1.065939	-0.698822	3.490695	1.006200	-0.791584

Table 14 .

 14

				Conformer II
		MP2/6-311++G(d,p)		B3LYP/6-311++G(d,p)
		a / Å	b / Å	c / Å	a / Å	b / Å	c / Å
	C 1	-2.708144	0.168173	0.659287	-2.775717	0.202118	0.583593
	H 2	-3.161653	1.091924	0.286868	-3.196255	1.126127	0.176734
	H 3	-2.475094	0.322358	1.718992	-2.613832	0.367447	1.654555
	H 4	-3.405041	-0.664944	0.559886	-3.477970	-0.620779	0.454659
	C 5	-1.422176	-0.132620	-0.082655	-1.449541	-0.136380	-0.070841
	O 6	-1.157139	-1.251430	-0.491195	-1.187824	-1.265570	-0.425241
	C 7	-0.484239	1.046838	-0.301386	-0.479083	1.023310	-0.267694
	H 8	-0.921432	1.632694	-1.123318	-0.909078	1.638198	-1.070934
	H 9	-0.516587	1.697688	0.582594	-0.506260	1.661313	0.624950
	C 10	0.948375	0.633945	-0.627023	0.954121	0.615598	-0.615337
	H 11	1.505687	1.512622	-0.974849	1.488880	1.496649	-0.988338
	H 12	0.931844	-0.089449	-1.449619	0.926387	-0.109286	-1.434627
	C 13	1.672254	0.021712	0.573315	1.729225	0.018720	0.566272
	H 14	1.109904	-0.849724	0.926490	1.195965	-0.861251	0.939165
	H 15	1.685071	0.752408	1.393069	1.749649	0.746121	1.388007
	C 16	3.103176	-0.397081	0.235411	3.162753	-0.373856	0.198647
	H 17	3.688998	0.462262	-0.107769	3.731613	0.489929	-0.160768
	H 18	3.610191	-0.826506	1.104576	3.695689	-0.787641	1.059111
	H 19	3.105152	-1.146909	-0.562119	3.172119	-1.129688	-0.592539

3: Nuclear coordinates in the principal axis system of conformer II of methyl butyl ketone calculated at the MP2/6-311++G(d,p) and the B3LYP/6-311++G(d,p) level of theory (for atom numbering see Figure

4

.1).

Table 14 . 4 :

 144 Nuclear coordinates in the principal axis system of conformer III of methyl butyl ketone calculated at the MP2/6-311++G(d,p) and the B3LYP/6-311++G(d,p) level of theory (for atom numbering see Figure4.1).

				Conformer III
		MP2/6-311++G(d,p)		B3LYP/6-311++G(d,p)
		a / Å	b / Å	c / Å	a / Å	b / Å	c / Å
	C 1	2.560845	1.125474	0.052366	2.592454	1.109445	0.059319
	H 2	2.366422	1.778858	0.908032	2.432024	1.741890	0.936882
	H 3	2.455782	1.731598	-0.854453	2.483524	1.749867	-0.822876
	H 4	3.574925	0.726816	0.100963	3.600295	0.695964	0.072876
	C 5	1.556441	-0.009541	0.000661	1.571501	-0.012210	-0.008759
	O 6	1.891343	-1.156674	-0.245237	1.897489	-1.149207	-0.272936
	C 7	0.107314	0.373274	0.258922	0.124559	0.377289	0.264516
	H 8	0.040917	0.696676	1.309035	0.078685	0.720969	1.308213

Table 14 . 5 :

 145 Rotational constants of conformer I of methyl butyl ketone calculated with the Gaussian09 package[62] at various levels of theory. ΔA, ΔB and ΔC are the deviations of the calculated values from the experimental ones.

	Method/Basis Set	A / GHz	ΔA / %	B / GHz	ΔB / %	C / GHz	ΔC / %
	MP2/6-311G(d,p)	7.465	-0.61	1.042	0.17	0.943	0.14
	MP2/6-311+G(d,p)	7.438	-0.96	1.041	0.05	0.942	0.07
	MP2/6-311++G(d,p)	7.439	-0.96	1.041	0.05	0.942	0.06
	MP2/6-311G(df,pd)	7.506	-0.07	1.049	0.78	0.949	0.77
	MP2/6-311+G(df,pd)	7.478	-0.43	1.048	0.66	0.948	0.70
	MP2/6-311++G(df,pd)	7.479	-0.42	1.048	0.66	0.948	0.69
	MP2/6-311G(3df,3pd)	7.553	0.57	1.053	1.13	0.951	0.99
	MP2/6-311G+(3df,3pd)	7.535	0.33	1.051	0.98	0.949	0.82
	MP2/6-311G++(3df,3pd)	7.535	0.33	1.051	0.98	0.949	0.82
	MP2/cc-pVDZ	7.433	-1.04	1.039	-0.20	0.938	-0.35
	MP2/cc-pVTZ	7.523	0.17	1.051	0.96	0.949	0.81
	B3LYP/6-311G(d,p)	7.542	0.42	1.031	-0.95	0.933	-0.88
	B3LYP/6-311+G(d,p)	7.524	0.18	1.029	-1.12	0.932	-1.02
	B3LYP/6-311++G(d,p)	7.526	0.21	1.029	-1.11	0.932	-1.03
	B3LYP/6-311G(df,pd)	7.556	0.60	1.034	-0.65	0.936	-0.59
	B3LYP/6-311+G(df,pd)	7.537	0.35	1.032	-0.83	0.935	-0.72
	B3LYP/6-311++G(df,pd)	7.539	0.38	1.032	-0.82	0.934	-0.73
	B3LYP/6-311G(3df,3pd)	7.583	0.97	1.036	-0.49	0.937	-0.44
	B3LYP/6-311G+(3df,3pd)	7.565	0.73	1.034	-0.65	0.936	-0.59
	B3LYP/6-311G++(3df,3pd)	7.566	0.73	1.034	-0.65	0.936	-0.60
	B3LYP/cc-pVDZ	7.499	-0.15	1.031	-0.95	0.933	-0.93
	B3LYP/cc-pVTZ	7.567	0.75	1.034	-0.60	0.936	-0.56
	B3PW91/6-311G(d,p)	7.561	0.67	1.039	-0.20	0.940	-0.15
	B3PW91/6-311+G(d,p)	7.545	0.46	1.037	-0.35	0.939	-0.26
	B3PW91/6-311++G(d,p)	7.547	0.49	1.037	-0.34	0.939	-0.27
	B3PW91/6-311G(df,pd)	7.571	0.80	1.041	0.07	0.942	0.12
	B3PW91/6-311+G(df,pd)	7.556	0.60	1.040	-0.09	0.941	0.01
	B3PW91/6-311++G(df,pd)	7.557	0.62	1.040	-0.08	0.941	0.00
	B3PW91/6-311G(3df,3pd)	7.600	1.19	1.043	0.25	0.944	0.26
	B3PW91/6-311G+(3df,3pd)	7.583	0.97	1.042	0.11	0.943	0.13
	B3PW91/6-311G++(3df,3pd)	7.584	0.97	1.042	0.11	0.942	0.12
	B3PW91/cc-pVDZ	7.528	0.23	1.037	-0.31	0.938	-0.31
	B3PW91/cc-pVTZ	7.583	0.97	1.042	0.11	0.942	0.11
	Exp. I

Table 14 . 6 :

 146 .2. Rotational constants of conformer I of methyl butyl ketone calculated with the Gaussian16 package[63] at various levels of theory. ΔA, ΔB and ΔC are the deviations of the calculated values from the experimental ones.

	Method/Basis Set	A / GHz	ΔA / %	B / GHz	ΔB / %	C / GHz	ΔC / %
	B3LYP-D3/6-311G(d,p)	7.533	0.29	1.035	-0.57	0.936	-0.56
	B3LYP-D3/6-311+G(d,p)	7.511	0.01	1.033	-0.73	0.935	-0.68
	B3LYP-D3/6-311++G(d,p)	7.513	0.04	1.033	-0.73	0.935	-0.68
	B3LYP-D3/6-311G(df,pd)	7.545	0.46	1.038	-0.28	0.939	-0.27
	B3LYP-D3/6-311+G(df,pd)	7.525	0.19	1.036	-0.45	0.938	-0.38
	B3LYP-D3/6-311++G(df,pd)	7.527	0.22	1.036	-0.44	0.938	-0.39
	B3LYP-D3/6-311G(3df,3pd)	7.573	0.84	1.039	-0.13	0.940	-0.12
	B3LYP-D3/6-311+G(3df,3pd)	7.558	0.63	1.038	-0.27	0.939	-0.27
	B3LYP-D3/6-311++G(3df,3pd)	7.558	0.64	1.038	-0.27	0.939	-0.28
	B3LYP-D3/cc-pVDZ	7.489	-0.29	1.035	-0.57	0.936	-0.61
	B3LYP-D3/cc-pVTZ	7.558	0.63	1.038	-0.23	0.939	-0.24
	B3LYP-D3/aug-cc-pVDZ	7.484	-0.35	1.033	-0.77	0.934	-0.74
	B3LYP-D3/aug-cc-pVTZ	7.554	0.57	1.038	-0.29	0.938	-0.30
	B3LYP-D3BJ/6-311G(d,p)	7.535	0.33	1.036	-0.43	0.938	-0.41
	B3LYP-D3BJ/6-311+G(d,p)	7.515	0.06	1.034	-0.60	0.936	-0.53
	B3LYP-D3BJ/6-311++G(d,p)	7.517	0.08	1.034	-0.60	0.936	-0.54
	B3LYP-D3BJ/6-311G(df,pd)	7.548	0.50	1.039	-0.14	0.940	-0.11
	B3LYP-D3BJ/6-311+G(df,pd)	7.529	0.24	1.037	-0.31	0.939	-0.23
	B3LYP-D3BJ/6-311++G(df,pd)	7.530	0.27	1.038	-0.30	0.939	-0.24
	B3LYP-D3BJ/6-311G(3df,3pd)	7.581	0.94	1.041	0.02	0.942	0.02
	B3LYP-D3BJ/6-311+G(3df,3pd)	7.560	0.66	1.039	-0.13	0.940	-0.12
	B3LYP-D3BJ/6-311++G(3df,3pd)	7.561	0.67	1.039	-0.13	0.940	-0.12
	B3LYP-D3BJ/cc-pVDZ	7.497	-0.19	1.036	-0.44	0.937	-0.48
	B3LYP-D3BJ/cc-pVTZ	7.565	0.72	1.040	-0.08	0.940	-0.10
	B3LYP-D3BJ/aug-cc-pVDZ	7.488	-0.30	1.034	-0.64	0.936	-0.61
	B3LYP-D3BJ/aug-cc-pVTZ	7.556	0.60	1.039	-0.15	0.940	-0.15
	M06-2X/6-311G(d,p)	7.575	0.86	1.046	0.54	0.946	0.53
	M06-2X/6-311+G(d,p)	7.559	0.65	1.045	0.40	0.945	0.43
	M06-2X/6-311++G(d,p)	7.562	0.69	1.045	0.41	0.945	0.42
	M06-2X/6-311G(df,pd)	7.582	0.95	1.048	0.74	0.948	0.73
	M06-2X/6-311+G(df,pd)	7.567	0.75	1.047	0.61	0.947	0.64
	M06-2X/6-311++G(df,pd)	7.570	0.79	1.047	0.62	0.947	0.63
	M06-2X/6-311G(3df,3pd)	7.614	1.38	1.050	0.88	0.949	0.86
	M06-2X/6-311+G(3df,3pd)	7.601	1.21	1.049	0.76	0.948	0.73
	M06-2X/6-311++G(3df,3pd)	7.601	1.21	1.049	0.77	0.948	0.73
	M06-2X/cc-pVDZ	7.552	0.55	1.047	0.57	0.946	0.53
	M06-2X/cc-pVTZ	7.599	1.17	1.050	0.85	0.949	0.80
	M06-2X/aug-cc-pVDZ	7.546	0.47	1.045	0.40	0.945	0.40
	M06-2X/aug-cc-pVTZ	7.596	1.14	1.049	0.80	0.948	0.75
	Exp. I

Table 14 . 7 :

 147 .2. Rotational constants of conformer II of methyl butyl ketone calculated with the Gaussian09 package[62] at various levels of theory. ΔA, ΔB and ΔC are the deviations of the calculated values from the experimental ones.

	Method/Basis Set	A / GHz	ΔA / %	B / GHz	ΔB / %	C / GHz	ΔC / %
	MP2/6-311G(d,p)	5.704	-2.73	1.257	1.01	1.171	1.54
	MP2/6-311+G(d,p)	5.583	-4.81	1.259	1.21	1.180	2.31
	MP2/6-311++G(d,p)	5.573	-4.97	1.259	1.20	1.181	2.38
	MP2/6-311G(df,pd)	5.729	-2.31	1.266	1.76	1.180	2.28
	MP2/6-311+G(df,pd)	5.606	-4.41	1.269	1.94	1.189	3.05
	MP2/6-311++G(df,pd)	5.597	-4.56	1.268	1.92	1.189	3.10
	MP2/6-311G(3df,3pd)	5.813	-0.89	1.272	2.20	1.179	2.19
	MP2/6-311G+(3df,3pd)	5.734	-2.24	1.271	2.14	1.183	2.52
	MP2/6-311G++(3df,3pd)	5.732	-2.27	1.271	2.16	1.183	2.54
	MP2/cc-pVDZ	5.801	-1.09	1.248	0.28	1.154	0.06
	MP2/cc-pVTZ	5.789	-1.29	1.267	1.85	1.176	1.97
	B3LYP/6-311G(d,p)	5.918	0.90	1.222	-1.78	1.135	-1.62
	B3LYP/6-311+G(d,p)	5.816	-0.84	1.219	-2.03	1.138	-1.30
	B3LYP/6-311++G(d,p)	5.818	-0.79	1.219	-2.04	1.138	-1.32
	B3LYP/6-311G(df,pd)	5.922	0.98	1.226	-1.48	1.139	-1.29
	B3LYP/6-311+G(df,pd)	5.817	-0.81	1.223	-1.71	1.143	-0.93
	B3LYP/6-311++G(df,pd)	5.817	-0.81	1.223	-1.70	1.143	-0.92
	B3LYP/6-311G(3df,3pd)	5.926	1.05	1.227	-1.40	1.140	-1.13
	B3LYP/6-311G+(3df,3pd)	5.862	-0.05	1.223	-1.68	1.141	-1.04
	B3LYP/6-311G++(3df,3pd)	5.861	-0.06	1.223	-1.68	1.141	-1.04
	B3LYP/cc-pVDZ	5.914	0.84	1.223	-1.73	1.133	-1.81
	B3LYP/cc-pVTZ	5.912	0.81	1.223	-1.71	1.138	-1.32
	B3PW91/6-311G(d,p)	5.907	0.71	1.232	-0.98	1.146	-0.66
	B3PW91/6-311+G(d,p)	5.824	-0.70	1.230	-1.15	1.149	-0.38
	B3PW91/6-311++G(d,p)	5.827	-0.64	1.230	-1.17	1.149	-0.40
	B3PW91/6-311G(df,pd)	5.910	0.77	1.236	-0.69	1.149	-0.35
	B3PW91/6-311+G(df,pd)	5.825	-0.69	1.234	-0.83	1.153	-0.02
	B3PW91/6-311++G(df,pd)	5.825	-0.68	1.234	-0.83	1.153	-0.02
	B3PW91/6-311G(3df,3pd)	5.929	1.09	1.236	-0.64	1.150	-0.29
	B3PW91/6-311G+(3df,3pd)	5.875	0.17	1.234	-0.87	1.151	-0.21
	B3PW91/6-311G++(3df,3pd)	5.875	0.17	1.233	-0.88	1.151	-0.22
	B3PW91/cc-pVDZ	5.904	0.67	1.230	-1.12	1.142	-0.99
	B3PW91/cc-pVTZ	5.915	0.86	1.232	-1.01	1.147	-0.54
	Exp. II

. 2 Table 14 . 8 :

 2148 Rotational constants of conformer II of methyl butyl ketone calculated with the Gaussian16 package[63] at various levels of theory. ΔA, ΔB and ΔC are the deviations of the calculated values from the experimental ones.

	Method/Basis Set	A / GHz	ΔA / %	B / GHz	ΔB / %	C / GHz	ΔC / %
	B3LYP-D3/6-311G(d,p)	5.893	0.48	1.239	-0.40	1.146	-0.60
	B3LYP-D3/6-311+G(d,p)	5.779	-1.46	1.238	-0.50	1.152	-0.10
	B3LYP-D3/6-311++G(d,p)	5.782	-1.41	1.238	-0.50	1.152	-0.12
	B3LYP-D3/6-311G(df,pd)	5.894	0.50	1.243	-0.09	1.151	-0.25
	B3LYP-D3/6-311+G(df,pd)	5.778	-1.48	1.242	-0.16	1.157	0.30
	B3LYP-D3/6-311++G(df,pd)	5.778	-1.48	1.242	-0.16	1.157	0.31
	B3LYP-D3/6-311G(3df,3pd)	5.895	0.51	1.245	0.02	1.153	-0.05
	B3LYP-D3/6-311+G(3df,3pd)	5.822	-0.74	1.243	-0.13	1.156	0.19
	B3LYP-D3/6-311++G(3df,3pd)	5.821	-0.74	1.243	-0.13	1.156	0.19
	B3LYP-D3/cc-pVDZ	5.899	0.59	1.239	-0.45	1.143	-0.89
	B3LYP-D3/cc-pVTZ	5.879	0.24	1.242	-0.21	1.151	-0.18
	B3LYP-D3/aug-cc-pVDZ	5.760	-1.78	1.238	-0.48	1.152	-0.14
	B3LYP-D3/aug-cc-pVTZ	5.825	-0.67	1.242	-0.18	1.155	0.09
	B3LYP-D3BJ/6-311G(d,p)	5.862	-0.05	1.240	-0.37	1.150	-0.28
	B3LYP-D3BJ/6-311+G(d,p)	5.747	-2.01	1.238	-0.49	1.156	0.21
	B3LYP-D3BJ/6-311++G(d,p)	5.748	-1.98	1.238	-0.48	1.156	0.21
	B3LYP-D3BJ/6-311G(df,pd)	5.864	-0.01	1.244	-0.06	1.154	0.08
	B3LYP-D3BJ/6-311+G(df,pd)	5.745	-2.04	1.243	-0.13	1.161	0.63
	B3LYP-D3BJ/6-311++G(df,pd)	5.744	-2.07	1.243	-0.13	1.161	0.65
	B3LYP-D3BJ/6-311G(3df,3pd)	5.864	-0.01	1.245	0.07	1.157	0.28
	B3LYP-D3BJ/6-311+G(3df,3pd)	5.789	-1.29	1.243	-0.11	1.159	0.51
	B3LYP-D3BJ/6-311++G(3df,3pd)	5.788	-1.30	1.243	-0.11	1.159	0.51
	B3LYP-D3BJ/cc-pVDZ	5.864	-0.01	1.240	-0.39	1.147	-0.55
	B3LYP-D3BJ/cc-pVTZ	5.846	-0.31	1.242	-0.19	1.155	0.14
	B3LYP-D3BJ/aug-cc-pVDZ	5.730	-2.31	1.239	-0.46	1.155	0.17
	B3LYP-D3BJ/aug-cc-pVTZ	5.793	-1.23	1.242	-0.16	1.158	0.42
	M06-2X/6-311G(d,p)	5.899	0.59	1.259	1.18	1.165	0.97
	M06-2X/6-311+G(d,p)	5.811	-0.92	1.259	1.21	1.170	1.41
	M06-2X/6-311++G(d,p)	5.815	-0.85	1.259	1.18	1.169	1.37
	M06-2X/6-311G(df,pd)	5.901	0.61	1.262	1.41	1.168	1.22
	M06-2X/6-311+G(df,pd)	5.810	-0.94	1.263	1.48	1.173	1.71
	M06-2X/6-311++G(df,pd)	5.810	-0.93	1.263	1.47	1.173	1.71
	M06-2X/6-311G(3df,3pd)	5.912	0.81	1.264	1.55	1.169	1.34
	M06-2X/6-311+G(3df,3pd)	5.857	-0.13	1.263	1.47	1.171	1.54
	M06-2X/6-311++G(3df,3pd)	5.858	-0.12	1.263	1.47	1.171	1.53
	M06-2X/cc-pVDZ	5.922	0.97	1.259	1.18	1.161	0.69
	M06-2X/cc-pVTZ	5.903	0.64	1.261	1.34	1.168	1.24
	M06-2X/aug-cc-pVDZ	5.789	-1.29	1.262	1.38	1.171	1.52
	M06-2X/aug-cc-pVTZ	5.864	-0.01	1.262	1.40	1.170	1.45
	Exp. II

. 2 Table 14 . 10 :

 21410 Rotational constants of conformer III of methyl butyl ketone calculated with the Gaussian16 package[63] at various levels of theory. ΔA, ΔB and ΔC are the deviations of the calculated values from the experimental ones.

	Method/Basis Set	A / GHz	ΔA / %	B / GHz	ΔB / %	C / GHz	ΔC / %
	B3LYP-D3/6-311G(d,p)	5.862	0.24	1.168	-0.46	1.038	-1.35
	B3LYP-D3/6-311+G(d,p)	5.830	-0.29	1.170	-0.33	1.038	-1.41
	B3LYP-D3/6-311++G(d,p)	5.832	-0.27	1.170	-0.36	1.038	-1.39
	B3LYP-D3/6-311G(df,pd)	5.873	0.43	1.172	-0.15	1.041	-1.08
	B3LYP-D3/6-311+G(df,pd)	5.842	-0.10	1.174	0.00	1.040	-1.15
	B3LYP-D3/6-311++G(df,pd)	5.843	-0.08	1.174	-0.01	1.040	-1.13
	B3LYP-D3/6-311G(3df,3pd)	5.898	0.87	1.169	-0.43	1.049	-0.32
	B3LYP-D3/6-311+G(3df,3pd)	5.888	0.70	1.167	-0.62	1.050	-0.22
	B3LYP-D3/6-311++G(3df,3pd)	5.942	1.62	1.167	-0.60	1.045	-0.69
	B3LYP-D3/cc-pVDZ	5.839	-0.14	1.165	-0.76	1.039	-1.23
	B3LYP-D3/cc-pVTZ	5.883	0.61	1.169	-0.42	1.046	-0.57
	B3LYP-D3/aug-cc-pVDZ	5.809	-0.66	1.172	-0.15	1.037	-1.46
	B3LYP-D3/aug-cc-pVTZ	5.888	0.69	1.166	-0.67	1.049	-0.29
	B3LYP-D3BJ/6-311G(d,p)	5.857	0.15	1.173	-0.05	1.040	-1.15
	B3LYP-D3BJ/6-311+G(d,p)	5.823	-0.43	1.175	0.07	1.040	-1.16
	B3LYP-D3BJ/6-311++G(d,p)	5.824	-0.40	1.174	0.04	1.040	-1.15
	B3LYP-D3BJ/6-311G(df,pd)	5.868	0.34	1.177	0.26	1.043	-0.87
	B3LYP-D3BJ/6-311+G(df,pd)	5.834	-0.23	1.178	0.40	1.043	-0.89
	B3LYP-D3BJ/6-311++G(df,pd)	5.835	-0.22	1.178	0.39	1.043	-0.87
	B3LYP-D3BJ/6-311G(3df,3pd)	5.895	0.81	1.172	-0.13	1.053	0.06
	B3LYP-D3BJ/6-311+G(3df,3pd)	5.855	0.13	1.177	0.27	1.048	-0.43
	B3LYP-D3BJ/6-311++G(3df,3pd)	5.855	0.14	1.177	0.26	1.048	-0.42
	B3LYP-D3BJ/cc-pVDZ	5.831	-0.28	1.170	-0.31	1.041	-1.08
	B3LYP-D3BJ/cc-pVTZ	5.872	0.41	1.174	0.06	1.048	-0.39
	B3LYP-D3BJ/aug-cc-pVDZ	5.801	-0.79	1.177	0.26	1.040	-1.21
	B3LYP-D3BJ/aug-cc-pVTZ	5.857	0.16	1.176	0.18	1.048	-0.47
	M06-2X/6-311G(d,p)	5.872	0.42	1.192	1.53	1.052	-0.01
	M06-2X/6-311+G(d,p)	5.846	-0.02	1.193	1.64	1.052	0.00
	M06-2X/6-311++G(d,p)	5.849	0.02	1.192	1.59	1.053	0.02
	M06-2X/6-311G(df,pd)	5.878	0.51	1.194	1.76	1.055	0.20
	M06-2X/6-311+G(df,pd)	5.852	0.08	1.196	1.90	1.055	0.20
	M06-2X/6-311++G(df,pd)	5.854	0.11	1.196	1.88	1.055	0.22
	M06-2X/6-311G(3df,3pd)	5.913	1.12	1.190	1.35	1.062	0.92
	M06-2X/6-311+G(3df,3pd)	5.907	1.02	1.187	1.16	1.064	1.05
	M06-2X/6-311++G(3df,3pd)	5.907	1.01	1.187	1.16	1.063	1.04
	M06-2X/cc-pVDZ	5.872	0.42	1.186	1.05	1.054	0.11
	M06-2X/cc-pVTZ	5.899	0.88	1.191	1.43	1.062	0.87
	M06-2X/aug-cc-pVDZ	5.839	-0.15	1.193	1.67	1.052	-0.02
	M06-2X/aug-cc-pVTZ	5.904	0.96	1.188	1.20	1.064	1.08
	Exp. III

Table 14 . 11 :

 1411 Fourier coefficients (in Hartree) of the one-dimensional expansion (as V(α) = a 0 + ∑ a n cos (3nα)

	5 n=1

Table 14 .12: Fourier

 14

			I	Conformer II
		MP2/6-311++G(d,p)	B3LYP/6-311++G(d,p)	MP2/6-311++G(d,p)	B3LYP/6-311++G(d,p)
	a 0	-310.242851042	-311.191304072	-310.243342333	-311.190848242
	a 1	0.000330184	0.000271721	0.000401487	0.000304285
	a 2	0.000093087	0.000051108	0.000052773	0.000048120
	a 3	-0.000029691	-0.000011542	-0.000010458	-0.000012014
	a 4	0.000013049	0.000003515	0.000006081	0.000003951
	a 5	-0.000005328	-0.000000341
	b 1			-0.000264251	-0.000181230
	b 2			0.000077768	0.000048386
	b 3			-0.000019774	-0.000009021
		Conformer III
		MP2/6-311++G(d,p)	B3LYP/6-311++G(d,p)
	a 0	-310.242212882	-311.190026493
	a 1	0.000325067	0.000272889
	a 2	0.000089818	0.000061964
	a 3	-0.000027240	-0.000017093
	a 4	0.000011054	0.000005777
	a 5	-0.000003561	0.000000599
	b 1	0.000033937	0.000008274
	b 2	0.000008203	0.000011052
	b 3	0.000003761	0.000000856
	b 4	-0.000005262	-0.000002505
	b 5	0.000004682	0.000002629

coefficients (in Hartree) of the one-dimensional expansion (as

V(α) = a 0 + ∑ a n cos (3nα) 5 n=1

  Potential energy curves of the butyl methyl group of conformer I, conformer II, and conformer III of methyl butyl ketone calculated at the MP2/6-311++G(d,p) level of theory. The potential energies were obtained by varying the dihedral angle α

	Figure 14.1:
		)	B3LYP/6-311++G(d,p)	MP2/6-311++G(d,p)	B3LYP/6-311++G(d,p)
	a 0	-310.240773117	-311.189289950	-310.241548917	-311.189019500
	a 1	0.002409344	0.002265828	0.002432271	0.002284049
	a 2	0.000064608	0.000042626	0.000062967	0.000044364
		Conformer III
	MP2/6-311++G(d,p)	B3LYP/6-311++G(d,p)
	a 0	-310.240232542	-311.188135242
	a 1	0.002194110	0.002109197
	a 2	0.000070148	0.000044585
	b 1	-0.000571478	-0.000399357

2 = (C 10 ,C 13 ,C 16 ,H 18 ) with a step width of 10°. All other geometry parameters were allowed to relax during the optimisations. Due to the symmetry of the methyl group, a rotation of 120° was sufficient. The resulting energies relative to that of the lowest energy conformations were parametrised with a onedimensional Fourier expansion. Figure 14.2: Potential energy curves of the butyl methyl group of conformer I, conformer II, and conformer III of methyl butyl ketone calculated at the B3LYP/6-311++G(d,p) level of theory. The potential energies were obtained by varying the dihedral angle α 2 = (C 10 ,C 13 ,C 16 ,H 18 ) with a step width of 10°. All other geometry parameters were allowed to relax during the optimisations. Due to the symmetry of the methyl group, a rotation of 120° was sufficient. The resulting energies relative to that of the lowest energy conformations were parametrised with a onedimensional Fourier expansion.

Table 14 . 14 :

 1414 Observed frequencies υ obs of 345 rotational transitions of conformer I of methyl butyl ketone. 218 additional frequencies of the (

Table 14 . 15 :

 1415 Observed frequencies υ obs of 380 rotational transitions of conformer II of methyl butyl ketone. 175 additional frequencies of the (01), (11) and (12) species are marked grey, with υ obs -υ cal referring to the respective BELGI-C 1 and XIAM(1Top) fit, as well as to the respective absolute and relative XIAM(2Tops) fit.

		K a ' K c '	J	K a	K c				υ obs -υ cal / kHz
		upper level			lower level	Species	υ obs / GHz	BELGI-C s	XIAM (1Top)	XIAM (absolute)	XIAM (relative)
	3	0	3	2	0	2	(00)	5.9419529	1	-3.2	-4.4
	3	0	3	2	0	2	(10)	5.9411138	-1	0.7	0.7
	3	1	3	2	1	2	(00)	5.7965183	2	-1.2	-2.4
	3	1	3	2	1	2	(10)	5.8645331	1	3.5	2.7
	3	1	2	2	1	1	(00)	6.0950503	1	-2.5	-3.8
	4	0	4	3	0	3	(00)	7.9173038	1	-3.7	-5.3
	4	0	4	3	0	3	(10)	7.9162175	-1	0.8	0.7
	4	1	4	3	1	3	(00)	7.7273788	3	-2.2	-3.7
	4	1	3	3	1	2	(00)	8.1253821	1	-4.3	-5.9
	5	0	5	4	0	4	(00)	9.8881304	0	-6.5	-8.4
	5	0	5	4	0	4	(10)	9.8868245	-1	1.6	1.4
	5	1	5	4	1	4	(00)	9.6571387	2	-3.5	-5.4
	5	1	5	4	1	4	(10)	9.6880978	-1	2.4	1.4
	5	1	5	4	1	4	(11)	9.6880882			-0.5	-1.8
	5	1	5	4	1	4	(12)	9.6881074			3.4	2.0
	5	1	4	4	1	3	(00)	10.1545331	1	-4.6	-6.6
	5	1	4	4	1	3	(10)	10.1222444	-2	-1.5	-2.0
	5	1	4	4	1	3	(11)	10.1222530			-0.6	1.3
	5	1	4	4	1	3	(12)	10.1222353			-3.2	-1.2
	5	2	4	4	2	3	(00)	9.9082637	2	-2.8	-4.6
	5	2	4	4	2	3	(10)	9.9189980	-3	2.0	1.4
	5	2	3	4	2	2	(00)	9.9309440	1	-4.1	-5.9
	5	2	3	4	2	2	(10)	9.9187568	0	0.9	0.5
	5	3	3	4	3	2	(00)	9.9145806	5	1.6	-0.1
	5	3	3	4	3	2	(10)	9.9140951	-3	4.5	4.0
	5	3	2	4	3	1	(00)	9.9147450	-1	-4.3	-6.0
	5	3	2	4	3	1	(10)	9.9137310	-1	1.8	1.7
	6	0	6	5	0	5	(00)	11.8533565	2	-5.0	-7.2
	6	0	6	5	0	5	(10)	11.8518521	-1	1.6	1.4
	6	1	6	5	1	5	(00)	11.5855538	2	-4.3	-6.5
	6	1	6	5	1	5	(10)	11.6049685	-1	2.3	1.2
	6	1	6	5	1	5	(11)	11.6049618			0.0	-1.2
	6	1	6	5	1	5	(12)	11.6049746			2.1	0.8
	6	1	5	5	1	4	(00)	12.1821754	2	-5.1	-7.4
	6	1	5	5	1	4	(10)	12.1610802	-2	-0.3	-0.7
	6	1	5	5	1	4	(11)	12.1610862			0.3	1.0
	6	1	5	5	1	4	(12)	12.1610736			-1.7	-1.0
	6	2	5	5	2	4	(00)	11.8878207	2	-3.7	-5.8
	6	2	5	5	2	4	(10)	11.9064611	-3	3.0	2.3
	6	2	4	5	2	3	(00)	11.9274276	2	-3.6	-5.7
	6	2	4	5	2	3	(10)	11.9070576	-1	0.6	0.3
	6	3	3	5	3	2	(10)	11.8979982	-1	1.8	1.7
	7	0	7	6	0	6	(00)	13.8119503	-4	-11.2	-13.7
	7	0	7	6	0	6	(10)	13.8102814	-1	2.2	1.9
	7	1	7	6	1	6	(00)	13.5123982	2	-4.7	-7.1
	7	1	7	6	1	6	(10)	13.5248566	-2	1.9	0.7
	7	1	6	6	1	5	(00)	14.2079618	2	-5.7	-8.1
	7	1	6	6	1	5	(10)	14.1934355	-2	1.0	0.7
	7	2	6	6	2	5	(00)	13.8662364	2	-3.9	-6.2
	7	2	6	6	2	5	(10)	13.8950845	-5	2.4	1.8
	7	2	5	6	2	4	(00)	13.9293840	3	-3.3	-5.6
	7	2	5	6	2	4	(10)	13.8985367	0	2.3	2.0
	7	3	5	6	3	4	(00)	13.8839686	4	-0.4	-2.4

Table 14 . 16 :

 1416 Observed frequencies υ obs of 234 rotational transitions of conformer III of methyl butyl ketone. 10 additional frequencies of the (11) and (12) species are marked grey, with υ obs -υ cal referring to the respective BELGI-C 1 and XIAM(1Top) fit, as well as to the respective absolute and relative XIAM(2Tops) fit.

	.2	0.4

Table 15 . 7 :

 157 Molecular parameters of conformer I and conformer II of heptan-2-one obtain from the BELGI-C s

Table 15 . 8 :

 158 Observed frequencies υ obs of 285 rotational transitions of conformer I of heptan-2-one. 121 additional frequencies of the (01), (11) and (12) species are marked grey, with υ obs -υ cal referring to the respective BELGI-C s and XIAM(1Top) fit, as well as to the respective absolute and relative XIAM(2Tops) fit.

	J'	K a ' K c '	J	K a	K c				υ obs -υ cal / kHz
	upper level			lower level	Species	υ obs / GHz	BELGI-C s	XIAM (1Top)	XIAM (absolute)	XIAM (relative)
	3	0	3	2	0	2	(00)	3.7748567	0	0.9	1.1
	3	0	3	2	0	2	(10)	3.7744660	-1	2.2	2.9
	3	1	3	2	1	2	(00)	3.7129461	2	2.1	2.3
	3	1	3	2	1	2	(10)	3.7571452	-1	-0.5	-0.7
	3	1	2	2	1	1	(00)	3.8381541	1	1.7	2.0
	3	1	2	2	1	1	(10)	3.7936425	-1	-2.0	-2.1
	4	0	4	3	0	3	(00)	5.0321805	0	1.2	1.4
	4	0	4	3	0	3	(10)	5.0316676	-2	2.5	3.3
	4	1	4	3	1	3	(00)	4.9503532	1	1.3	1.5
	4	1	4	3	1	3	(10)	4.9939195	-3	-2.4	-2.7
	4	1	3	3	1	2	(00)	5.1172944	0	1.0	1.4
	4	1	3	3	1	2	(10)	5.0733073	2	0.7	0.6
	5	0	5	4	0	4	(00)	6.2886805	0	1.2	1.5
	5	0	5	4	0	4	(10)	6.2880553	1	5.7	6.6
	5	1	5	4	1	4	(00)	6.1875576	1	1.6	1.8
	5	1	4	4	1	3	(00)	6.3962247	0	0.8	1.2
	5	1	4	4	1	3	(10)	6.3588855	2	-0.5	-0.7
	5	2	4	4	2	3	(00)	6.2923255	3	3.3	3.5
	5	2	3	4	2	2	(00)	6.2964346	-3	-2.3	-2.1
	6	0	6	5	0	5	(00)	7.5441533	1	2.0	2.3
	6	0	6	5	0	5	(10)	7.5434167	-3	2.3	3.3
	6	1	6	5	1	5	(00)	7.4245099	2	2.4	2.6
	6	1	6	5	1	5	(10)	7.4527503	1	1.3	0.7
	6	1	5	5	1	4	(00)	7.6748898	0	0.7	1.1
	6	1	5	5	1	4	(10)	7.6459921	7	4.5	4.2
	6	2	5	5	2	4	(00)	7.5504088	3	3.1	3.3
	6	2	5	5	2	4	(10)	7.5536989	-2	0.0	-0.2
	6	2	4	5	2	3	(00)	7.5576033	-1	-0.2	0.0
	6	2	4	5	2	3	(10)	7.5535201	-3	-4.2	-4.5
	7	0	7	6	0	6	(00)	8.7983964	2	2.9	3.2
	7	0	7	6	0	6	(10)	8.7975609	-3	2.7	3.7
	7	1	7	6	1	6	(00)	8.6611619	2	2.3	2.5
	7	1	7	6	1	6	(10)	8.6818855	3	2.2	1.5
	7	1	6	6	1	5	(00)	8.9532328	0	0.5	0.8
	7	1	6	6	1	5	(10)	8.9317129	2	-0.8	-1.2
	7	2	6	6	2	5	(00)	8.8082801	-2	-1.4	-1.3
	7	2	6	6	2	5	(10)	8.8136546	-2	-0.7	-1.0
	7	2	5	6	2	4	(00)	8.8197921	2	1.8	2.0
	7	2	5	6	2	4	(10)	8.8135001	1	-0.9	-1.4
	8	0	8	7	0	7	(00)	10.0512088	1	1.5	1.7
	8	0	8	7	0	7	(10)	10.0502853	-3	2.0	2.8
	8	1	8	7	1	7	(00)	9.8974691	2	2.2	2.4
	8	1	8	7	1	7	(10)	9.9125064	-1	-2.4	-3.2
	8	1	7	7	1	6	(00)	10.2311946	0	-0.3	-0.3
	8	1	7	7	1	6	(10)	10.2152082	-3	-5.2	-5.8
	8	2	7	7	2	6	(00)	10.0659176	3	2.6	2.6
	8	2	7	7	2	6	(10)	10.0740136	1	1.8	1.3
	8	2	6	7	2	5	(00)	10.0831611	1	0.6	0.6
	8	2	6	7	2	5	(10)	10.0740136	-4	-6.0	-6.6
	9	0	9	8	0	8	(00)	11.3024002	0	-0.1	0.0
	9	0	9	8	0	8	(10)	11.3013986	-3	0.9	1.5
	9	1	9	8	1	8	(00)	11.1333882	2	1.7	1.9
	9	1	9	8	1	8	(10)	11.1443693	1	-1.1	-2.0

Table 15 . 9 :

 159 Observed frequencies υ obs of 448 rotational transitions of conformer II of heptan-2-one. 97 additional frequencies of the (01), (11) and (12) species are marked grey, with υ obs -υ cal referring to the respective BELGI-C 1 and XIAM(1Top) fit, as well as to the respective absolute and relative XIAM(2Tops) fit.

	J'	K a ' K c '	J	K a	K c				υ obs -υ cal / kHz
	upper level			lower level	Species	υ obs / GHz	BELGI-C 1	XIAM (1Top)	XIAM (absolute)	XIAM (relative)
	2	0	2	1		1	(00)	3.1485604	1	1.4	1.4
	2	0	2	1		1	(10)	3.1485459	0	0.9	1.1
	3	0	3	2		2	(00)	4.7219324	0	0.1	0.0
	3	0	3	2		2	(10)	4.7219082	1	1.7	2.0
	3	1	3	2		2	(00)	4.6602309	0	0.2	0.2
	3	1	3	2		2	(10)	4.6790352	-1	1.3	1.3
	3	1	2	2		1	(00)	4.7860860	0	0.2	0.2
	3	1	2	2		1	(10)	4.7674331	1	-0.3	-0.4
	4	0	4	3		3	(00)	6.2942187	0	-0.6	-0.6
	4	0	4	3		3	(10)	6.2941777	1	2.0	2.3
	4	1	4	3		3	(00)	6.2132102	0	0.2	0.1
	4	1	4	3		3	(10)	6.2242566	0	2.5	2.5

Table 16 . 2 :

 162 Rotational constants of the C 1 conformer of octan-2-one calculated at different levels of theory using the Gaussian09 package[62]. ΔA, ΔB and ΔC are the relative deviations of the calculated values from the experimental ones.

	Method/Basis Set	A / GHz	ΔA / %	B / GHz	ΔB / %	C / GHz	ΔC / %
	MP2/6-311G(d,p)	4.065	-2.83	0.534	0.99	0.513	1.12
	MP2/6-311+G(d,p)	3.977	-4.93	0.535	1.33	0.516	1.66
	MP2/6-311++G(d,p)	3.962	-5.29	0.536	1.42	0.517	1.78
	MP2/6-311G(df,pd)	4.079	-2.49	0.538	1.74	0.517	1.85
	MP2/6-311+G(df,pd)	3.991	-4.61	0.539	2.06	0.520	2.39
	MP2/6-311++G(df,pd)	3.979	-4.89	0.540	2.14	0.520	2.48
	MP2/6-311G(3df,3pd)	4.128	-1.32	0.540	2.19	0.518	2.04
	MP2/6-311G+(3df,3pd)	4.069	-2.75	0.540	2.18	0.519	2.26
	MP2/6-311G++(3df,3pd)	4.065	-2.84	0.540	2.22	0.519	2.30
	MP2/cc-pVDZ	4.139	-1.07	0.529	0.16	0.508	0.00
	MP2/cc-pVTZ	4.115	-1.65	0.538	1.80	0.517	1.81
	B3LYP/6-311G(d,p)	4.224	0.98	0.518	-1.87	0.499	-1.72
	B3LYP/6-311+G(d,p)	4.146	-0.89	0.518	-1.96	0.500	-1.49
	B3LYP/6-311++G(d,p)	4.147	-0.87	0.518	-1.95	0.500	-1.49
	B3LYP/6-311G(df,pd)	4.223	0.95	0.520	-1.53	0.501	-1.35
	B3LYP/6-311+G(df,pd)	4.148	-0.85	0.520	-1.60	0.502	-1.12
	B3LYP/6-311++G(df,pd)	4.146	-0.91	0.520	-1.58	0.502	-1.10
	B3LYP/6-311G(3df,3pd)	4.225	1.00	0.521	-1.37	0.502	-1.19
	B3LYP/6-311G+(3df,3pd)	4.171	-0.30	0.520	-1.55	0.502	-1.11
	B3LYP/6-311G++(3df,3pd)	4.170	-0.31	0.520	-1.55	0.502	-1.10
	B3LYP/cc-pVDZ	4.236	1.26	0.518	-1.87	0.498	-1.87
	B3LYP/cc-pVTZ	4.212	0.67	0.520	-1.63	0.501	-1.30
	B3PW91/6-311G(d,p)	4.208	0.59	0.523	-1.00	0.504	-0.73
	B3PW91/6-311+G(d,p)	4.152	-0.75	0.523	-1.06	0.505	-0.57
	B3PW91/6-311++G(d,p)	4.152	-0.75	0.523	-1.05	0.505	-0.57
	B3PW91/6-311G(df,pd)	4.207	0.57	0.525	-0.65	0.506	-0.38
	B3PW91/6-311+G(df,pd)	4.152	-0.74	0.525	-0.71	0.507	-0.22
	B3PW91/6-311++G(df,pd)	4.150	-0.80	0.525	-0.68	0.507	-0.19
	B3PW91/6-311G(3df,3pd)	4.219	0.86	0.526	-0.53	0.506	-0.28
	B3PW91/6-311G+(3df,3pd)	4.178	-0.13	0.525	-0.70	0.506	-0.24
	B3PW91/6-311G++(3df,3pd)	4.177	-0.15	0.525	-0.70	0.506	-0.24
	B3PW91/cc-pVDZ	4.216	0.78	0.522	-1.16	0.503	-1.01
	B3PW91/cc-pVTZ	4.207	0.56	0.524	-0.84	0.505	-0.45
	Exp. C 1 [a]

Table 16 . 3 :

 163 Rotational constants of the C 1 conformer of octan-2-one calculated at different levels of theory using the Gaussian16 package[63]. ΔA, ΔB and ΔC are the relative deviations of the calculated values from the experimental ones.

	Method/Basis Set	A / GHz	ΔA / %	B / GHz	ΔB / %	C / GHz	ΔC / %
	B3LYP-D3/6-311G(d,p)	4.201	0.41	0.525	-0.56	0.504	-0.72
	B3LYP-D3/6-311+G(d,p)	4.117	-1.60	0.525	-0.55	0.506	-0.40
	B3LYP-D3/6-311++G(d,p)	4.117	-1.59	0.525	-0.54	0.506	-0.40
	B3LYP-D3/6-311G(df,pd)	4.201	0.42	0.527	-0.23	0.506	-0.37
	B3LYP-D3/6-311+G(df,pd)	4.116	-1.63	0.527	-0.19	0.508	-0.02
	B3LYP-D3/6-311++G(df,pd)	4.113	-1.69	0.527	-0.16	0.508	0.01
	B3LYP-D3/6-311G(3df,3pd)	4.198	0.35	0.528	-0.05	0.507	-0.17
	B3LYP-D3/6-311+G(3df,3pd)	4.143	-0.97	0.527	-0.16	0.507	-0.03
	B3LYP-D3/6-311++G(3df,3pd)	4.142	-0.98	0.527	-0.16	0.508	-0.03
	B3LYP-D3/cc-pVDZ	4.207	0.56	0.525	-0.59	0.503	-0.87
	B3LYP-D3/cc-pVTZ	4.191	0.18	0.527	-0.31	0.506	-0.31
	B3LYP-D3/aug-cc-pVDZ	4.098	-2.04	0.526	-0.41	0.506	-0.31
	B3LYP-D3/aug-cc-pVTZ	4.146	-0.90	0.527	-0.20	0.507	-0.08
	B3LYP-D3BJ/6-311G(d,p)	4.181	-0.07	0.526	-0.49	0.505	-0.47
	B3LYP-D3BJ/6-311+G(d,p)	4.096	-2.10	0.526	-0.48	0.507	-0.15
	B3LYP-D3BJ/6-311++G(d,p)	4.097	-2.08	0.526	-0.49	0.507	-0.16
	B3LYP-D3BJ/6-311G(df,pd)	4.181	-0.07	0.528	-0.14	0.507	-0.10
	B3LYP-D3BJ/6-311+G(df,pd)	4.094	-2.13	0.528	-0.11	0.509	0.24
	B3LYP-D3BJ/6-311++G(df,pd)	4.091	-2.21	0.528	-0.08	0.509	0.27
	B3LYP-D3BJ/6-311G(3df,3pd)	4.178	-0.14	0.529	0.05	0.508	0.10
	B3LYP-D3BJ/6-311+G(3df,3pd)	4.123	-1.45	0.528	-0.09	0.509	0.22
	B3LYP-D3BJ/6-311++G(3df,3pd)	4.122	-1.47	0.528	-0.08	0.509	0.23
	B3LYP-D3BJ/cc-pVDZ	4.183	-0.01	0.526	-0.48	0.505	-0.59
	B3LYP-D3BJ/cc-pVTZ	4.169	-0.34	0.527	-0.24	0.507	-0.05
	B3LYP-D3BJ/aug-cc-pVDZ	4.079	-2.50	0.526	-0.35	0.507	-0.07
	B3LYP-D3BJ/aug-cc-pVTZ	4.126	-1.38	0.528	-0.13	0.509	0.17
	M06-2X/6-311G(d,p)	4.203	0.47	0.533	0.87	0.511	0.71
	M06-2X/6-311+G(d,p)	4.137	-1.12	0.534	1.01	0.513	1.03
	M06-2X/6-311++G(d,p)	4.138	-1.09	0.534	0.99	0.513	1.01
	M06-2X/6-311G(df,pd)	4.203	0.46	0.534	1.14	0.513	0.98
	M06-2X/6-311+G(df,pd)	4.135	-1.17	0.535	1.31	0.514	1.33
	M06-2X/6-311++G(df,pd)	4.134	-1.20	0.535	1.31	0.514	1.34
	M06-2X/6-311G(3df,3pd)	4.206	0.53	0.535	1.30	0.513	1.13
	M06-2X/6-311+G(3df,3pd)	4.164	-0.47	0.535	1.27	0.514	1.26
	M06-2X/6-311++G(3df,3pd)	4.164	-0.47	0.535	1.27	0.514	1.26
	M06-2X/cc-pVDZ	4.221	0.89	0.533	0.90	0.511	0.59
	M06-2X/cc-pVTZ	4.206	0.54	0.534	1.08	0.513	1.03
	M06-2X/aug-cc-pVDZ	4.110	-1.77	0.535	1.33	0.514	1.29
	M06-2X/aug-cc-pVTZ	4.171	-0.30	0.535	1.23	0.514	1.24
	Exp. C 1 [a]

Table 16 . 4 :

 164 Rotational constants of the C s conformer of octan-2-one calculated at different levels of theory using the Gaussian09 package[62]. ΔA, ΔB and ΔC are the relative deviations of the calculated values from the experimental ones.

	Method/Basis Set	A / GHz	ΔA / %	B / GHz	ΔB / %	C / GHz	ΔC / %
	MP2/6-311G(d,p)	6.279	-0.47	0.438	0.05	0.417	0.04
	MP2/6-311+G(d,p)	6.258	-0.80	0.438	-0.04	0.417	-0.02
	MP2/6-311++G(d,p)	6.261	-0.76	0.438	-0.03	0.417	-0.03
	MP2/6-311G(df,pd)	6.315	0.10	0.441	0.65	0.420	0.65
	MP2/6-311+G(df,pd)	6.294	-0.22	0.440	0.55	0.419	0.58
	MP2/6-311++G(df,pd)	6.296	-0.20	0.440	0.55	0.419	0.58
	MP2/6-311G(3df,3pd)	6.348	0.63	0.442	1.01	0.421	0.92
	MP2/6-311G+(3df,3pd)	6.339	0.48	0.442	0.87	0.420	0.78
	MP2/6-311G++(3df,3pd)	6.339	0.48	0.442	0.88	0.420	0.79
	MP2/cc-pVDZ	6.249	-0.94	0.436	-0.32	0.415	-0.41
	MP2/cc-pVTZ	6.330	0.35	0.442	0.84	0.420	0.75
	B3LYP/6-311G(d,p)	6.340	0.50	0.433	-1.03	0.413	-1.02
	B3LYP/6-311+G(d,p)	6.330	0.35	0.433	-1.17	0.412	-1.14
	B3LYP/6-311++G(d,p)	6.332	0.38	0.433	-1.17	0.412	-1.14
	B3LYP/6-311G(df,pd)	6.353	0.70	0.435	-0.73	0.414	-0.72
	B3LYP/6-311+G(df,pd)	6.342	0.53	0.434	-0.87	0.414	-0.83
	B3LYP/6-311++G(df,pd)	6.345	0.57	0.434	-0.86	0.414	-0.83
	B3LYP/6-311G(3df,3pd)	6.374	1.04	0.435	-0.58	0.415	-0.57
	B3LYP/6-311G+(3df,3pd)	6.365	0.90	0.435	-0.71	0.414	-0.70
	B3LYP/6-311G++(3df,3pd)	6.365	0.90	0.435	-0.71	0.414	-0.70
	B3LYP/cc-pVDZ	6.302	-0.10	0.433	-1.04	0.413	-1.05
	B3LYP/cc-pVTZ	6.365	0.89	0.435	-0.67	0.414	-0.67
	B3PW91/6-311G(d,p)	6.356	0.76	0.437	-0.28	0.416	-0.27
	B3PW91/6-311+G(d,p)	6.347	0.62	0.436	-0.40	0.416	-0.37
	B3PW91/6-311++G(d,p)	6.350	0.65	0.436	-0.39	0.415	-0.38
	B3PW91/6-311G(df,pd)	6.366	0.91	0.438	0.00	0.417	0.01
	B3PW91/6-311+G(df,pd)	6.357	0.77	0.437	-0.12	0.417	-0.09
	B3PW91/6-311++G(df,pd)	6.359	0.80	0.437	-0.11	0.417	-0.09
	B3PW91/6-311G(3df,3pd)	6.388	1.26	0.439	0.16	0.418	0.15
	B3PW91/6-311G+(3df,3pd)	6.379	1.12	0.438	0.04	0.417	0.04
	B3PW91/6-311G++(3df,3pd)	6.379	1.12	0.438	0.04	0.417	0.04
	B3PW91/cc-pVDZ	6.327	0.30	0.436	-0.40	0.415	-0.42
	B3PW91/cc-pVTZ	6.378	1.10	0.438	0.05	0.417	0.03
	Exp. C s [a]

Table 16 . 5 :

 165 Rotational constants of the C s conformer of octan-2-one calculated at different levels of theory using the Gaussian16 package[63]. ΔA, ΔB and ΔC are the relative deviations of the calculated values from the experimental ones.

	Method/Basis Set	A / GHz	ΔA / %	B / GHz	ΔB / %	C / GHz	ΔC / %
	B3LYP-D3/6-311G(d,p)	6.331	0.36	0.435	-0.67	0.414	-0.68
	B3LYP-D3/6-311+G(d,p)	6.318	0.16	0.434	-0.80	0.414	-0.78
	B3LYP-D3/6-311++G(d,p)	6.320	0.18	0.434	-0.80	0.414	-0.79
	B3LYP-D3/6-311G(df,pd)	6.343	0.54	0.436	-0.37	0.415	-0.38
	B3LYP-D3/6-311+G(df,pd)	6.331	0.36	0.436	-0.51	0.415	-0.48
	B3LYP-D3/6-311++G(df,pd)	6.333	0.38	0.436	-0.50	0.415	-0.49
	B3LYP-D3/6-311G(3df,3pd)	6.365	0.90	0.437	-0.23	0.416	-0.24
	B3LYP-D3/6-311+G(3df,3pd)	6.357	0.77	0.436	-0.35	0.416	-0.37
	B3LYP-D3/6-311++G(3df,3pd)	6.357	0.78	0.436	-0.35	0.416	-0.37
	B3LYP-D3/cc-pVDZ	6.293	-0.25	0.435	-0.68	0.414	-0.71
	B3LYP-D3/cc-pVTZ	6.356	0.75	0.436	-0.31	0.416	-0.33
	B3LYP-D3/aug-cc-pVDZ	6.296	-0.20	0.434	-0.79	0.414	-0.79
	B3LYP-D3/aug-cc-pVTZ	6.355	0.73	0.436	-0.36	0.415	-0.38
	B3LYP-D3BJ/6-311G(d,p)	6.335	0.43	0.436	-0.51	0.415	-0.51
	B3LYP-D3BJ/6-311+G(d,p)	6.324	0.24	0.435	-0.64	0.414	-0.62
	B3LYP-D3BJ/6-311++G(d,p)	6.325	0.26	0.435	-0.64	0.414	-0.62
	B3LYP-D3BJ/6-311G(df,pd)	6.347	0.61	0.437	-0.20	0.416	-0.20
	B3LYP-D3BJ/6-311+G(df,pd)	6.336	0.44	0.436	-0.34	0.416	-0.31
	B3LYP-D3BJ/6-311++G(df,pd)	6.337	0.46	0.436	-0.34	0.416	-0.31
	B3LYP-D3BJ/6-311G(3df,3pd)	6.373	1.02	0.438	-0.05	0.417	-0.07
	B3LYP-D3BJ/6-311+G(3df,3pd)	6.361	0.83	0.437	-0.18	0.416	-0.19
	B3LYP-D3BJ/6-311++G(3df,3pd)	6.361	0.83	0.437	-0.18	0.416	-0.19
	B3LYP-D3BJ/cc-pVDZ	6.300	-0.13	0.436	-0.52	0.415	-0.56
	B3LYP-D3BJ/cc-pVTZ	6.364	0.87	0.437	-0.14	0.416	-0.16
	B3LYP-D3BJ/aug-cc-pVDZ	6.301	-0.12	0.435	-0.64	0.414	-0.63
	B3LYP-D3BJ/aug-cc-pVTZ	6.359	0.79	0.437	-0.19	0.416	-0.20
	M06-2X/6-311G(d,p)	6.360	0.81	0.440	0.41	0.419	0.39
	M06-2X/6-311+G(d,p)	6.350	0.65	0.439	0.31	0.418	0.31
	M06-2X/6-311++G(d,p)	6.352	0.70	0.439	0.31	0.418	0.30
	M06-2X/6-311G(df,pd)	6.367	0.92	0.441	0.63	0.420	0.61
	M06-2X/6-311+G(df,pd)	6.357	0.77	0.440	0.53	0.419	0.53
	M06-2X/6-311++G(df,pd)	6.360	0.81	0.440	0.53	0.419	0.52
	M06-2X/6-311G(3df,3pd)	6.392	1.33	0.441	0.75	0.420	0.72
	M06-2X/6-311+G(3df,3pd)	6.386	1.23	0.441	0.65	0.420	0.61
	M06-2X/6-311++G(3df,3pd)	6.386	1.23	0.441	0.65	0.420	0.61
	M06-2X/cc-pVDZ	6.338	0.47	0.440	0.44	0.419	0.40
	M06-2X/cc-pVTZ	6.384	1.20	0.441	0.73	0.420	0.69
	M06-2X/aug-cc-pVDZ	6.339	0.49	0.439	0.35	0.418	0.34
	M06-2X/aug-cc-pVTZ	6.383	1.19	0.441	0.70	0.420	0.66
	Exp. C s [a]

Table 16 . 6 :

 166 Fourier coefficients (in Hartree) of the potential energy curves of the acetyl methyl group and the hexyl methyl group of the two assigned conformers of octan-2-one calculated at the MP2/6-311++G(d,p) and B3LYP/6-311++G(d,p) level of theory, respectively. The potential was expanded in a one-dimensional Fourier expansion as V(α) = a 0 + ∑ a n cos (3nα)

			5 n=1	+ ∑ b m sin (3mα) 5 m=1 .
				Acetyl Methyl Group
		C 1 Conformer		C s Conformer
		MP2/6-311++G(d,p)	B3LYP/6-311++G(d,p)	MP2/6-311++G(d,p)	B3LYP/6-311++G(d,p)
	a 0	-388.635064525		-389.839582650	-388.634382298	-389.840020813
	a 1	0.000401669		0.000313881	0.000327684	0.000268086
	a 2	0.000053377		0.000043365	0.000094335	0.000047466
	a 3	-0.000012523		-0.000008247	-0.000029086	-0.000009050
	a 4	0.000005010		0.000002428	0.000013319	0.000002767
	a 5				-0.000005491	-0.000001152
	b 1	-0.000254678		-0.000163444
	b 2	0.000077579		0.000049706
	b 3	-0.000017669		-0.000008526
				Hexyl Methyl Group
		C 1 Conformer		C s Conformer
		MP2/6-311++G(d,p)	B3LYP/6-311++G(d,p)	MP2/6-311++G(d,p)	B3LYP/6-311++G(d,p)
	a 0	-388.633285083		-389.837758450	-388.632307583	-389.838002675
	a 1	0.002409193		0.002268471	0.002399412	0.002267712
	a 2	0.000062258		0.000043192	0.000058742	0.000040742

Table 16 . 8 :

 168 380 observed frequencies of the C 1 conformer of octan-2-one, with the υ obs -υ cal values referring to the respective BELGI-C 1 and XIAM(1Top) fit. 135 additional transitions have been added to the XIAM(2Tops) fit (marked grey).

	J' upper level K a ' K c '	J	K a lower level K c	Species	υ obs / GHz	υ obs -υ cal / kHz BELGI-C 1 XIAM (1Top) XIAM (2Tops)
	5	0	5	4	4	(00)	5.1780561	4	3.6	3.7
	5	1	5	4	4	(00)	5.1278585	0	-0.1	0.1
	5	1	5	4	4	(10)	5.1369387	0	0.5	0.7
	5	1	4	4	3	(00)	5.2309986	1	0.8	0.9
	5	1	4	4	3	(10)	5.2220790	-3	-3.2	-3.1
	6	0	6	5	5	(00)	6.2126951	4	3.8	3.9
	6	1	6	5	5	(00)	6.1531789	-1	-1.3	-1.1
	6	1	6	5	5	(10)	6.1592369	-1	-0.5	-0.3
	6	1	5	5	4	(00)	6.2769395	2	2.2	2.3
	6	1	5	5	4	(10)	6.2710768	-1	-1.9	-1.7
	7	0	7	6	6	(00)	7.2468008	-1	-0.9	-0.8
	7	1	7	6	6	(00)	7.1783676	0	0.1	0.4
	7	1	7	6	6	(10)	7.1824825	-1	-0.4	-0.2
	7	1	6	6	5	(00)	7.3227347	2	1.8	1.9
	7	1	6	6	5	(10)	7.3188510	0	-0.6	-0.3
	8	0	8	7	7	(00)	8.2802986	1	0.8	0.9
	8	0	8	7	7	(10)	8.2802856	-2	-1.2	-0.9
	8	1	8	7	7	(00)	8.2033988	-1	-0.9	-0.7
	8	1	8	7	7	(10)	8.2063033	-1	-0.2	0.0
	8	1	7	7	6	(00)	8.3683589	0	0.0	0.2
	8	1	7	7	6	(10)	8.3657258	0	-0.2	0.0
	8	2	7	7	6	(00)	8.2866359	0	-0.1	0.1
	8	2	7	7	6	(10)	8.2902746	-1	-0.9	-0.6
	8	2	6	7	5	(00)	8.2939296	-1	-0.6	-0.4
	8	2	6	7	5	(10)	8.2905164	0	0.1	0.3
	9	0	9	8	8	(00)	9.3130930	-2	-2.6	-2.4
	9	0	9	8	8	(10)	9.3130754	3	3.8	4.0
	9	1	9	8	8	(00)	9.2282562	-1	-0.9	-0.8
	9	1	9	8	8	(10)	9.2303962	0	0.2	0.3
	9	1	8	8	7	(00)	9.4137888	0	0.0	0.3
	9	1	8	8	7	(10)	9.4119601	1	0.7	1.0
	9	2	8	8	7	(00)	9.3220597	0	0.3	0.5
	9	2	8	8	7	(10)	9.3270863	-3	-2.7	-2.4
	9	2	7	8	6	(00)	9.3324672	-1	-0.6	-0.4
	9	2	7	8	6	(10)	9.3276953	0	0.2	0.5
	9	3	7	8	6	(10)	9.3253446	-2	-3.1	-2.6
	9	3	6	8	5	(10)	9.3253446	2	1.3	1.7
	10	0	10	9	9	(00)	10.3451114	-2	-2.2	-2.1
	10	0	10	9	9	(10)	10.3450721	0	-0.1	0.0
	10	1	10	9	9	(00)	10.2529172	-3	-3.5	-3.5
	10	1	10	9	9	(10)	10.2545660	-1	-0.4	-0.4
	10	1	9	9	8	(00)	10.4589954	0	0.4	0.7
	10	1	9	9	8	(10)	10.4577004	1	0.8	1.2
	10	2	9	9	8	(00)	10.3573413	1	1.6	1.9
	10	2	9	9	8	(10)	10.3639595	-2	-1.8	-1.5
	10	2	8	9	7	(00)	10.3716282	0	-0.4	-0.2
	10	2	8	9	7	(10)	10.3652957	-1	-0.3	0.0
	10	3	8	9	7	(00)	10.3615735	3	3.5	3.8
	10	3	8	9	7	(10)	10.3618005	1	0.3	0.8
	10	3	7	9	6	(00)	10.3617466	-5	-4.9	-4.5
	10	3	7	9	6	(10)	10.3617876	-1	-1.6	-1.2
	11	0	11	10	10	(00)	11.3762741	0	-0.3	-0.2
	11	0	11	10	10	(10)	11.3762099	-1	-0.4	-0.3
	11	1	11	10	10	(00)	11.2773716	-1	-0.9	-1.0

Table 16 . 9 :

 169 244 observed frequencies of the C s conformer of octan-2-one, with the υ obs -υ cal values referring to the respective BELGI-C s and XIAM(1Top) fit. 87 additional transitions have been added to the XIAM(2Tops) fit (marked grey).

	J' upper level K a ' K c '	J	K a lower level K c	Species	υ obs / GHz	υ obs -υ cal / kHz BELGI-C s XIAM (1Top) XIAM (2Tops)
	5	0	5	4		0	4	(00)	4.2734750	-1	-1.0	-1.2
	5	1	5	4		1	4	(00)	4.2223618	4	3.4	3.2
	5	1	4	4		1	3	(00)	4.3263110	0	-0.2	-0.5
	6	0	6	5		0	5	(00)	5.1275659	1	1.2	0.9
	6	1	6	5		1	5	(00)	5.0666803	2	1.4	1.2
	6	1	6	5		1	5	(10)	5.0950036	2	2.8	2.7
	6	1	5	5		1	4	(00)	5.1914194	1	0.5	0.1
	6	1	5	5		1	4	(10)	5.1628733	1	0.6	0.3
	7	0	7	6		0	6	(00)	5.9813217	-1	-1.3	-1.6
	7	1	7	6		1	6	(00)	5.9109167	-1	-0.9	-1.2
	7	1	7	6		1	6	(10)	5.9354101	1	1.5	1.4
	7	1	6	6		1	5	(00)	6.0564424	1	0.8	0.4
	7	1	6	6		1	5	(10)	6.0316860	3	3.3	2.9
	8	0	8	7		0	7	(00)	6.8346989	3	2.5	2.3
	8	1	8	7		1	7	(00)	6.7550587	-3	-3.0	-3.3
	8	1	8	7		1	7	(10)	6.7752694	5	5.2	5.1
	8	1	7	7		1	6	(00)	6.9213622	-2	-2.2	-2.4
	8	1	7	7		1	6	(10)	6.9008483	0	0.5	0.2
	9	0	9	8		0	8	(00)	7.6876327	2	2.1	1.9
	9	1	9	8		1	8	(00)	7.5990987	0	0.1	-0.2
	9	1	9	8		1	8	(10)	7.6153274	2	1.9	1.8
	9	1	8	8		1	7	(00)	7.7861674	-4	-4.6	-4.8
	9	1	8	8		1	7	(10)	7.7695843	2	2.4	2.2
	10	0	10	9		0	9	(00)	8.5400724	0	-0.1	-0.2
	10	1	10	9		1	9	(00)	8.4430166	1	0.5	0.3
	10	1	10	9		1	9	(10)	8.4559021	-1	-1.0	-1.0
	10	1	9	9		1	8	(00)	8.6508497	1	0.8	0.8
	10	1	9	9		1	8	(10)	8.6375452	-2	-1.2	-1.3
	11	0	11	10	0	10	(00)	9.3919690	0	-0.4	-0.4
	11	1	11	10	1	10	(00)	9.2868014	-1	-0.7	-1.0
	11	1	11	10	1	10	(10)	9.2970225	0	0.7	0.7
	11	1	10	10	1	9	(00)	9.5153798	1	0.7	0.9
	11	1	10	10	1	9	(10)	9.5046876	-1	-1.0	-0.8
	12	0	12	11	0	11	(00)	10.2432680	-2	-2.2	-2.1
	12	1	12	11	1	11	(00)	10.1304433	-2	-2.1	-2.4
	12	1	12	11	1	11	(10)	10.1385877	4	4.6	4.6
	12	1	11	11	1	10	(00)	10.3797437	-2	-2.4	-2.0
	12	1	11	11	1	10	(10)	10.3710808	2	1.9	2.3
	13	0	13	12	0	12	(00)	11.0939225	-3	-2.9	-2.7

Table 17 . 2 :

 172 Rotational constants of the ap conformer of 3-penten-2-one calculated with the Gaussian09 package[62] at different levels of theory. ΔA, ΔB and ΔC are the deviations of calculated values from the experimental ones.

	Method/Basis Set	A / GHz	ΔA / %	B / GHz	ΔB / %	C / GHz	ΔC / %
	MP2/6-311G(d,p)	8.332	-0.44	1.910	-0.24	1.584	-0.29
	MP2/6-311+G(d,p)	8.328	-0.48	1.910	-0.20	1.584	-0.26
	MP2/6-311++G(d,p)	8.328	-0.48	1.910	-0.20	1.584	-0.26
	MP2/6-311G(df,pd)	8.384	0.18	1.922	0.42	1.594	0.37
	MP2/6-311+G(df,pd)	8.382	0.15	1.922	0.41	1.594	0.36
	MP2/6-311++G(df,pd)	8.380	0.14	1.922	0.42	1.594	0.36
	MP2/6-311G(3df,3pd)	8.416	0.56	1.928	0.72	1.599	0.68
	MP2/6-311G+(3df,3pd)	8.412	0.51	1.927	0.68	1.599	0.64
	MP2/6-311G++(3df,3pd)	8.412	0.51	1.927	0.69	1.599	0.64
	MP2/cc-pVDZ	8.273	-1.14	1.895	-1.00	1.572	-1.02
	MP2/cc-pVTZ	8.404	0.42	1.927	0.69	1.599	0.62
	B3LYP/6-311G(d,p)	8.367	-0.02	1.906	-0.44	1.583	-0.38
	B3LYP/6-311+G(d,p)	8.371	0.03	1.906	-0.42	1.583	-0.36
	B3LYP/6-311++G(d,p)	8.371	0.02	1.906	-0.41	1.583	-0.35
	B3LYP/6-311G(df,pd)	8.390	0.25	1.911	-0.16	1.587	-0.11
	B3LYP/6-311+G(df,pd)	8.393	0.29	1.912	-0.13	1.587	-0.07
	B3LYP/6-311++G(df,pd)	8.393	0.29	1.912	-0.13	1.588	-0.07
	B3LYP/6-311G(3df,3pd)	8.414	0.54	1.915	0.05	1.591	0.12
	B3LYP/6-311G+(3df,3pd)	8.412	0.51	1.915	0.06	1.591	0.12
	B3LYP/6-311G++(3df,3pd)	8.412	0.51	1.915	0.06	1.591	0.12
	B3LYP/cc-pVDZ	8.326	-0.51	1.897	-0.89	1.576	-0.83
	B3LYP/cc-pVTZ	8.406	0.44	1.914	0.00	1.589	0.05
	B3PW91/6-311G(d,p)	8.402	0.39	1.916	0.10	1.591	0.14
	B3PW91/6-311+G(d,p)	8.406	0.45	1.917	0.13	1.592	0.18
	B3PW91/6-311++G(d,p)	8.406	0.44	1.917	0.14	1.592	0.18
	B3PW91/6-311G(df,pd)	8.421	0.62	1.921	0.35	1.595	0.39
	B3PW91/6-311+G(df,pd)	8.425	0.67	1.922	0.39	1.595	0.43
	B3PW91/6-311++G(df,pd)	8.425	0.67	1.922	0.40	1.596	0.44
	B3PW91/6-311G(3df,3pd)	8.444	0.90	1.925	0.58	1.599	0.62
	B3PW91/6-311G+(3df,3pd)	8.443	0.88	1.926	0.61	1.599	0.65
	B3PW91/6-311G++(3df,3pd)	8.443	0.88	1.926	0.61	1.599	0.65
	B3PW91/cc-pVDZ	8.363	-0.06	1.906	-0.42	1.583	-0.36
	B3PW91/cc-pVTZ	8.435	0.79	1.924	0.53	1.598	0.56
	Exp. ap

Table 17 . 3 :

 173 Rotational constants of the ap conformer of 3-penten-2-one calculated with the Gaussian16 package[63] at different levels of theory. ΔA, ΔB and ΔC are the deviations of calculated values from the experimental ones.

	Method/Basis Set	A / GHz	ΔA / %	B / GHz	ΔB / %	C / GHz	ΔC / %
	B3LYP-D3/6-311G(d,p)	8.367	-0.02	1.908	-0.34	1.584	-0.30
	B3LYP-D3/6-311+G(d,p)	8.370	0.02	1.908	-0.32	1.584	-0.27
	B3LYP-D3/6-311++G(d,p)	8.370	0.02	1.908	-0.31	1.584	-0.27
	B3LYP-D3/6-311G(df,pd)	8.390	0.25	1.913	-0.06	1.588	-0.02
	B3LYP-D3/6-311+G(df,pd)	8.393	0.28	1.913	-0.04	1.589	0.00
	B3LYP-D3/6-311++G(df,pd)	8.392	0.28	1.913	-0.03	1.589	0.01
	B3LYP-D3/6-311G(3df,3pd)	8.413	0.53	1.917	0.15	1.592	0.20
	B3LYP-D3/6-311+G(3df,3pd)	8.411	0.50	1.917	0.16	1.592	0.20
	B3LYP-D3/6-311++G(3df,3pd)	8.411	0.50	1.917	0.16	1.592	0.20
	B3LYP-D3/cc-pVDZ	8.325	-0.52	1.899	-0.79	1.577	-0.74
	B3LYP-D3/cc-pVTZ	8.405	0.44	1.916	0.10	1.591	0.14
	B3LYP-D3/aug-cc-pVDZ	8.337	-0.38	1.902	-0.66	1.579	-0.61
	B3LYP-D3/aug-cc-pVTZ	8.407	0.46	1.916	0.12	1.591	0.16
	B3LYP-D3BJ/6-311G(d,p)	8.377	0.10	1.914	-0.03	1.588	-0.02
	B3LYP-D3BJ/6-311+G(d,p)	8.381	0.14	1.914	-0.01	1.589	0.00
	B3LYP-D3BJ/6-311++G(d,p)	8.380	0.14	1.914	0.00	1.589	0.01
	B3LYP-D3BJ/6-311G(df,pd)	8.400	0.37	1.919	0.25	1.593	0.26
	B3LYP-D3BJ/6-311+G(df,pd)	8.403	0.41	1.919	0.28	1.593	0.29
	B3LYP-D3BJ/6-311++G(df,pd)	8.403	0.40	1.920	0.28	1.593	0.29
	B3LYP-D3BJ/6-311G(3df,3pd)	8.424	0.66	1.923	0.47	1.596	0.49
	B3LYP-D3BJ/6-311+G(3df,3pd)	8.421	0.63	1.923	0.48	1.596	0.49
	B3LYP-D3BJ/6-311++G(3df,3pd)	8.421	0.63	1.923	0.48	1.596	0.49
	B3LYP-D3BJ/cc-pVDZ	8.335	-0.40	1.905	-0.49	1.581	-0.47
	B3LYP-D3BJ/cc-pVTZ	8.416	0.56	1.922	0.42	1.595	0.43
	B3LYP-D3BJ/aug-cc-pVDZ	8.347	-0.26	1.907	-0.36	1.583	-0.34
	B3LYP-D3BJ/aug-cc-pVTZ	8.417	0.58	1.923	0.44	1.596	0.45
	M06-2X/6-311G(d,p)	8.417	0.57	1.925	0.58	1.598	0.57
	M06-2X/6-311+G(d,p)	8.419	0.60	1.925	0.59	1.598	0.59
	M06-2X/6-311++G(d,p)	8.419	0.60	1.925	0.59	1.598	0.59
	M06-2X/6-311G(df,pd)	8.433	0.76	1.929	0.76	1.601	0.76
	M06-2X/6-311+G(df,pd)	8.435	0.80	1.929	0.78	1.601	0.78
	M06-2X/6-311++G(df,pd)	8.435	0.79	1.929	0.79	1.601	0.79
	M06-2X/6-311G(3df,3pd)	8.456	1.05	1.933	0.97	1.604	0.98
	M06-2X/6-311+G(3df,3pd)	8.454	1.02	1.933	0.98	1.604	0.98
	M06-2X/6-311++G(3df,3pd)	8.454	1.02	1.933	0.98	1.604	0.98
	M06-2X/cc-pVDZ	8.386	0.21	1.919	0.26	1.593	0.27
	M06-2X/cc-pVTZ	8.453	1.00	1.933	1.01	1.605	1.01
	M06-2X/aug-cc-pVDZ	8.393	0.29	1.921	0.36	1.594	0.36
	M06-2X/aug-cc-pVTZ	8.454	1.02	1.934	1.02	1.605	1.02
	Exp. ap

Table 17 . 4 :

 174 Rotational constants of the sp conformer of 3-penten-2-one calculated with the Gaussian09 package[62] at different levels of theory. ΔA, ΔB and ΔC are the deviations of calculated values from the experimental ones.

	Method/Basis Set	A / GHz	ΔA / %	B / GHz	ΔB / %	C / GHz	ΔC / %
	MP2/6-311G(d,p)	9.106	-0.57	1.859	-0.17	1.574	-0.26
	MP2/6-311+G(d,p)	9.070	-0.96	1.857	-0.29	1.571	-0.43
	MP2/6-311++G(d,p)	9.070	-0.96	1.857	-0.29	1.571	-0.43
	MP2/6-311G(df,pd)	9.159	0.00	1.871	0.48	1.584	0.38
	MP2/6-311+G(df,pd)	9.128	-0.33	1.869	0.34	1.581	0.20
	MP2/6-311++G(df,pd)	9.128	-0.33	1.869	0.34	1.581	0.20
	MP2/6-311G(3df,3pd)	9.187	0.31	1.875	0.65	1.587	0.56
	MP2/6-311G+(3df,3pd)	9.153	-0.06	1.873	0.56	1.585	0.43
	MP2/6-311G++(3df,3pd)	9.153	-0.06	1.873	0.56	1.585	0.42
	MP2/cc-pVDZ	9.040	-1.29	1.847	-0.82	1.564	-0.91
	MP2/cc-pVTZ	9.149	-0.10	1.875	0.70	1.587	0.53
	B3LYP/6-311G(d,p)	9.194	0.39	1.857	-0.27	1.575	-0.20
	B3LYP/6-311+G(d,p)	9.164	0.06	1.855	-0.38	1.573	-0.34
	B3LYP/6-311++G(d,p)	9.164	0.06	1.855	-0.38	1.573	-0.34
	B3LYP/6-311G(df,pd)	9.208	0.54	1.862	0.00	1.579	0.06
	B3LYP/6-311+G(df,pd)	9.181	0.25	1.861	-0.10	1.577	-0.08
	B3LYP/6-311++G(df,pd)	9.181	0.24	1.861	-0.10	1.577	-0.08
	B3LYP/6-311G(3df,3pd)	9.232	0.80	1.864	0.10	1.581	0.18
	B3LYP/6-311G+(3df,3pd)	9.201	0.47	1.863	0.05	1.579	0.08
	B3LYP/6-311G++(3df,3pd)	9.201	0.47	1.863	0.05	1.579	0.08
	B3LYP/cc-pVDZ	9.141	-0.19	1.851	-0.61	1.569	-0.56
	B3LYP/cc-pVTZ	9.206	0.52	1.864	0.07	1.580	0.11
	B3PW91/6-311G(d,p)	9.225	0.73	1.868	0.31	1.584	0.35
	B3PW91/6-311+G(d,p)	9.201	0.46	1.866	0.22	1.582	0.23
	B3PW91/6-311++G(d,p)	9.200	0.46	1.866	0.22	1.582	0.23
	B3PW91/6-311G(df,pd)	9.235	0.84	1.873	0.54	1.587	0.57
	B3PW91/6-311+G(df,pd)	9.214	0.60	1.871	0.46	1.586	0.46
	B3PW91/6-311++G(df,pd)	9.213	0.60	1.871	0.47	1.586	0.46
	B3PW91/6-311G(3df,3pd)	9.259	1.10	1.874	0.65	1.589	0.70
	B3PW91/6-311G+(3df,3pd)	9.232	0.80	1.874	0.61	1.588	0.62
	B3PW91/6-311G++(3df,3pd)	9.232	0.80	1.874	0.61	1.588	0.62
	B3PW91/cc-pVDZ	9.182	0.26	1.861	-0.07	1.578	-0.02
	B3PW91/cc-pVTZ	9.233	0.82	1.874	0.61	1.588	0.61
	Exp. sp

2X/6-311++G(d,p) Acetyl Group Propenyl Group Acetyl Group Propenyl Group

	5 n=1 Synperiplanar (sp) Conformer + ∑ b m sin (3mα) 5 m=1 . Acetyl Group Propenyl Group -269.831531192 -269.830877283 0.000741400 -0.001467556 0.000078308 0.000035468 Acetyl Group B3LYP/6-311++G(d,p) Antiperiplanar (ap) Conformer MP2/6-311++G(d,p) Acetyl Group Propenyl Group -269.832045492 -269.831538208 0.000863777 -0.001415888 0.000069608 0.000053992 Acetyl Group Propenyl Group Propenyl Group -270.638462883 -270.637646900 -270.638694308 -270.637847533 J K a K c Species υ obs / GHz υ obs -υ cal / kHz lower level 0 Top 1 Top Acetyl 1 Top Propenyl 2 Tops 5 1 5 (00) 19.9514258 -3.6 -4.9 -3.7 -5.3 5 1 5 (01) 19.9514258 2.5 1.0 5 1 5 (10) 19.9512900 -2.8 -3.1 5 1 5 (11) 19.9512900 4.4 5 1 5 (12) 19.9512900 1.8 5 1 4 (00) 21.8890490 0.8 -0.7 0.5 -1.2 5 1 4 (01) 21.8890288 -2.0 -3.8 5 1 4 (10) 21.8885529 1.7 0.9 5 1 4 (11) 21.8885310 -4.9 5 1 4 (12) 21.8885310 -1.7 5 2 4 (00) 20.9624422 -5.2 -6.5 -5.5 -7.1 5 2 4 (01) 20.9624786 -0.7 -2.3 5 2 4 (10) 20.9621983 1.5 0.8 5 2 4 (11) 20.9621103 -2.5 5 2 4 (12) 20.9623492 4.2 5 2 3 (00) 21.3654423 1.3 -0.1 1.0 -0.7 5 2 3 (01) 21.3654055 5.1 3.4 J K a K c Species υ obs / GHz υ obs -υ cal / kHz lower level 0 Top 1 Top Acetyl 1 Top Propenyl 2 Tops 6 4 (12) 24.6072142 5.5 6 3 (00) 24.6365019 -1.7 -2.8 -2.1 -3.8 6 3 (01) 24.6348368 -0.6 -2.4 6 3 (10) 24.6332467 1.9 0.8 6 3 (11) 24.6357485 2.9 6 3 (12) 24.6304256 2.0 5 5 (00) 4.8748949 -4.1 -5.1 -3.5 -5.3 5 5 (01) 4.8748735 -4.7 -6.6 5 5 (10) 4.8740018 0.1 -0.5 5 5 (11) 4.8739721 1.4 5 5 (12) 4.8739922 -1.5 6 6 (00) 6.8125172 -0.6 -1.8 -0.2 -2.1 6 6 (01) 6.8124851 -0.7 -2.7 6 6 (10) 6.8112586 -1.5 -2.5 6 6 (11) 6.8112234 2.4 6 6 (12) 6.8112424 4.1 1 1 (00) 6.7801860 1.0 0.4 1.1 0.2 J K a K c Species υ obs / GHz υ obs -υ cal / kHz lower level 0 Top 1 Top Acetyl 1 Top Propenyl 2 Tops 10 10 (10) 19.0064413 -2.0 -6.3 10 10 (11) 19.0061882 2.7 10 10 (12) 19.0061882 -1.6 2 1 (00) 19.3759668 -0.7 -2.0 -0.9 -2.6 2 1 (01) 19.3775913 -0.6 -2.1 2 1 (10) 19.3799414 2.0 1.5 2 1 (11) 19.3753782 1.4 2 1 (12) 19.3843028 2.4 3 2 (00) 18.9432150 -2.2 -3.3 -2.5 -4.0 3 2 (01) 18.9429851 -2.8 -4.1 3 2 (10) 18.9441861 -0.3 -0.8 3 2 (11) 18.9423669 0.8 3 2 (12) 18.9454352 3.4 4 3 (00) 18.4267253 0.3 -0.7 -0.1 -1.4 4 3 (01) 18.4261181 0.1 -1.0 4 3 (10) 18.4270371 -0.5 -1.0 4 3 (11) 18.4258972 0.1 J K a K c Species υ obs / GHz υ obs -υ cal / kHz lower level 0 Top 1 Top Acetyl 1 Top Propenyl 2 Tops 6 1 6 (00) 20.0465272 5.3 3.9 5.4 3.6 6 1 6 (01) 20.0467384 5.7 3.7 6 1 6 (10) 20.0459966 -1.1 -1.6 6 1 6 (11) 20.0462038 -3.5 6 1 6 (12) 20.0462170 5.8 7 1 7 (00) 23.9344003 -0.4 -1.8 -0.1 -2.3 7 1 7 (01) 23.9345856 -0.9 -3.2 7 1 7 (10) 23.9338465 -0.2 -0.8 7 1 7 (11) 23.9340353 2.9 7 1 7 (12) 23.9340353 0.6 5 2 4 (00) 4.4262980 2.2 1.5 2.5 1.7 5 2 4 (01) 4.4271672 2.4 1.4 5 2 4 (10) 4.4258175 3.3 3.1 5 2 4 (11) 4.4264488 1.4 5 2 4 (12) 4.4269218 1.7 6 2 5 (00) 8.9469331 2.3 1.5 2.4 1.6 6 2 5 (01) 8.9477438 -2.2 -3.3 J K a K c Species υ obs / GHz υ obs -υ cal / kHz lower level 0 Top 1 Top Acetyl 1 Top Propenyl 2 Tops 3 0 3 (12) 19.0299127 0.9 4 0 4 (00) 21.7885510 -2.2 -3.6 -2.8 -4.2 4 0 4 (01) 21.7882931 6.3 4.9 4 0 4 (10) 21.7885927 1.5 1.1 4 0 4 (11) 21.7883264 -2.3 4 0 4 (12) 21.7883169 -3.6 5 0 5 (00) 24.4614860 2.5 1.1 2.1 0.5 5 0 5 (01) 24.4612264 1.1 -0.5 5 0 5 (10) 24.4615986 2.4 2.0 5 0 5 (11) 24.4613400 -0.3 5 0 5 (12) 24.4613400 4.5 3 1 3 (00) 10.3398589 1.1 0.4 1.4 -0.1 3 1 3 (01) 10.3414945 1.4 0.1 3 1 3 (10) 10.3437589 1.9 1.5 3 1 3 (11) 10.3391688 1.5 3 1 3 (12) 10.3481692 1.4 4 1 4 (00) 7.5591991 2.8 2.2 3.2 4 2 2 (10) 17.3309986 1.2 -0.7 4 2 2 (11) 17.3328136 -0.4 4 2 2 (12) 17.3291837 1.3 5 0 5 (00) 20.3662089 0.9 0.9 0.6 0.6 5 0 5 (01) 20.3661908 -0.8 -0.8 5 0 5 (10) 20.3658184 1.0 0.5 5 0 5 (11) 20.3658009 -0.1 5 0 5 (12) 20.3658009 -0.7 5 1 5 (00) 19.7303153 0.0 0.0 -0.2 -0.2 5 1 5 (01) 19.7303093 -0.6 -0.7 5 1 5 (10) 19.7301964 1.0 0.5 5 1 5 (11) 19.7301806 3.5 5 1 5 (12) 19.7302058 2.3 5 1 4 (00) 21.4271112 0.4 0.4 -0.4 -0.5 5 1 4 (01) 21.4270927 -1.6 -1.9 5 1 4 (10) 21.4263992 -0.1 -1.4 5 1 4 (11) 21.4263992 2.6 3 3 (01) 8.3275531 3.4 2.6 3 3 (10) 8.3255514 4.0 2.8 3 3 (11) 8.3251532 3.1 3 3 (12) 8.3253757 1.9 4 4 (00) 8.9603920 -0.1 -0.8 -1.3 -2.3 4 4 (01) 8.9601051 2.0 0.9 4 4 (10) 8.9577023 2.1 0.5 4 4 (11) 8.9573506 3.8 4 4 (12) 8.9574789 2.5 5 5 (00) 9.7943764 2.0 1.2 0.4 -0.8 5 5 (01) 9.7940856 1.8 0.5 5 5 (10) 9.7913652 3.9 1.7 5 5 (11) 9.7910305 0.1 5 5 (12) 9.7911144 1.9 6 6 (00) 10.8552740 -3.2 -4.0 -5.3 -6.6 6 6 (01) 10.8549890 2.4 0.9 6 6 (10) 10.8519467 3.4 0.5 1.7 J' a a a b a J' K a ' K c ' upper level 6 1 6 6 1 6 6 1 6 6 1 6 6 1 6 6 1 5 6 1 5 6 1 5 6 1 5 6 1 5 6 2 5 6 2 5 6 2 5 6 2 5 6 2 5 6 2 4 6 2 4 J' K a ' K c ' upper level 7 3 5 7 3 4 7 3 4 7 3 4 7 3 4 7 3 4 5 1 4 5 1 4 5 1 4 5 1 4 5 1 4 6 1 5 6 1 5 6 1 5 6 1 5 6 1 5 1 1 0 J' K a ' K c ' upper level 10 1 9 10 1 9 10 1 9 2 2 0 2 2 0 2 2 0 2 2 0 2 2 0 3 2 1 3 2 1 3 2 1 3 2 1 3 2 1 4 2 2 4 2 2 4 2 2 4 2 2 J' K a ' K c ' upper level 7 0 7 7 0 7 7 0 7 7 0 7 7 0 7 8 0 8 8 0 8 8 0 8 8 0 8 8 0 8 6 1 5 6 1 5 6 1 5 6 1 5 6 1 5 7 1 6 7 1 6 J' K a ' K c ' upper level 4 1 4 5 1 5 5 1 5 5 1 5 5 1 5 5 1 5 6 1 6 6 1 6 6 1 6 6 1 6 6 1 6 2 2 0 2 2 0 2 2 0 2 2 0 2 2 0 3 2 1 5 2 3 5 2 3 5 2 3 6 0 6 6 0 6 6 0 6 6 0 6 6 0 6 6 1 6 6 1 6 6 1 6 6 1 6 6 1 6 6 1 5 6 1 5 6 1 5 6 1 5 3 1 2 3 1 2 3 1 2 3 1 2 4 1 3 4 1 3 4 1 3 4 1 3 4 1 3 5 1 4 5 1 4 5 1 4 5 1 4 5 1 4 6 1 5 6 1 5 6 1 5 K a ' K c ' J K a K c Species υ obs / GHz υ obs -υ cal / kHz upper level lower level 0 Top 1 Top Acetyl 1 Top Propenyl 2 Tops J' K a ' K c ' J K a K c Species υ obs / GHz υ obs -υ cal / kHz upper level lower level 0 Top 1 Top Acetyl 1 Top Propenyl 2 Tops 18. 3
	a 6 1 4 7 6 6	2 1 2 1 1 1	4 0 2 6 5 5	0.000549174 5 2 3 1 1 4 3 6 2 5 5 1 4 6 6	(10) (01) (12) (10) (12) (11)	-0.001413105 21.3648925 6.7799440 18.4269588 8.9461414 21.4263732 10.8516302		0.000582244 0.9 0.9	5.0	-0.001475783 0.2 4.2 -0.3 0.4 2.7 4.1
	a 6 1 5 7 6 6	2 1 2 1 2 1	4 0 3 6 5 5	5 1 5 6 5 6	2 2 2	3 1 4 5 4 6	(11) (10) (00) (11) (00) (12)	0.000041700 21.3649728 6.7801139 17.8769472 8.9468380 20.6072385 10.8516851	4.7 -0.9	0.2 3.8 -1.2	4.2 -1.7	0.000040458 5.4 0.0 3.1 0.3 -2.0 3.8
	b 6 1 5 7 6 7	2 1 2 1 2 1	4 0 3 6 5 6	0.000037825 5 2 3 1 1 5 4 6 2 5 5 2 4 7 7	(12) (11) (10) (12) (01) (00)	21.3647370 6.7797915 17.8771005 8.9470772 20.6072894 12.1689317	0.3	0.000031401 -1.7 -0.6	0.6 -2.5	1.2 -0.3 -2.3 1.6 0.2 -3.7
	6 1 5 8 6 7	3 1 2 1 2 1	4 0 3 7 5 6	5 1 5 7 5 7	3 2 2	3 1 4 6 4 7	(00) (12) (12) (00) (10) (01)	B3PW91/6-311++G(d,p) 21.0747944 6.7799440 17.8766222 13.5692110 -2.6 1.8 20.6139596 12.1686451	0.6 -3.3 1.1	1.4 -2.6 2.7	-0.2 0.1 -0.2 -3.4 0.2 1.2
	6 2 6 8 6 7	3 1 2 1 2 1	4 1 4 7 5 6	Acetyl Group 5 3 3 2 2 6 5 7 2 6 5 2 4 7 7	(01) (00) (00) (01) (12) (10)	Propenyl Group 21.0775792 7.1176869 17.3533364 13.5699950 20.6151216 12.1652447	Acetyl Group -4.7 -5.4 1.1 0.3 3.1	Propenyl Group -0.1 -1.6 -4.6 -5.6 0.7 -0.5 -0.2 -1.2 4.3 -0.6
	a 6 2 6 8 6 7	3 1 2 1 2 1	4 1 4 7 4 6	-270.527788358 5 3 3 2 2 6 5 7 2 6 5 2 3 7 7	(10) (01) (01) (10) (00) (11)	-270.527007892 21.0781625 7.1174296 17.3526066 13.5681526 20.8848685 12.1649396	-270.528076175 4.5 -0.6 -2.0 -2.2	3.5 0.4 -3.0	-270.527245100 3.6 2.5 -0.6 -1.5 -3.1 5.6
	a 6 2 6 8 6 7	3 1 2 1 2 1	4 1 4 7 4 6	0.000579993 5 3 3 2 2 6 5 7 2 6 5 2 3 7 7	(11) (10) (10) (11) (01) (12)	-0.001411559 21.0752455 7.1175280 17.3534416 13.5688709 20.8848089 12.1649770		0.000594398 4.2 -1.0	0.0	-0.001470613 0.4 4.0 -1.5 1.3 -0.4 3.3
	a 6 2 6 8 6 8	3 1 2 1 2 1	4 1 4 7 4 7	5 2 6 7 5 8	3 2 2	3 2 5 6 3 8	(12) (11) (11) (12) (10) (00)	0.000041017 21.0795547 7.1172329 17.3526066 13.5690024 20.8772888 13.7578376	0.0	1.2 -0.7	-3.6	0.000038967 5.2 0.5 5.2 0.3 -0.5 -4.4
	b 6 2 6 10 6 8	3 1 2 1 2 1	3 1 4 9 4 7	0.000040754 5 3 2 2 2 6 5 9 2 8 5 2 3 8 8	(00) (12) (12) (00) (11) (01)	21.0901989 7.1172853 17.3528245 23.0263457 20.8783848 13.7575550	-2.7 2.5	0.000033058 -3.9 2.9	-3.1 1.7 3.9	-4.6 0.5 -1.0 2.0 -3.7 2.6
	6 3 7 10 6 8	3 1 2 1 2 1	3 2 5 9 4 7	5 3 7 9 5 8	3 2 2	2 3 6 8 3 8	(01) (00) (00) (01) (12) (10)	B3LYP-D3/6-311++G(d,p) 21.0874033 7.6462034 -1.5 16.9200716 -3.6 23.0270694 20.8761183 13.7537393	-2.3 -4.4 2.4	0.4 -1.2 -4.0 3.0	-1.2 -2.5 -5.2 3.0 0.7 -2.3
	6 3 7 10 7 8	3 1 2 1 0 1	3 2 5 9 7 7	Acetyl Group 5 3 2 3 3 7 6 9 2 8 6 0 6 8 8	(10) (01) (01) (10) (00) (11)	Propenyl Group 21.0860900 7.6459282 16.9193519 23.0248087 23.6492254 13.7534410	Acetyl Group -2.0 0.1 1.0 0.6	Propenyl Group -0.8 -5.4 -6.7 -1.3 -2.3 -3.8 0.8 0.6 4.4
	a 6 3 7 10 7 8	3 1 2 1 0 1	3 2 5 9 7 7	-270.645969192 5 3 2 3 3 7 6 9 2 8 6 0 6 8 8	(11) (10) (10) (11) (01) (12)	-270.645339633 21.0889908 7.6459239 16.9201234 23.0255116 23.6492009 13.7534717	-270.646017775 -2.7 0.0	-2.0	-270.645249783 -0.9 -3.0 -0.6 0.7 -2.2 4.2
	a 6 3 7 10 7 9	3 1 2 1 0 1	3 2 5 9 7 8	0.000687934 5 3 2 3 3 7 6 9 2 8 6 0 6 9 9	(12) (11) (11) (12) (10) (00)	-0.001400721 21.0846905 7.6456446 16.9193390 23.0255576 23.6487961 15.6370890	-2.8	0.000638501 4.2 -3.0	-7.2	-0.001467062 3.1 3.0 -0.3 -2.0 3.9 -7.4
	a 6 3 7 10 7 9	5 1 2 2 0 1	2 2 5 8 7 8	-0.000037939 5 5 1 3 3 7 6 9 3 7 6 0 6 9 9	(00) (12) (12) (00) (11) (01)	0.000045808 21.0459357 7.6456706 16.9194638 5.7034654 23.6487682 15.6368128	1.5 1.3	0.9 2.0	0.7 1.5 5.1	0.000047683 -0.6 0.4 0.4 2.5 -2.3 4.3
	b 6 4 8 10 7 9	5 1 2 2 0 1	2 3 6 8 7 8	0.000046285 5 5 1 4 4 8 7 9 3 7 6 0 6 9 9	(01) (00) (00) (01) (12) (10)	21.0459357 8.3914092 16.6407597 5.7051860 23.6487682 15.6325133	-1.8 -3.8	0.000035444 -2.7 -4.5 0.7	2.8 -1.4 -4.2 2.9	1.6 -3.0 -5.3 3.4 -2.4 -4.9
	6 4 8 10 7 9 a a a b M06-a 5 1 5 5 0 (00) 21.0459357 1 3 4 4 (01) 8.3911364 2 6 8 7 (01) 16.6400632 2 8 9 3 7 (10) 5.7028070 1 7 6 1 6 (00) 22.9920473 1 8 9 9 (11) 15.6322198 B3LYP-D3BJ/6-311++G(d,p) 0.6 0.2 Acetyl Group Propenyl Group Acetyl Group -0.1 -1.5 -0.3 -270.655931367 -270.655211450 -270.655748650 0.000641648 -0.001409779 0.000614372 0.000043083 0.000042805 0.000032289 -270.502608933 -270.502239892 -270.502665217 a 0.000979987 -0.001411423 0.000739654 a 0.000045758 b 0.000065085 0.00003806 (00) 17.5520232 -0.5 -1.6 5 3 3 4 3 2 (01) 17.5541660 5 3 3 4 3 2 (10) 17.5540889 1.8 6 5 1 5 5 0 (01) 21.0459276 7 0 7 6 0 6 (00) 23.8946960 -3.5 -4.9 7 0 7 6 0 6 (01) 23.8946703 7 0 7 6 0 6 (10) 23.8944977 -2.5 7 0 7 6 0 6 (11) 23.8944726 7 0 7 6 0 6 (12) 23.8944726 7 1 7 6 1 6 (00) 23.2390465 -1.9 -3.3 7 1 7 6 1 6 (01) 23.2390363 7 1 7 6 1 6 (10) 23.2389036 2.7 7 1 7 6 1 6 (11) 23.2388924 7 1 7 6 1 6 (12) 23.2388924 7 1 6 6 1 5 (00) 25.4830811 -1.3 -2.7 7 1 6 6 1 5 (01) 25.4830603 7 1 6 6 1 5 (10) 25.4825283 5.2 7 1 6 6 1 5 (11) 25.4825058 7 1 6 6 1 5 (12) 25.4825058 7 2 6 6 2 5 (00) 24.4259662 0.8 -0.5 7 2 6 6 2 5 (01) 24.4259710 4 1 3 4 4 (10) 8.3909776 0.1 4 1 3 4 4 (11) 8.3906982 4 1 3 4 4 (12) 8.3907203 5 1 4 5 5 (00) 9.3849557 2.5 1.5 5 1 4 5 5 (01) 9.3846764 5 1 4 5 5 (10) 9.3843063 1.2 5 1 4 5 5 (11) 9.3840271 5 1 4 5 5 (12) 9.3840449 6 1 5 6 6 (00) 10.6606918 -3.6 -4.8 6 1 5 6 6 (01) 10.6604231 6 1 5 6 6 (10) 10.6597625 -0.2 6 1 5 6 6 (11) 10.6594875 6 1 5 6 6 (12) 10.6595051 7 1 6 7 7 (00) 12.2490752 -3.1 -4.3 7 1 6 7 7 (01) 12.2488143 7 1 6 7 7 (10) 12.2477857 0.2 7 1 6 7 7 (11) 12.2475192 7 1 6 7 7 (12) 12.2475312 8 2 6 8 7 (10) 16.6407041 0.7 8 2 6 8 7 (11) 16.6399695 8 2 6 8 7 (12) 16.6400424 9 2 7 9 8 (00) 16.5737608 0.6 0.0 9 2 7 9 8 (01) 16.5730974 9 2 7 9 8 (10) 16.5735180 -3.4 9 2 7 9 8 (11) 16.5728378 9 2 7 9 8 (12) 16.5728797 10 2 8 10 9 (00) 16.7696308 1.0 0.7 10 2 8 10 9 (01) 16.7690112 10 2 8 10 9 (10) 16.7691312 1.9 10 2 8 10 9 (11) 16.7684978 10 2 8 10 9 (12) 16.7685259 11 2 9 11 10 (00) 17.2709661 2.3 2.6 11 2 9 11 10 (01) 17.2704026 11 2 9 11 10 (10) 17.2701133 2.6 11 2 9 11 10 (11) 17.2695328 11 2 9 11 10 (12) 17.2695623 11.4120718 1.5 1.5 5 3 3 6 2 4 (01) 11.4049029 5 3 3 6 2 4 (10) 11.4030677 0.6 5 3 3 6 2 4 (11) 11.4094778 5 3 3 6 2 4 (12) 11.3929693 6 3 4 7 2 5 (00) 7.4370384 -2.1 -1.9 6 3 4 7 2 5 (01) 7.4326722 6 3 4 7 2 5 (10) 7.4320214 0.2 6 3 4 7 2 5 (11) 7.4354816 6 3 4 7 2 5 (12) 7.4233818 3 0 3 2 1 2 (00) 4.3192306 4.9 4.4 3 0 3 2 1 2 (01) 4.3195030 3 0 3 2 1 2 (10) 4.3190850 -2.0 3 0 3 2 1 2 (11) 4.3193360 3 0 3 2 1 2 (12) 4.3193852 4 0 4 3 1 3 (00) 8.1985635 4.1 3.3 4 0 4 3 1 3 (01) 8.1988219 10 2 8 9 3 7 (11) 5.7036662 10 2 8 9 3 7 (12) 5.7053805 11 2 9 10 3 8 (00) 10.5092860 -0.1 1.6 11 2 9 10 3 8 (01) 10.5108740 11 2 9 10 3 8 (10) 10.5079728 -2.1 11 2 9 10 3 8 (11) 10.5090935 12 2 10 11 3 9 (00) 15.5081626 -1.7 1.4 12 2 10 11 3 9 (01) 15.5096838 12 2 10 11 3 9 (10) 15.5063162 -2.4 12 2 10 11 3 9 (11) 15.5075671 12 2 10 11 3 9 (12) 15.5081069 1 1 1 0 0 0 (00) 9.9574395 -0.7 -1.5 1 1 1 0 0 0 (01) 9.9571384 1 1 1 0 0 0 (10) 9.9572654 0.6 1 1 1 0 0 0 (11) 9.9570399 1 1 1 0 0 0 (12) 9.9568896 2 1 2 1 0 1 (00) 13.1346866 1.4 0.3 7 1 7 6 1 6 (01) 22.9920473 7 1 7 6 1 6 (10) 22.9918730 1.3 7 1 7 6 1 6 (11) 22.9918517 7 1 7 6 1 6 (12) 22.9918730 7 1 6 6 1 5 (00) 24.9628836 4.9 4.5 7 1 6 6 1 5 (01) 24.9628557 7 2 6 6 2 5 (00) 24.0212286 -3.9 -4.7 7 2 6 6 2 5 (01) 24.0212471 7 2 6 6 2 5 (10) 24.0241335 0.7 7 2 6 6 2 5 (11) 24.0235698 7 2 6 6 2 5 (12) 24.0247168 4 1 3 4 1 4 (00) 2.8405725 4.5 4.1 4 1 3 4 1 4 (01) 2.8405564 4 1 3 4 1 4 (10) 2.8406451 1.6 4 1 3 4 1 4 (11) 2.8405019 4 1 3 4 1 4 (12) 2.8407738 5 1 4 5 1 5 (10) 4.2577415 -0.6 9 1 8 9 9 (12) 15.6322481 10 1 9 10 10 (00) 17.8108283 -1.1 -0.6 10 1 9 10 10 (01) 17.8105512 10 1 9 10 10 (10) 17.8056948 -0.6 10 1 9 10 10 (11) 17.8054033 10 1 9 10 10 (12) 17.8054306 11 1 10 11 11 (00) 20.2701159 2.0 3.5 11 1 10 11 11 (01) 20.2698332 11 1 10 11 11 (10) 20.2643413 -2.1 11 1 10 11 11 (11) 20.2640442 11 1 10 11 11 (12) 20.2640745 2 2 0 2 1 (00) 21.9014425 2.1 2.2 2 2 0 2 1 (01) 21.9035940 2 2 0 2 1 (10) 21.9547549 1.5 2 2 0 2 1 (11) 21.9483231 2 2 0 2 1 (12) 21.9594491 3 2 1 3 2 (00) 21.5128293 -6.2 -6.2 2.6 (00) -0.2 -1.5 -1.2 -2.8 -2.2 -3.2 -2.0 0.1 -0.3 2.7 Propenyl Group -270.654940658 -0.001475199 0.000045000 -270.501996592 -0.001477474 0.000048275 -0.9 -2.2 -0.5 -1.9 1.2 3.2 1.9 -3.6 -5.4 -2.2 -4.1 -3.0 -1.2 -0.9 -1.8 -3.8 -3.5 -5.5 2.3 0.4 -1.1 -1.7 -3.5 -0.2 -2.0 4.3 2.8 5.3 0.5 -1.3 -0.2 -2.1 -0.3 3.2 5.5 2.9 1.1 -3.9 -5.7 0.6 1.7 3.9 -3.4 -5.3 -2.4 -4.4 -1.1 0.0 4.6 -3.3 -5.1 0.8 -1.1 -1.3 2.6 3.7 0.0 1.9 -1.0 0.0 -0.9 -0.4 -1.2 -4.3 4.1 -4.9 -0.1 -0.3 -1.0 -1.1 0.8 4.9 -4.5 0.2 1.3 4.1 5.2 1.0 2.9 0.6 0.7 -0.8 -0.5 0.2 0.2 0.5 -3.1 -2.7 -3.3 -2.7 -0.1 -0.1 1.9 4.8 4.4 4.1 3.7 -2.1 0.2 0.7 4.1 3.3 1.4 0.5 -0.2 -2.2 -0.9 1.6 1.2 3.2 -3.2 -0.7 -3.9 1.0 -0.5 3.7 -4.2 -1.7 -1.6 -0.8 -1.8 -1.1 -2.0 0.4 0.0 1.1 1.1 0.0 7.5 7.1 1.1 -4.6 0.1 4.0 3.9 -2.9 -3.3 -4.8 -5.4 0.2 -0.5 -0.2 -0.5 0.1 3.5 2.8 -1.8 -2.7 0.0 2.9 3.6 -3.1 4.4 -6.5 -5.5 5.4 5.6 -7.1 2.0 4.1 -4.6 -1.8 6.4 8.2 -9.5 -1.3 3.5 1.2 1.1 0.1 1.9 2.5 -1.0 -0.1 -7.1 -7.2 4 0 4 3 1 3 (10) 8.1982999 0.3 0.1 2 1 2 1 0 1 (01) 13.1343988 -4.3 -5.3 5 1 4 5 1 5 (11) 4.2576368 2.5 3 2 1 3 2 (01) 21.5127946 4.4 5.3
	5 7 8 4 2 5 3	3 2 1 0 1 1 2	3 6 7 4 2 4 1	4 6 8 3 1 5 3	3 2 1 0 1	2 5 8 3 1 5 2	(11) (10) (00) (11) (10) (12) (10)	17.5530442 24.4256261 14.1703981 8.1985481 13.1345474 4.2578131 21.5534987	-1.2	0.5 -2.2 -0.8 -3.8	-2.1	5.6 -0.4 -3.4 -1.5 -1.0 0.2 -2.7
	5 7 8 4 2 1 3	3 2 1 0 1 1 2	3 6 7 4 2 0 1	4 6 8 3 1 1 3	3 2 1 0 0	2 5 8 3 1 1 2	(12) (11) (01) (12) (11) (00) (11)	17.5543188 24.4255835 14.1701399 8.1985743 13.1342917 7.5819738 21.5472319	1.2	0.8	-0.4 0.7	3.7 3.1 -1.8 1.9 0.6 0.1 -1.0
	5 7 8 5 2 1 3	3 2 1 0 1 1 2	2 6 7 5 2 0 1	4 6 8 4 1 1 3	3 2 1 0 0	1 5 8 4 1 1 2	(00) (12) (10) (00) (12) (01) (12)	17.5578238 24.4256878 14.1686732 12.1402516 13.1342412 7.5817159 21.5580952	2.2 1.1	1.1 -0.8 0.0	1.8 1.1 1.2	0.4 4.2 -2.9 0.0 0.3 0.7 1.0
	5 7 8 5 3 1 4	3 2 1 0 1 1 2	2 5 7 5 3 0 2	4 6 8 4 2 1 4	3 2 1 0 0	1 4 8 4 2 1 3	(01) (00) (11) (01) (00) (10) (00)	17.5556660 25.0498219 14.1684153 12.1404988 16.1538041 7.5830930 21.0358400	-0.5 2.8 0.8	-1.8 1.6 4.4 0.9	-2.0 -0.8 0.1 2.4 -0.1	-3.4 -2.6 3.4 -1.2 1.2 4.0 -0.1
	5 7 8 5 3 1 4	3 2 1 0 1 1 2	2 5 7 5 3 0 2	4 6 8 4 2 1 4	3 2 1 0 0	1 4 8 4 2 1 3	(10) (01) (12) (10) (01) (11) (01)	17.5551495 25.0498054 14.1684209 12.1398802 16.1535275 7.5821603 21.0352685		3.3 0.2	-2.0 2.6 3.0	2.6 -3.9 0.3 -0.1 1.4 2.1 3.6
	5 7 9 5 3 1 4	3 2 1 0 1 1 2	2 5 8 5 3 0 2	4 6 9 4 2 1 4	3 2 1 0 0	1 4 9 4 2 1 3	(11) (10) (00) (11) (10) (12) (10)	17.5561829 25.0492052 16.4288434 12.1401201 16.1537092 7.5834993 21.0568688	2.5	1.3 2.2 3.0 -3.8	0.4	-1.5 0.3 0.3 -2.4 2.7 1.2 -3.0
	5 7 9 5 3 2 4	3 2 1 0 1 1 2	2 5 8 5 3 1 2	4 6 9 4 2 2 4	3 2 1 0 0	1 4 9 4 2 2 3	(12) (11) (01) (12) (11) (00) (11)	17.5549089 25.0492393 16.4285883 12.1401393 16.1534420 7.8742592 21.0519024	-3.4	-3.9	2.4 -4.1	0.9 -1.6 2.2 4.6 0.2 -4.8 -1.0
	6 7 9 6 3 2 4	0 2 1 0 1 1 2	6 5 8 6 3 1 2	5 6 9 5 2 2 4	0 2 1 0 0	5 4 9 5 2 2 3	(00) (12) (10) (00) (12) (01) (12)	20.6133048 25.0491405 16.4266257 16.1032514 16.1534196 7.8739878 21.0603065	-1.1 -0.4	-2.5 3.1 -1.7	-1.4 -0.4 4.3	-2.9 2.1 0.1 -1.9 2.2 3.7 -1.8
	6 7 9 6 4 2 5	0 3 1 0 1 1 2	6 5 8 6 4 1 3	5 6 9 5 3 2 5	0 3 1 0 0	5 4 9 5 3 2 4	(01) (00) (11) (01) (00) (10) (00)	20.6132820 24.6020255 16.4263689 16.1034837 19.0302258 7.8727356 20.5052192	-1.5 0.0 1.3	-2.6 -1.3 5.0 1.2	-3.6 -1.9 0.2 -0.5 0.3	-5.2 -3.6 3.5 -1.4 -1.7 4.2 0.2
	6 7 9 6 4 2 5	0 3 1 0 1 1 2	6 5 8 6 4 1 3	5 6 9 5 3 2 5	0 3 1 0 0	5 4 9 5 3 2 4	(10) (01) (12) (10) (01) (11) (01)	20.6130952 24.6036809 16.4263689 16.1027911 19.0299547 7.8722257 20.5044988		1.6 0.9	0.4 0.9 1.4	1.1 -1.3 -2.9 0.5 -0.3 1.6 1.9
	6 7 10 6 4 2 5	0 3 1 0 1 1 2	6 5 9 6 4 1 3	5 6 10 5 3 2 5	0 3 1 0 0	5 4 10 5 3 2 4	(11) (10) (00) (11) (10) (12) (10)	20.6130729 24.6044021 19.0091932 16.1030241 19.0301926 7.8726802 20.5120167	-1.3	3.5 -0.7 1.7 -4.8	-5.5	-0.9 2.3 -3.5 5.0 1.4 1.5 -4.6
	6 7 10 6 4 3 5	0 3 1 0 1 1 2	6 5 9 6 4 2 3	5 6 10 5 3 3 5	0 3 1 0 0	5 4 10 5 3 3 4	(12) (11) (01) (12) (11) (00) (11)	20.6130729 24.6018894 19.0089424 16.1030241 19.0299292 8.3278322 20.5088565	-3.1	-3.7	3.8 -4.0	-0.3 2.9 5.6 -1.9 3.7 -4.9 -2.0

-Methyl-3-buten-2-one 18.1. Nuclear CoordinatesTable 18 . 1 :

 181 Nuclear coordinates of the two conformers of 3-methyl-3-buten-2-one calculated at the MP2/6-311++G(d,p) level of theory. Atoms are labelled according to Figure 8.1.

	18.3. Fourier Coefficients
		Antiperiplanar (ap) Conformer	Synperiplanar (sp) Conformer
		a / Å	b / Å	c / Å	a / Å	b / Å	c / Å
	C 1	1.777394	0.874321	-0.000052	1.445455	1.213628	-0.229726
	H 2	1.689830	1.511184	0.884899	1.159904	1.610871	-1.209614
	H 3	1.689033	1.511890	-0.884391	2.523160	1.051550	-0.197133
	H 4	2.750049	0.382027	-0.000691	1.160330	1.958357	0.519877
	C 5	0.697885	-0.191498	0.000054	0.733787	-0.099689	0.026686
	O 6	0.986227	-1.382943	-0.000006	1.356004	-1.133367	0.225363
	C 7	-0.743812	0.217474	0.000166	-0.773800	-0.080388	-0.001104
	C 8	-1.102394	1.517423	0.000008	-1.414769	-1.241787	-0.232164
	H 9	-0.370550	2.317911	-0.000346	-0.850103	-2.158159	-0.370985
	H 10	-2.149830	1.805754	-0.000153	-2.498852	-1.287777	-0.280386
	C 11	-1.745006	-0.904754	-0.000080	-1.498451	1.225886	0.200802
	H 12	-1.604265	-1.541397	-0.877907	-1.263246	1.660747	1.178306
	H 13	-1.604536	-1.541465	0.877738	-1.219751	1.961209	-0.560693
	H 14	-2.764636	-0.512220	-0.000178	-2.579365	1.073573	0.148103

Table 18 . 4 :

 184 Fourier coefficients (in Hartree) of the acetyl methyl group and the isopropenyl methyl group of the two conformers of 3-methyl-3-buten-2-one calculated at the MP2/6-311++G(d,p) level of theory. The potential was expanded in a one-dimensional Fourier expansion following the formula V(α) = a 0 + ∑ a n cos (3nα)

	5 n=1	+ ∑ b m sin (3mα) 5 m=1 .
		Antiperiplanar (ap) Conformer	Synperiplanar (sp) Conformer
		Acetyl Group	Propenyl Group	Acetyl Group	Propenyl Group
	a 0	-269.832387233	-269.831959908	-269.829082075	-269.828452892
	a 1	0.001013816	0.001405405	0.001089828	0.001740071
	a 2	0.000048753		0.000001810	0.000053289
	a 3	0.000013228		0.000038937	0.000022374
	a 4			-0.000002657	-0.000051192
	a 5			-0.000022825	-0.000000772
	b 1	0.000068306		0.000071020	0.000073431
	b 2	0.000029390		0.000050724	0.000085568
	b 3			0.000025289	0.000037359
	b 4			0.000025479	-0.000009522
	b 5			0.000010869	-0.000026569

Table 19 . 1 :

 191 Nuclear coordinates of conformer I of 3-methylbutan-2-one calculated at the MP2/6-311++G(d,p) and the B3LYP/6-311++G(d,p) level of theory.

				Conformer I
		MP2/6-311++G(d,p)		B3LYP/6-311++G(d,p)
		a / Å	b / Å	c / Å	a / Å	b / Å	c / Å
	C 1	1.872721	0.670380	-0.527582	-1.872081	0.687086	0.512872
	H 2	2.799191	0.414161	-0.012193	-2.793851	0.445437	-0.015191
	H 3	1.982237	0.466122	-1.598842	-2.006879	0.478475	1.580317
	H 4	1.659828	1.738628	-0.421295	-1.652890	1.754560	0.422766
	C 5	0.723897	-0.158057	0.009144	-0.729017	-0.161699	-0.010136
	O 6	0.902651	-1.111889	0.749980	-0.928082	-1.122238	-0.722412
	C 7	-0.678225	0.276650	-0.402118	0.686734	0.261190	0.394888
	H 8	-0.603740	0.806395	-1.360737	0.617812	0.766445	1.366058
	C 9	-1.611314	-0.924108	-0.542568	1.627214	-0.941611	0.509966
	H 10	-1.676705	-1.461823	0.406620	1.683349	-1.477514	-0.439444
	H 11	-2.613823	-0.593138	-0.830894	2.633086	-0.613053	0.785216
	H 12	-1.245844	-1.623519	-1.300371	1.280235	-1.647680	1.268731
	C 13	-1.198967	1.260197	0.659629	1.205626	1.286917	-0.636165
	H 14	-0.541552	2.128509	0.771245	0.548583	2.156813	-0.720402
	H 15	-2.194388	1.620932	0.382993	2.196335	1.644835	-0.344280
	H 16	-1.271370	0.754316	1.627824	1.287423	0.825276	-1.623792

Table 19 . 2 :

 192 Nuclear coordinates of conformer II of 3-methylbutan-2-one calculated at the MP2/6-311++G(d,p) and the B3LYP/6-311++G(d,p) level of theory.

	Conformer II
	MP2/6

-311++G(d,p) B3LYP/6-311++G(d,p) a / Å

			b / Å	c / Å	a / Å	b / Å	c / Å
	C 1	-1.816227	0.810816	0.280012	-1.823236	0.819975	0.284810
	H 2	-1.599922	1.454957	1.136402	-1.620355	1.443834	1.158489
	H 3	-1.899533	1.446704	-0.608082	-1.898497	1.482610	-0.583799
	H 4	-2.766606	0.293988	0.422587	-2.777110	0.305741	0.400811
	C 5	-0.716906	-0.211780	0.049968	-0.726097	-0.203662	0.038756
	O 6	-0.966199	-1.308752	-0.424529	-0.988414	-1.291851	-0.426841
	C 7	0.704647	0.214288	0.396938	0.708734	0.205215	0.384667
	H 8	0.687535	0.537360	1.448071	0.686042	0.522398	1.436905
	C 9	1.692573	-0.934898	0.228776	1.686239	-0.960841	0.233821
	H 10	1.734031	-1.252327	-0.817038	1.734567	-1.296956	-0.804583
	H 11	2.693605	-0.618749	0.537906	2.689340	-0.657018	0.545314
	H 12	1.396588	-1.801081	0.825372	1.380459	-1.816672	0.838413
	C 13	1.098768	1.425944	-0.464600	1.138518	1.426164	-0.455642
	H 14	0.448538	2.287551	-0.289370	0.484616	2.287550	-0.301789
	H 15	2.126131	1.726196	-0.237915	2.153503	1.727503	-0.185026
	H 16	1.049362	1.165328	-1.527720	1.136089	1.181298	-1.522089

Table 19 . 3 :

 193 Nuclear coordinates of conformer III of 3-methylbutan-2-one calculated at the MP2/6-311++G(d,p) and the B3LYP/6-311++G(d,p) level of theory.

				Conformer III
		MP2/6-311++G(d,p)		B3LYP/6-311++G(d,p)
		a / Å	b / Å	c / Å	a / Å	b / Å	c / Å
	C 1	-1.150232	1.071099	0.844645	-1.194260	1.033761	0.866512
	H 2	-0.499837	1.101902	1.723264	-0.548773	1.079134	1.747105
	H 3	-1.041451	2.027054	0.321226	-1.122207	2.004006	0.363789
	H 4	-2.190101	0.949428	1.150317	-2.228857	0.873141	1.167236
	C 5	-0.766678	-0.057096	-0.094839	-0.771328	-0.061703	-0.096591
	O 6	-1.615108	-0.768601	-0.611321	-1.596936	-0.762779	-0.643094
	C 7	0.714806	-0.283630	-0.363317	0.723350	-0.267450	-0.356517
	H 8	0.755592	-0.938779	-1.240363	0.768939	-0.911250	-1.239554
	C 9	1.463532	1.018942	-0.661363	1.468275	1.043881	-0.650593
	H 10	1.483666	1.675373	0.214578	1.478638	1.709234	0.217453
	H 11	2.499854	0.797511	-0.935235	2.507966	0.831471	-0.914207
	H 12	1.004367	1.565796	-1.491203	1.017883	1.584027	-1.488060
	C 13	1.342403	-1.023196	0.827874	1.359787	-1.026666	0.824523
	H 14	0.812583	-1.957824	1.034771	0.838623	-1.967184	1.018888
	H 15	2.387684	-1.262697	0.608371	2.403724	-1.260519	0.598317
	H 16	1.324032	-0.405273	1.731912	1.346458	-0.430826	1.742104

Table 19 . 4 :

 194 Fourier coefficients (in Hartree) of the internal rotations of the acetyl methyl group (α 1 = ∡(H ,C 1 ,C 5 ,C 7 )) and the two isopropyl methyl groups (α 2 = ∡(C 5 ,C 7 ,C 9 ,H 10 ) and α 3 = ∡(C 5 ,C 7 ,C 13 ,H 14 )) of the three conformers of 3-methylbutan-2-one calculated at the MP2/6-311++G(d,p) level of theory.

-Heptan-2-one

cm -1 . Complexation with water[33] [43][44] or noble gases[132] [133] changes the

Acknowledgements

The two institutions agreed to award of assistance are clearly identified and referenced as such. This work was supported by the Agence Nationale de la Recherche ANR (project ID ANR-18-CE29-0011). Simulations were performed with computing resources granted by RWTH Aachen University under project rwth0249. Conformer III Conformer IV a / Å b / Å c / Å a / Å b / Å c / Å C

Conformer I features a C 1 structure, where the γ-carbon of the propyl chain is in an almost synclinal position, and conformer II exhibits a "pseudo-C s " structure, where the propyl chain is tilted out of the heavy atom acetyl plane by approximately 10°. Comparisons with other methyl alkyl ketones yielded that those ketones with C 1 structure also have acetyl methyl barrier heights of about 240 cm -1 , while those with "pseudo-C s " structure exhibit barriers to internal rotation of approximately 180 cm -1 . Based on this observation, we suggested two different classes of methyl alkyl ketones associated with different torsional barriers.

ΔX =

(X cal -X exp ) • 100 X exp (11.1) In general, calculations using the MP2 method, or the B3LYP, B3PW91 and M06-2X functional, respectively, yield mediocre or even insufficient agreements, while the results are much better applying the B3LYP functional including Grimme's dispersion correction (B3LYP-D3 and B3LYP-D3BJ). Consequently, dispersion might be an important effect, which should not be neglected, even in relative short ketones. However, this is a rather undifferentiated observation and it is much more sensible to distinguish between conformers with different symmetry (C 1 and C s ) and also between the different rotational constants.

Considering the C s conformers of the linear aliphatic ketones pentan-2-one (see Chapter 3), hexan-2-one (see Chapter 4), heptan-2-one (see Chapter 5) and octan-2-one (see Chapter 6), all investigated calculation methods mostly yield deviations lower than about 1%, which might explain why in these cases the C s conformer is much easier to assign than the corresponding C 1 conformer. The same observations can also be made for 3-penten-2-one (see Chapter 7) and 3-methyl-3-buten-2-one (see Chapter 8), where only conformers with C s symmetry could be identified in the spectrum. It is noteworthy that the MP2/6-311++G(d,p) level of theory calculates excellent values for the B and C rotational constants for all C s conformers, as is illustrated in Figure 11.1, while the A constant is determined precisely enough for assignment. This might be a reason for the frequent use of this level throughout the microwave spectroscopic community [21] [100] [101] [102] [105] [106] [107] [116] [117] [118]. The B3LYP/6-311++G(d,p) level of theory, another combination often utilized throughout this dissertation, yields a very good agreement for the A rotational constant.

In contrast, when calculating the rotational constants of the C 1 conformers of the methyl n-alkyl ketones pentan-2-one (see Chapter 3), hexan-2-one (see Chapter 4), heptan-2-one (see Chapter 5) and octan-2-one (see Chapter 6), the prediction of the A rotational constant poses a large problem, since deviations of up to 5% can be observed. Deviations of the B and C rotational constants are up to 2% as well. Molecules with the same C 1 -γ structure, such as methyl butyrate [20], ethyl valerate [128] or heptanal [126], also exhibit large deviations between the calculated and the experimental rotational constants. The C 1 -γ conformers are probably stabilised by weak hydrogen bonds. Hence, these hydrogen interactions might be the reason behind the failure of the calculations. Reasonable results are mainly shown by the DFT calculation including Grimme's dispersion without (B3LYP-D3) and with Becke-Johnsons

Frequency Lists