Jonas Bruckhuisen
email: jonas.bruckhuisen@univ-littoral.fr

Guillaume Dhont
email: guillaume.dhont@univ-littoral.fr

Anthony Roucou
email: anthony.roucou@uclouvain.be

Atef Jabri
email: jabri_atef@yahoo.fr

Hamdi Bayoudh
email: bayoudhhamdi@yahoo.fr

Thi Thanh Tran

Manuel Goubet
email: manuel.goubet@univ-lille.fr

Marie-Aline Martin-Drumel
email: marie-aline.martin@universite-paris-saclay.fr

Arnaud Cuisset
email: arnaud.cuisset@univ-littoral.fr

secondary organic aerosols in the atmosphere

Keywords: oxygenated aromatic compounds, precursors of secondary organic aerosols, terahertz gas phase spectroscopy, quantum chemistry methods, intramolecular hydrogen bonds composés aromatiques oxygénés, précurseurs d'aérosols organiques secondaires, spectroscopie térahertz en phase gazeuse, méthodes de chimie quantique, liaisons hydrogène intramoléculaires results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . spectra . . . . . . . . . . . . . . catechol, intramolecular hydrogen bond, rovibrational spectroscopy, terahertz, lowfrequency modes Bruckhuisen, J

Quantum chemical study and THz spectroscopy of biogenic oxygenated volatile organic compounds precursors of

Introduction

The global combustion of biomass leads to the emission of huge amounts of primary, carbonaceous particles and trace gases into the atmosphere. Biomass burning emissions are the second largest global atmospheric source of gas phase non-methane organic compounds [97]. These emissions have a significant influence to the local air quality, the climate and even to the human health [17].

Figure 1 illustrates the wide variety of emissions produced by the combustion of wood within an enclosed residential wood burner (middle/black) and a commercial heating application such as a fixed grate domestic stove (right, panel). Besides the gaseous emissions containing CO 2 , CO, different NO x and SO x , a wide range of volatile organic compounds (VOCs) are produced [99]. The combustion of wood consisting mainly of cellulose, hemicellulose and lignin is typically inefficient resulting in partially oxidized organic molecules. The pyrolysis of these polymers lead to different families of VOCs: lignin leads to benzene derivatives such as phenol or catechol [94], (hemi-)cellulose leads to furan compounds, polyaromatic hydrocarbons (PAHs) as well as dioxins (polychlorinated dibenzo-p-dioxins (PCDDs) and polychlorinated dibenzofurans (PCDFs)) [83].

In addition, organic and inorganic aerosols are emitted, as well as organic carbon (OC) and black carbon (BC). Different particulate matter (PM) emissions of different size and composition occurs. And not to be neglected are the ashes and inorganic residues.

Unfortunately, the compositions and contributions of especially the gaseous emissions of higher molecular weight remain sometimes unsettled. Often within minutes after the emission, these VOCs undergo complex photo-chemical reactions within the smoke plumes [6]. This causes a change in the concentrations of the main atmospheric reactants such as ozone O 3 , hydroxyl radical OH or Figure 1 -Illustration of the wide variety of emissions and processes that can result from the combustion of biomass in an enclosed residential wood burner (middle/black) or fixed grate domestic stove (right/ schema inside the panel). The different processes have different impact to the air quality, the climate and the human health. The image is taken from: Energy Fuels 2021, 35.18, 14213-14240 [99].

nitrogen oxides NO x and can lead to the formation of secondary organic aerosols (SOAs). The overall influence on the climate is difficult to estimate due to the different radiative forces of all these complex potential processes with sometimes contrary impact (see Figure 2) [99]. For the aerosols especially, the error bars in Figure 2 of the aerosol related radiative forces do not even allow to clearly classify their contribution as cooling or warming. Therefore a better understanding of the atmospheric reactions and precise quantification of these compounds in the atmosphere is of great interest.

To obtain a better understanding of this whole topic, three general steps might be named:

• The identification and quantification of the different compounds emitted Figure 2 -Cooling and warming radiative forces of the main influences since 1750. The contribution of biomass burning with greenhouse gases emitted as well as VOCs reacting in the atmosphere and forming aerosols is not clear [25]. by biomass burning. McDonald et al. [74] for instance investigated the emission rates of fine particles and gaseous compounds from residual wood combustion such as 2-methylfuran (whose reaction with NO 3 will be discussed in Chapter 6) being 127.63 ± 51.36 / 209.86 ± 165.84 mg/kg for soft/hard wood fireplace burning. This first step will not be part of the presented work of this PhD.

• The investigation of atmospheric reactions via either simulated/simplified reactions in an atmospheric simulation chamber (ASC) or by quantum chemical computations. Potential reaction paths can be proposed, reaction Introduction rates determined and products identified.

• The observation of the reactants in the atmosphere via sampling and subsequent investigation or in-situ monitoring by spectroscopy. This a nontrivial task. Sufficient sensitivity is required to detect the trace-gas concentrations and high selectivity is necessary to distinguish the complex atmospheric compositions. Furthermore, the approach needs to be robust and fast to be able to monitor everything within a few minutes at demanding and different sites.

As it will be described more in detail in Chapter 6 and 9, atmospheric reactions are simulated in an ASC at the LPCA Dunkirk called "CHamber for the Atmospheric Reactivity and the Metrology of the Environment" (CHARME) [36]. After a molecular candidate (VOC) was shown to be emitted by biomass combustion, its reactions within controlled conditions with the main reactants of the atmosphere (e.g. O 3 or NO 3 ) are simulated. Unfortunately for common VOCs there is no possibility for now to monitor their concentration, reactions and intermediates/transition states live and in-situ. The kinetics are usually followed by measuring the concentrations of known references and the products are sampled and analyzed subsequently. Therefore only the final and stable products can be identified [36]. Combinations of different analytical techniques usually based on mass-spectrometry, gas chromatography or sometimes optics are used. Additionally specific instruments as ozone-or NO x -analyzer are applied [36].

These kind of simulations can be supported by quantum chemical calculations providing insights in case no experimental access is given. Crucial steps within reaction paths including intermediates and transition states can be estimated as well as their energies and the enthalpy of reaction [32].

To monitor and analyze the full atmospheric reaction processes in ASC as well as in the atmosphere, the analysis needs to be non-invasive, sensitive to all compounds at given concentrations, robust to perturbations/interference and in real-time. High resolution optical molecular spectroscopy is potentially able to fulfill all these requirements. Especially techniques exciting the rotation and/or the vibration of molecules are applicable. The rotational and vibrational properties of molecules are very sensitive to the structure and geometry of the isolated molecules and especially rotational spectroscopy is very selective, able to recognize molecular compounds in complex chemical mixtures, even molecules with close chemical structures such as isomers or conformers [90,93]. With the knowledge where to observe rotational transitions in the spectrum, mixtures of several compounds can be resolved within a short time. The three major limitations are: (I) pressure induced broadening foils the sensitivity at ambient pressure; (II) due to the spectroscopic selection rules not all molecules are observable or sufficiently intense (e.g.: only polar compounds may be observed in pure rotational spectroscopy); (III) only rotational transitions of volatile and medium-sized molecules may be resolved at the Doppler limit at room temperature.

Nevertheless THz spectroscopy is a promising technique for atmospheric science and, together with quantum chemical calculations, it can provide the required starting knowledge gained under controlled and simplified conditions (in the laboratory) for further applications in the atmosphere. THz spectroscopy includes pure rotational spectroscopy in the mm-wave range up to rovibrational spectroscopy of low frequency modes in the far-IR region. Once the rotational and vibrational parameters of the targeted molecules are determined at simplified conditions, e.g. at low temperature reducing the number of populated states and thus of transitions, the complexity or the spectral range can be extended.

The structure of isolated VOCs in the gas phase with > 10 atoms often exhibits plenty potential geometries/conformers. As they all have the same molecular structure (number and types of atoms and bonds) and the differences in the special orientation can be overcome by just rotating around a bond, a lot of analytical approaches face serious difficulties to distinguish them. Even though these conformers often differ only about a few kJ/mol, their properties can vary a lot [54]. Together, quantum chemistry, which can calculate accurate potential energy surfaces, and rotational spectroscopy, which is very sensitive to geometrical changes, can elucidate the conformational landscape of a molecule [53].

Usually, these kind of VOCs have several low-frequency vibrational modes, sufficiently thermally populated at room temperature [11]. Because rotational spectroscopy is very sensitive to geometrical changes, the vibrationally induced changes are enough to observe and distinguish them. Even the contribution of Introduction isotopes lead to different rotational spectra [92]. Therefore, room temperature pure rotational mm-wave spectroscopy as it is carried out at the LPCA in Dunkirk gives access to a large spectral range, from 70 to > 900 GHz, containing rotational transitions of high quantum numbers (J and K) enabling the determination of high accuracy rotational parameters including higher order centrifugal distortion constants of the ground state (GS) and of the vibrationally excited states (ES). But as a consequence to that, the room temperature rotational spectra in the mm-wave/submm-wave domain of medium-sized molecules are very congested due to a huge number of lines and the line by line analyses are complex and very time consuming.

In case the molecules exhibit additional geometrical features the combination of computational chemistry and THz spectroscopy can be used to investigate them. In this work two features will be explored: (I) intramolecular hydrogen bonds and (II) functional groups with the potential to undergo large amplitude motions (LAMs).

(I) Hydrogen bonds (HBs) in general play fundamental roles in structural chemistry (e.g. solvation or molecular geometry) and intramolecular hydrogen bonds (IHBs) in particular determine to a large extend the structures of molecules in living matter (e.g. protein folding or molecular docking) [33]. While there is a whole repertoire of techniques commonly used to investigate intermolecular HBs (e.g. X-ray diffraction, neutron scattering, IR-spectroscopy or NMR-spectroscopy) [102,50,4], robust techniques to study IHBs are rather rare. High resolution gas phase THz spectroscopy of isolated molecules with its sensitivity to geometrical features thus seems to be a promising approach. Quantum chemistry is of an essential help here because it computes the electronic density ρ of molecules which can carry the signatures of IHBs. Different quantum chemical tools are based on this: the Quantum Theory of Atoms in Molecules (QTAIM) [13] investigates the electronic density through its critical points, the Non-Covalent Interaction (NCI) index is based on the reduced density gradient [57,28] and brings new information for weak IHBs.

(II) An important phenomenon of intramolecular dynamics commonly observed in rotational spectroscopy are LAMs causing the rotational energy levels, hence the spectroscopic lines, to split. Two typical types of LAMs are the inter-nal rotation and the inversion tunneling [84]. In the case a molecule contains a functional group which is able to rotate around a single bond, internal rotation occurs [81]. In the case a molecule possesses two energetic equivalent structures separated by a potential barrier, the involved functional group might be able to tunnel between both similar structures. If the barrier hindering this rotation or tunneling is of the right order, the splitting of energy levels is observable as it is often the case for the internal rotation of methyl groups. This thesis will be organized in 4 parts: (I) is a general introduction to the methods used. A brief summary of the fundamentals of molecular absorption spectroscopy and quantum chemistry is followed by a description of the used experiments and tools. (II) reports the THz study of catechol and a theoretical study of intramolecular hydrogen bonds. (III) gives first an investigation of the atmospheric reactivity of furan compounds and then the rotational spectroscopy including internal rotation of the two isomers of methylfuran. (IV) introduces two experimental developments for future prospects: a heating system for our spectrometer and the installation of this spectrometer into an atmospheric simulation chamber. [6] M. J. Alvarado et al. "Investigating the links between ozone and organic aerosol chemistry in a biomass burning plume from a prescribed fire in California chaparral". In: Atmospheric Chemistry and Physics 15.12 (2015), pp. 6667-6688. doi: 10.5194/acp-15-6667-2015.

Bibliography of the current chapter

Part I

Introduction

The general procedure of a combined THz spectroscopic and quantum chemical (QC) investigation of a VOC of atmospheric interest is illustrated in Figure 3. Depending of course on the aimed results and the previously already reported work, not all steps are always part of our projects.

After identifying a candidate, its properties need to be suitable and it needs to be ensured the aimed work was not already done. Depending on the previous knowledge and the availability of starting parameters, QC investigations of the conformational landscape, the low-frequency vibrations and their rotational parameters provide the first information the spectroscopy can be based on. The aimed rotational, vibrational and rovibrational spectroscopy should be carried out successively leading to a global fit. In case additional and maybe unexpected effects such as intramolecular hydrogen bonds or line splittings occur, QC or dedicated tools are required to resolve these effects. The work can now be rewarded by publishing the results in a dedicated scientific journal.

Chapter1

Basics of molecular spectroscopy

Outline of the current chapter The present chapter brings the fundamental concepts of high resolution rotational and rovibrational molecular spectroscopy, as well as the quantum chemical approaches employed in the investigation of the physico-chemical properties of the molecules. Section 1.1 deals with rotational spectroscopy, introducing an effective Hamiltonian to model the energy levels of an asymmetric top. Section 1.2 presents the rovibrational spectroscopy and Section 1.3 discusses the molecules with large amplitude motions, especially the energy splittings caused by internal rotation.

The total energy of a molecule in a free field environment is composed of its translational energy and of its quantized rotational, vibrational and electronic 16 CHAPTER 1. Basics of molecular spectroscopy energies [52]:

E tot = E trans + E elect + E vib + E rot .
(1.1)

The translation of the molecular center of mass is separable and will not be discussed in the manuscript, hence we assume E trans = 0. The quantized energies of E rot vary from 10 -5 to 0.01 eV. The difference ∆E between two consecutive levels of same nature depends on the degree of freedom: typically,

∆E elect ∆E vib ∆E rot .
The expression molecular absorption spectroscopy used in this manuscript relates to the consequence of the interaction of an electromagnetic radiation with matter, i.e. the excitation of rotational, vibrational or rovibrational transitions of isolated molecules in the gas phase. The absorption of radiation of defined frequency can be accurately measured and directly associated to the difference between two energy levels of the molecule [90]. These transitions are very specific of a molecule and depend on some physico-chemical properties and the structure/geometry of the molecule.

The rovibronic wavefunction Ψ of the molecule can be given in the Born-Oppenheimer approximation as a product of the electronic Ψ elect , vibrational Ψ vib , and rotational Ψ rot wavefunctions:

Ψ = Ψ elect × Ψ vib × Ψ rot .
(1.2)

Rotational spectroscopy

In molecular absorption spectroscopy, the lowest energy transitions are transitions between rotational energy levels in the microwave (MW), millimeter-wave (MMW), submillimeter-wave (subMMW) or THz domains from 3 GHz to 3 THz or from 0.1 m -1 to 100 cm -1 . The energies E rot of the rotational levels are the eigenvalues of the time-independent Schrödinger equation of the rotational Hamiltonian:

Ĥrot Ψ rot = E rot Ψ rot .

(1.3)

1.1. Rotational spectroscopy 17

All molecules consist of a one-, two or three-dimensional set of nuclei represented as point masses. The moments of inertia of the nuclei of mass m i in the molecule-fixed axes are defined as:

I x = i m i y 2 i + z 2 i , I y = i m i x 2 i + z 2 i , I z = i m i x 2 i + y 2 i . (1.4)
For the model of the rigid rotor, neglecting centrifugal distortion, the Hamiltonian is given by [43,67]:

Ĥ0 rot = 1 2       Ĵ2 x I x + Ĵ2 y I y + Ĵ2 z I z       , ( 1.5)
with Ĵx , Ĵy and Ĵz being the components of the angular momentum of the rigid rotor in the body-fixed system. The inertial tensor is diagonalized in the principal axes system referring to the a-, b-and c-axes:

Ĥ0 rot = 1 2       P 2 a I a + P 2 b I b + P 2 c I c       = A P 2 a + B P 2 b + C P 2 c . (1.6)
A, B and C are the rotational constants defined in the principal axes system [104].

The values of the principal moments of inertia I a , I b and I c or those of the rotational constants A, B and C characterize the type of rotor at hand: linear rotor, spherical top, prolate or oblate symmetric top, and, regarding the molecules of interest for this thesis, asymmetric rotors with I c I b I a . Introduced by Ray, the degree κ of asymmetry is defined as:

κ = 2B -A -C A -C .
(1.7)

The limit κ -1 corresponds to a prolate top, while the other limit κ +1 is for an oblate top. κ 0 is for a totally asymmetric top. While the rotational levels of a prolate top are described with J, K a (|K a | ≤ J) quantum numbers and an oblate top with J, K c (|K c | ≤ J), the three quantum numbers J, K a and K c are used for an asymmetric top. An asymmetric top can be seen as an intermediate between a prolate and an oblate top. The correlation of the energy levels of an asymmetric CHAPTER 1. Basics of molecular spectroscopy top with the two kinds of symmetric tops is shown in Figure 1.1.

Figure 1.1 -Energy level diagram for an asymmetric top with assignment J K a K c . The limiting cases of the prolate and oblate top correspond to κ = -1 and +1 respectively.

The transition moment R J K a K c ←J K a K c for a rotational transition from the lower rotational state having the quantum numbers J , K a , K c to the upper state with quantum numbers J , K a , K c is:

R J K a K c ←J K a K c = Ψ J K a K c rot µ Ψ J K a K c rot dτ, (1.8)
where µ is the permanent electric dipole moment. For a transition to happen, its transition moment needs to be non-zero which means that the permanent electric dipole moment of the molecule needs to be non-zero (µ 0). In general not all rotational transitions are allowed. The selection rules for the rotational transitions of an asymmetric top are:

• ∆J = 0, ±1. Transitions with ∆J = -1 belong to the P -, ∆J = 0 to the Q-and ∆J = +1 to the R-branch.

• The selection rules for K a and K c depend on the component µ a , µ b or µ c of the dipole moment. The transitions involving the µ a component of the dipole moment are called a-type transitions. It is the same for the b-and caxes leading to b-and c-type transitions. It is important to note that the dipole transition implies that the parity of ∆K a and/or ∆K c changes, see Table 1.1.

transition type K value ∆J ∆K a ∆K c a (µ a 0) K a = 0 ±1 even odd K a 0 0, ±1 even odd b (µ b 0) 0, ±1 odd odd c (µ c 0) K c = 0 ±1 odd even K c 0 0, ±1 odd even Table 1.1 -Rotational selection rules for the quantum numbers J, K a and K c of an asymmetric top.

So far the considerations used the simplified model of the "rigid rotor". For a more precise description, it is necessary to introduce an additional perturbative treatment of the distortion of the nuclear distances caused by centrifugal forces upon rotation of the molecule [43,67]. Adding these new terms as a correction to the rigid rotor Hamiltonian Ĥ0 rot , the rotational Hamiltonian can be written as a series of powers in the angular momentum:

Ĥrot = Ĥ0 rot + Ĥdist = Ĥ2 + Ĥ4 + Ĥ6 + • • • (1.9)
The rigid rotor Hamiltonian Ĥ0 rot is the Hamiltonian Ĥ2 of order two in Ĵ while Ĥdist contains the centrifugal distortion of quartic Ĥ4 , sextic Ĥ6 and higher orders in Ĵ. Depending on the reductions A and S, the correction terms for the effective Hamiltonian are defined in I r representation (x, y, z → b, c, a) by Watson [43,67] as: Ĥ(A) dist = -∆ J P 4 -∆ JK P 2 P 2 a -∆ K P 4 a -2δ J P 2 (P 2 b -P where P + and P -are the step-up and step-down operators:

P + = P b + iP c , P -= P b -iP c .
(1.12)

The two Hamiltonians Ĥ(A) dist and Ĥ(S) dist of Equation 1.10 and Equation 1.11 are developed up to the quartic terms giving the five distortion constants ∆ J , ∆ JK , ∆ K , δ J and δ K for the A reduction and D J , D JK , D K , d 1 and d 2 as the five quartic distortion constants for the Watson S reduction. These Hamiltonians can be extended further including the sextic or even octic distortion constants if needed. The asymmetric top molecules treated in this work are usually well described with the A reduction of Watson. Nearly symmetric rotors would be better treated with the S reduction [START_REF] James | A planarity relation for sextic centrifugal distortion constants[END_REF].

Rotational spectroscopy is not limited to transitions between rotational levels of the vibrational ground state. At room temperature, not only the vibrational ground state (GS) is populated, but also some low frequency vibrationally excited states (ES). Rotational transitions may also happen between the rotational levels of these ES. The populations N j of the vibrational levels can be easily estimated using the Boltzmann distribution at the thermodynamic equilibrium:

N j N = e -E j /(kT ) i e -E i /(kT ) .
(1.13)

If we consider a first vibrationally excited state at 200 cm -1 , which is reasonable for the targeted molecules in this work, the ratio between the population of this excited state and the population of the ground state is N ES /N GS 0.37. The population of this vibrationally excited state is around a third of the GS population. Due to the vibrationally introduced changes in the geometry and therefore in the moments of inertia, each vibrational state has its characteristic spectrum of rotational transitions with its own set of rotational constants.

1.2

The combined rotational and vibrational excitation: rovibrational spectroscopy As illustrated in Figure 1.2 and indicated by the Equations 1.1 and 1.2, not only the rotation of molecules can be addressed by molecular absorption spectroscopy but, going to higher energies, also the vibration. There are four different possibilities: I. in a fundamental band, all the transitions leave the rovibrational levels of the vibrational ground state and arrive at rovibrational levels of a vibrational CHAPTER 1. Basics of molecular spectroscopy excited state characterized by a single quanta in a single mode,

GS ν i 2ν i ν i + ν j 3ν i 2ν j ν j (I) (I) (IV) (IV) (II) (II) (V) (V) (III)
v i = 1 ← v i = 0
II. in an overtone band, the transitions start from the vibrational ground state, as in a fundamental band, but arrive at the rovibrational levels of a vibrational excited state characterized by several quanta in a single mode,

v i = 2, 3, . . . ← v i = 0
III. in a combination band, the lower or upper level is a vibrationnaly excited mode with at least two excited modes.

v i = 1, v j = 1 ← v i = 0, v j = 0
IV. or V. in hot bands: the rovibrational transitions start from low frequency vibrationally excited states,

v i = 2, 3, . . . ← v i = 1

Fundamental bands

A fundamental band corresponds to a transition from a rovibrational level in the vibrational ground state (no vibrational mode is excited) to a rovibrational level with a single quanta in a single vibrational mode.

Molecular vibrational transitions are described in a first approximation with the model of the harmonic oscillator [12]. A molecule of N atoms has 3N degrees of freedom of independent displacements. Three of them are translations and three other are rotations of the molecule, leading to 3N -6 vibrational modes for a non-linear molecule. An estimation of the potential energy can be derived from the potential energy of a diatomic molecule approximated by a parabola (harmonic approximation) as it is shown in Figure 1.3 a) in red. The potential is given by Hooke's law for a spring:

V = 1 2 kx 2 , x = r -r e , (1.14)
where k is the force constant of the bond and r e is the bond length at equilibrium. Applied to the Schrödinger equation for the relative motion of two atoms: -

V = 1 2 kx 2 Morse potential dissociation energy displacement energy R e a) displacement energy R e v = 0 v = 1 v = 2 v = 3 v = 4 J = 0 J = 1 J = 2 J = 4 J = 5 J = 6 J = 3 b) Figure 1.
2 2m ef f d 2 Ψ vib dx 2 + 1 2 kx 2 Ψ vib = EΨ vib , (1.15)
with the vibrational wave function Ψ vib :

Ψ vib = 2 v v!π 1 2 -1 2 H v (y)e (-y 2 /2) , (1.16)
H ν (y) are the Hermite polynomials of y with y being:

y =       4π 2 vm ef f h       1 2
x.

(1.17)

The resulting energies E vib for the fundamental modes are:

E vib = ω i v i + 1 2 ; i ∈ {0, 1, 2, . . . , 3N -6} . (1.18)
In the harmonic approximation, the energy levels of one mode are equally CHAPTER 1. Basics of molecular spectroscopy separated by ω i . However, this approximation only suits well around the equilibrium position. The potential can be improved using the potential function proposed by Morse (shown in blue in Figure 1.3) or more generally by introducing anharmonic correction terms to the harmonic potential:

V = k 2 x 2 2! + k 3 x 3 3! + k 4 x 4 4! + • • • (1.19)
This leads to the vibrational energy of a fundamental mode [63]:

E vib = ω i v i + 1 2 -ω i χ e v i + 1 2 2 + • • • (1.20)
In a polyatomic molecule, if there are no resonant states, the vibrational energy levels of any mode are given as

E (v 1 , v 2 , . . .) hc = k ω k v k + 1 2 + k≥l χ k,l v k + 1 2 v l + 1 2 + • • • (1.21)
The anharmonicity also affects the selection rules for vibrational transitions. While only bands with the selection rule ∆v = ±1 could be observed in an IR spectrum following the harmonic oscillator model, as a consequence of the anharmonicity, also overtones of the type ∆v = ±2, ±3, ... and combinations are possible too, however with lower intensities.

The transition dipole moment is given by:

R v v = Ψ v µΨ v dx (1.22)
with the electric dipole moment µ expressed as a Taylor series expansion around the equilibrium position:

µ = µ e + dµ dx e x + 1 2
d 2 µ dx 2 e x 2 + • • • (1.23)
The subscript e refers to the equilibrium configuration of the molecule. Ψ v and Ψ v are eigenfunctions of the same Hamiltonian and therefore orthogonal, leading to an expression for the transition moment R v v in case of v v :

1.2. Rovibrational spectroscopy 25 R ν ν dµ dx e Ψ ν xΨ ν dx + • • • (1.24)
The transition intensity is proportional to the square of the magnitude of the transition moment. Therefore R v v = 0 is a forbidden transition while R v v 0 is an allowed transition.

Hot bands

Comparing a rovibrational spectrum recorded at room temperature with one at low temperature, additional bands, so called hot bands, can occur, see (IV) and (V) in Figure 1.2. In Section 1.1 the relative population for the fictional vibrational mode at 200 cm -1 was calculated showing that a considerable portion of the molecules occupy this vibrationally ES at room temperature. Those molecules can get excited towards higher vibrational levels as well, as long as these transitions fulfill the vibrational selection rules. Different transition types are possible when starting from a vibrationally excited state v i = 1; for example a transition to a higher level of the same mode v i = 2 (IV) or to another mode Equation 1.21). The energies of these transitions are then given as [56]:

v i = 1, v j = 1 (V) (see
(IV ) E v i =2 -E v i =1 = E v i =1 + 2χ i,i (1.25) and (V ) E v i =1,v j =1 -E v j =1 = E v i =1 + χ i,j (1.26)
The contribution of the anharmonic correction is usually small compared to the energies of the fundamental modes. The hot bands are therefore close to the fundamental band forming a series of weaker satellite bands with decreasing intensities. Based on Equation 1.20 the frequencies of these hot bands can be used to determine the anharmonic correction χ by [76]:

χ i,i = 2v i -v i -v i 2 (1.27)
and

v i + v j -v i -v j = χ i,j (1.28)
1.3 Large amplitude motions and internal rotation

Hamiltonians to describe large amplitude motions

While discussing the rotation in Section 1.1 and 1.2, the entire molecule was rotating as a rigid molecule. However, there is a class of molecules with one or more internal rotors which can rotate with respect to the rigid molecule frame. Depending on the barrier heights induced by sterical and/or electronic effects hindering the internal rotation, these so called Large Amplitude Motions (LAMs) lead to a splitting of the levels. The barrier can be described by a potential energy curve as the function of the torsional angle α [84]:

V (α) = a 0 + ∞ k=1 a k cos (kN α) . (1.29)
Depending on the nature of the LAM, a periodic N-folded potential V with N equivalent positions of the internal rotor as shown in Figure 1.4 is obtained.

In this work, splittings caused by the internal rotation of a methyl group in methylfuran and the tunneling splitting in catechol are treated in Chapter 7 and 4, respectively. The potential for the torsion of a methyl group with C 3v symmetry can be expressed as [7]:

V (α) = V 3 2 (1 -cos 3α) + V 6 2 (1 -cos 6α) + • • • (1.30)
Usually the first two terms of Equation 1.30 are sufficient to reproduce the potential V within the experimental accuracy. V 3 corresponds to the barrier height and V 6 is a higher-order correction. In Figure 1.4 a) the 3-folded potential for the methyl internal rotation is illustrated. Supposing a barrier height below 900 cm -1 [81], for which as a rule of thumb the resulting splitting can possibly be resolved in rotational spectroscopy, tunneling effects through the barriers are visible. This leads to a splitting of the three degenerate energy levels into the non-degenerate species A (σ = 0) and a doubly degenerate species E (σ = 1). In Figure 1.4 b) a 2-folded potential is given as an example for the inversion tunneling in catechol. The rotational energy levels split into two non-degenerate levels (+) and (-). To enable the analyses of rotational spectra containing line splitting caused by LAM, specific Hamiltonians are necessary. There are plenty of approaches for different cases but for the molecules treated in the work we will focus on asymmetric rotors coupled to a quasi symmetric C 3v rotating methyl and a C 2 hydroxy group.

CHAPTER 1. Basics of molecular spectroscopy

For a molecule with LAM, the total angular momentum Ĵ in the body-fixed or P in the principal axes system need to be extended by an additional angular momentum. The component Ĵα or P α describes the torsion of the internal rotor group.     

I a 0 0 λ a I α 0 I b 0 λ b I α 0 0 I c λ c I α λ a I α λ b I α λ c I α I α                  (1.32)
As long as we are in the Principal Axis System PAS, I can not be diagonalized anymore. λ g defines the angle between the internal rotor axis i and the principal axis g = a, b, c by:

λ g = cos (i, g) (1.33)
The Hamiltonian for the overall rotation Ĥrot containing the centrifugal distortion term introduced in Section 1.1 is extended by the torsional Hamiltonian Ĥtors and a term describing the internal rotation or to be more precise the torsional-rotational interaction Ĥint :

Ĥ = Ĥrot + Ĥtors + Ĥint (1.34)
To reduce the cross terms of Equation 1.32 and to simplify the diagonalization of the Hamiltonain, as it is done with the BELGI code, the Rho Axis Method RAM can be used. Therefore the PAS is rotated until the the z-axis is parallel to the vector ρ (see Equation 1.37). For the Hamiltonian this means:

Ĥtors = F (ρ a -ρJ z ) 2 + V (α) (1.35) 1.3. Large Amplitude Motions/Internal rotation 29 H R = A (cos θ RAM J z -sin θ RAM J x ) 2 + B (sin θ RAM J z + cos θ RAM J x ) 2 + CJ 2 y (1.36)
with,

ρ g = λ g I α I g , F = 2 2rI α , r = 1 - g λ 2 g I α I g (1.37)
and

θ RAM = arctan ρ x ρ z = arctan I z λ x I x λ z (1.38)
By grouping the terms, we get for prolate asymmetric tops of the reduction A and the representation I r :

Ĥrot = A RAM J 2 a + B RAM J 2 b + C RAM J 2 c + D ab (J a J b + J b J a ) (1.39)
Multiplying the powers of the rotational angular momentum components J i with the powers of the torsional operators p α (which is the internal rotation angular momentum conjugate to the torsion angle α), (1cos 3α), (1cos 6α) etc., Ĥint is obtained. Some resulting lower order terms of this multiplication are given in Table 1.2.

As already mentioned above these Hamiltonians treating the splitting are usually necessary to analyze rotational spectra containing internal rotation because (I) the frequency difference between the two species A (σ = 0) and E (σ = 1) resulting from the same rotational transition can vary strongly depending on the barrier height (kHz -GHz), (II) this frequency difference changes a lot with the quantum numbers J K a and (III) the order in energy of A and E can switch with the rotational transition. As an additional selection rule for the internal rotation only transitions of σ = 0 (A ↔ A and E ↔ E) are allowed.

In case of the inversion tunneling the description of the resulting splitting is simpler. The tunneling effect lifts the degeneracy and causes a splitting of the rotational level into two levels (+) and (-) of opposite symmetry. The wave functions Ψ + and Ψ -are linear combination of the wave functions of the two CHAPTER 1. Basics of molecular spectroscopy

Operator 1 1 -cos 3α p 2 α J a p α 1 -cos 6α p 4 α J a p 3 α 1 V 3 /2 F ρ V 6 /2 k 4 k 3 J 2 (B + C)/2 F v G v L v N v M v k 3J J 2 a A -(B + C)/2 k 5 k 2 k 1 K 2 K 1 k 3K J 2 b -J 2 c (B -C)/2 c 2 c 1 c 4 c 11 c 3 c 12 J a J b + J b J a D ab or E ab d ab ∆ ab δ ab d ab6 ∆∆ ab δδ ab J 4 a ∆ J f v g v l v n v m v o v J 2 J 2 a ∆ JK φ v γ v λ v v v µ v θ v J 2 a ∆ K f k g k l k n k m k o k -2J 2 (J 2 b -J 2 c ) δ J c 6 c 5 c 7 -{J 2 a , (J 2 b -J 2 c )} δ K c 9 c 8 c 10 J 6 H J J 4 J 2 a H JK h J1 h J2 h J3 J 2 J 4 a H KJ h K1 h K2 h K3 h K5 h K4 h K6 J 6 a H K J 4 (J 2 b -J 2 c ) h J J 2 {J 2 a , (J 2 b -J 2 c )} h JK {J 4 a , (J 2 b -J 2 c )} h K Table 1.2 -
The first lowest torsion-rotation RAM Hamiltonian terms as they are used in the BELGI-C s code for global treatment of internal rotation. These resulting terms are suitable for asymmetric top molecules with C s symmetry containing a C 3v internal rotor [65].

The parameters in black are related to the overall rotation of the molecule, those in blue to the internal rotation of the GS and in the ones in red to the internal rotation of the first torsionaly excited state (v t = 1).

equivalent configurations φ 1 and φ 2 :

Ψ + = 1 √ 2 (φ 1 + φ 2 ) Ψ -= 1 √ 2 (φ 1 -φ 2 ) (1.40)
The resulting energy levels of the linear combinations for Ψ + of Equation 1.40 are always lower and therefore the order stays always the same independent from the values of J and K a . If there are no other effects influencing the tunneling, the energy difference ∆E t remains constant and can directly be derived from the splitting ∆ν. Depending on the sign of the dipole moment µ g being changed during the tunneling or not the selection rules and hence the energy difference

Intensities of molecular absorption lines

In Section 1, only the nature of rotational, rovibrational and vibrational transitions were discussed. We are now able to explain the frequency of an observed line but so far we hardly spoke about its intensity. The only argument given in Section 1.2 is the Boltzmann distribution at the thermodynamical equilibrium with Equation 1.13. But not just (I) the number of molecules undergoing a transition is defining its intensity. The intensities of absorption lines are depending also on (II) the interaction pathlength, (III) the actual line strength associated with the dipole moment µ and the energies of the involved energy levels, (IV) the partition function and (V) the line profile depending on the recording of the spectrum.

Beer-Lambert law

The fundamental equation to describe absorption effects was invented by Beer and Lambert based on the discovery of Bouguer [18]. It relates the transmitted intensity I to the incident intensity I 0 through the concentration of the absorbing molecules N (in molecule • cm -3 ) along a interaction path L (in cm) and the molecular cross section σ ab (ν) (in cm 2 • mol -1 ):

I(ν) = I 0 e -σ ab (ν)N L (1.41)
The transmitted intensity I can also be expressed with the line intensity S(ν, T ) in (cm • mol -1 ): and with the normalized line profile g(ν, T , P ) described in Section 1.3.2 the absorption coefficient in cm -1 is defined by: α(ν) = σ ab (ν)N = S(ν, T )g(ν, T , P )N , (1.43) and the absorbance (without an unit) by: ln

I(ν) = I 0 e -S(ν,T )g(ν,T ,P )N L , ( 1
I 0 I = αL = A ν (1.44)

Intensities of molecular transitions

The following definitions were taken from the HITRAN high-resolution transmission molecular absorption database [42]. There are other possibilities as for instance the JPL (Jet Propulsion Laboratory of the NASA) database with a slightly different definition but for molecules of atmospheric interest HITRAN is usually preferred.

The emission spectral line intensity S(ν, T ) appears in HITRAN as S ij for a single molecule per unit volume in [cm -1 /molecule • cm -2 ]:

1.3. Large Amplitude Motions/Internal rotation 33

S ij = I a A ij 8πcν 2 ij g e c 2 E /T 1 -e -c 2 ν ij /T Q(T ) with c 2 = hc k B , (1.45)
with the frequency of the transition in vacuum ν ij (cm -1 ), the upper state statistical weight g , the lower state energy E (cm -1 ), the Einstein coefficient for a spontaneous emission A ij (s -1 ) and the total internal partition sum Q(T ). The Einstein coefficient A ij for transitions induced by electric dipole with the unit [s -1 ] is given by:

A ij = 64π 4 3h ν 3 ij g g R ij • 10 -36 (1.46)
R ij is the weighted transition-moment square. The total internal partition sum Q(T ) can be expressed by:

Q(T ) = i g i e - c 2 E i T (1.47)

Partition functions

The total partition function Q(T ) or as it is called in HITRAN, the total internal partition sum of Equation 1.47 can be approximated as the product of the different contributions derived from the spin-rotation partition function (g ns Q rot ), the torsion partition function (Q tor ) for the internal rotation of a methyl group and the vibration partition function (Q vib ):

Q(T ) = g gs i (2J i + 1) e E i kT g ns Q rot Q tor Q vib (1.48)
Expressed this way the relation of Q(T ) to the rotational angular momentum J of level i is emphasized. For asymmetric tops the rotational partition function Q rot can be approximated in case of temperatures significantly above 0 K or accordingly low rotational constants by: E) are the energies of the torsional levels ν t for the A and E symmetries.

Q rot = J,K a ,K c (2J +
Q tor = ν max t ν t =0          e - E (tor) (ν t ,A) k B T + e - E (tor) (ν t ,E) k B T          (1.50)
The vibration partition function Q vib is expressed in the harmonic approximation:

Q vib = 3N -7 i=1 1 1 -e E (vib) i /k B T (1.51)
For Q vib 3N -7 (with N as the number of atoms in the molecule) instead of 3N -6 fundamental modes of vibration are used because the torsion is already treated by Q tor of Equation 1.50.

Molecular absorption line profiles

According to the theories presented so far a spectroscopic line should be monochromatic with one sharp line of one discrete frequency in the spectrum. In reality, there are several effects and parameters causing to a broadening of the spectroscopic line. Some effects can be suppressed by adjusting the corresponding parameters to decrease the line width and to reach higher resolution. Some other represent the fundamental limitations on the resolution. Depending on which effects are given or dominant at certain measuring condition, we can define four regions for the line profile: (I) the natural, (II) the Gaussian, (III) the Lorentzian and (IV) the Voigt line profile:

Natural broadening ∆ν n : it can be explained with Heisenberg's uncertainty principle relating the uncertainty of the ES energy ∆E to the lifetime of that state ∆t:

∆ν n = ∆E h 1 2π∆t with ∆t = 1 A = 3hc 3 16π 3 ν 3 |µ| 2 , (1.52)
with the Einstein coefficient A, the transition frequency ν and the dipole moment µ. The natural broadening marks the fundamental limitation of the spectral resolution and can not be avoided. In high resolution THz spectroscopy of gases the natural broadening may be neglected compared to broadening effects.

Doppler broadening: at relatively low pressure the line width is Doppler limited. The exciting radiation is shifted in frequency due to the thermal agitation of the molecules towards or away from the source:

g D (ν, T , P ) = 1 ∆ν D ln 2 π exp       -ln 2 ν -ν 0 ∆ν D 2       with ∆ν D = ν 0 c 2N A kT ln 2 M 1 2 = 3.581 × 10 7 ν T M 1 2 (1.53)
Assuming the pressure to be sufficiently low the velocity of the molecules hence the resulting Doppler broadening g D (ν, T , P ) depends on the frequency of the source ν 0 , the molar mass M and the temperature T . The line shape can be approximated by a Gauss profile (see black function in Figure 1.6). To benefit from the exceptional selectivity of the THz high resolution spectroscopy, measurements are performed at the Doppler limit reached at very low pressure. SubMHz ∆ν D line widths are obtained at room temperature in the mm-wave domain.

Collisional broadening: at high pressure the molecular collisions become the dominant broadening effect g L (ν, T , P ). The broadening is not defined by the velocity of the molecules but the mean time between two collisions τ:

g L (ν, T , P ) ν πν 0 ∆ν L (ν -ν 0 ) 2 + (∆ν L ) 2 with ∆ν L = 1 (2πτ) (1.54)
The resulting line shape can be described by the Lorentzian line profile (red profile in Figure 1.6). The Lorentzian linewidth is proportional to the pressure of the gas in pure sample (∆ν L = γ self × P ) or the pressure of a perturber X in a diluted sample (∆ν L = γ X × P X ) with γ the broadening coefficients. Even at few mbar of pressure, ∆ν L reaches several MHz in the THz frequencies.

Voigt profile : at medium pressure both effects, Doppler and collision are contributing to the broadening. With the Voigt line profile, both Gauss and Lorentzian profiles can be combined as shown in blue in Figure 1.6 with an equal contribution:

g V (ν, T , P ) = g G (ν, T , P ) ⊗ g L (ν, T , P ) (1.55)
More sophisticated line profiles have been defined, yielding to Voigt profile deviations [80] but those will not be considered in this thesis. Chapter 2

Quantum chemistry methods

Outline of the current chapter Quantum chemical calculations and computational chemistry techniques are driven by two major limitations. The Schrödinger equation (Equation 1.3) of a molecular system can not be solved exactly, hence we need numerical approximations on computers. A lot of the following approaches and theories introduced in this section mainly aim to either simplify the studied system or to adapt to the operating modes of computers. Therefore balancing the computation costs and the accuracy by selecting a suitable level of theory for the given system is one of the main tasks of a computational chemist. To evaluate the quality of the obtained results is an other not trivial challenge.

The Born-Oppenheimer approximation

At the molecular scale and without the influence of relativistic effects, the dominant fundamental interaction is electromagnetic. The potential Vij between two particles (which can be electrons e or nuclei n) can therefore be described using the simple Coulomb interaction between charges q i and q j separated by distance

d ij : Vij = 1 4π 0 q i q j d ij . (2.1)
The Schrödinger equation for a molecule is The Born-Oppenheimer approximation resides on the difference of masses between the electrons and the nuclei. Due to the much larger value of the nuclear masses, the nuclei are considered as fixed. The single molecular Schrödinger equation 2.2 then becomes two equations. The first Schrödinger equation, with the clamped nucleus Hamiltonian Ĥe , describes the electrons with electronic energy E e (R):

Ĥtot Ψ tot (R, r) = E tot Ψ tot (R,
Ĥe Ψ e (r; R) = E e (R)Ψ e (r; R).

(2.

3)

The electronic wave function Ψ e depends parametrically on the nuclei coordinates. The second Schrödinger equation is about the motion of the nuclei:

Tn + E e (R) Ψ n (R) = E tot Ψ n (R).
(2.4) Equation 2.4 suggests to interpret the electronic energy E e (R) as a multidimensional potential energy surface PES depending on 3N -6 degrees of freedom (for a nonlinear molecule). The minima on this hypersurface represent stable conformers and transitions states are given by first-order saddle points with a maximum in one direction and minima in all the other directions.

The degrees of freedom define different motions in the molecule as it is shown in Figure 2.1: the distance between two atoms can vary (stretching), the angle between three atoms can change (bending) and the dihedral angle of four atoms can rotate (torsion). Additionally long-range interactions can occur by e.g. intramolecular hydrogen bonds or van der Waals forces.

The Hartree-Fock (HF) theory

In the Hartree-Fock (HF) method, the antisymmetric total wave function is the product of molecular orbitals (MO), which are single-electron wave functions. The electron-electron interactions are not computed exactly but averaged thus the electrons move in the mean field generated by the other electrons. To ensure an antisymmetrical total wave function and to respect the Pauli principle, saying CHAPTER 2. Quantum chemistry methods stretch non-bond bend torsion

Figure 2.1 -The typical motions in a molecule: a stretching mode changes the bond length between two atoms, a bending mode changes the angle defined by three atoms and a torsion changes the dihedral angle between two planes defined by four atoms. Long-range interactions through an hydrogen bond or van der Waals forces are possible, too.

that two electrons as indistinguishable fermions can not have all quantum numbers equal, the total wave function is constructed as a Slater determinant containing the single-electron MOs built as products of the spatial orbital and the spin (α or β), called spin-orbitals:

Φ SD = 1 √ N ! φ 1 (1) φ 2 (1) . . . φ N (1) φ 1 (2) φ 2 (2) . . . φ N (2) . . . . . . . . . . . . φ 1 (N ) φ 2 (N ) . . . φ N (N ) ; φ i |φ j = δ ij .
(2.5)

The variational principle with the Slater determinant as the test function leads to the best set of MOs. The Fock operator Fi is defined from the oneelectron operator ĥi describing the kinetic energy of the electron i in the field of all nuclei, Ĵ the Coulomb and K the exchange interactions:

Fi = ĥi + N elec j Ĵj -Kj .
(2.6)

Møller-Plesset second-order 45

The total energy is given with:

E = N elec i ε i - 1 2 N elec ij Ĵij -Kij +V nm with ε i = φ i | Fi |φ i = ĥi + N elec j Ĵij -Kij .
(2.7)

V nm is the nuclear repulsion operator which is independent of the electron coordinates and thus constant. Because Fi depends through Ĵ and K on all occupied MOs the Hartree-Fock equations form a set of pseudo-eigenvalue equations which means that to determine a specific Fock orbital, all other orbitals need to be known. Therfore a iterative method is needed to produce "selfconsistent field" orbitals.

The electron-correlation method Møller-Plesset second-order (MP2)

One approach to improve over the mean-field theory of Hartree-Fock is to use a perturbation method. With the assumption that the studied system is somehow close to a known one, the exact Hamiltonian is splitted into two parts: the reference Ĥ0 for the known system and the perturbation Ĥ [77]:

Ĥ = Ĥ0 + λ Ĥ .
(2.8)

The parameter λ represents in this case the strength of the perturbation. The first-order correction to the energy is null E(MP 1) = 0 and hence we have to go up to the second-order to get some correction to the Hartree-Fock energy. The Møller-Plesset perturbation theory of second-order the Schrödinger equation is [77]:

Ĥ0 Ψ 2 + Ĥ Ψ 1 = W 0 Ψ 2 + W 1 Ψ 1 + W 2 Ψ 0 (2.9)
This equation contains two unknown correction terms to each the wave function Ψ 1 and Ψ 2 and to the energy W 1 and W 2 . The second-order correction for Møller-Plesset is given as: CHAPTER 2. Quantum chemistry methods

E(MP 2) = occ i<j vir a<b φ i φ j |φ a φ b -φ i φ j |φ b φ a 2 ε i + ε j -ε a -ε b .
(2.10)

The Density Functional Theory (DFT)

It was found that the GS electronic energy can be reproduced completely by a functional of the electron density ρ. The breakthrough of DFT in computational chemistry is strongly related with Kohn and Sham who suggested to calculate the kinetic energy of the electrons from a set of orbitals modeling the electron density and to split the kinetic energy functional into a part which can be computed exactly and a small correction term [66]. The DFT energy E DFT is defined as the sum of the non-interacting kinetic energy T S , the attractive potential between nuclei and electrons E ne , the Coulomb interaction potential J and the exchange-correlation energy E XC :

E DFT [ρ] = T S [ρ] + E ne [ρ] + J[ρ] + E XC [ρ] (2.11)
In this case the exchange-correlation energy E XC contains the difference between exact kinetic energy T and non-interacting kinetic energy T S , the exchange and the correlation energies as the remaining parts of the electron-electron interaction energy subtracted by the Coulomb potential J:

E XC [ρ] = (T [ρ] -T S [ρ]) + (E ee [ρ] -J[ρ]) (2.
12)

The exchange-correlation functional is not known and a lot of approximate functionals have been proposed such as B3LYP [16,69,96] and M06-2X [106].

An explanation for the non-interacting kinetic energy T S missing some kinetic energy is the use of an approximate density ρ approx to calculate it. An exact density would require an infinite number of natural orbitals to be considered and therefore the density is given as a set of one-electron orbitals:

ρ approx = N elec i=1 |φ i | 2
(2.13) 2.6. Basis sets 47

Basis sets

In computational chemistry, the unknown molecular orbitals are typically decomposed in a set of known atomic orbitals. Two mathematical functions commonly used as "basis functions" are: Slater-Type Orbitals (STOs) and Gaussian-Type Orbitals (GTOs). Each individual function defines a "primitive" and a fixed linear combination specifies a "contracted" function. The collection of these basis functions is then called the "basis set". To represent a molecular orbital completely and accurately, an infinite number of functions would be necessary. Therefore a compromise between computational effort and accuracy needs to be found for each study. In general, the smaller the basis set is, the smaller the computational effort is, but the accuracy is poorer. Even though the computational effort scales formally as at least M 4 basis the computational effort is not just defined by the number of basis functions. The type and choice of basis functions influences the accuracy.

The smallest basis set is the Single Zeta (SZ) basis set giving the minimum description of the occupied orbitals. The term zeta ζ is derived from the exponent of the functional describing STOs:

χ ζ,n,l,m (r, θ, ϕ) = N Y l,m (θ, ϕ) r n-1 e -ζr , (2.14)
with N the normalization constant and Y l,m the spherical harmonic functions. For a hydrogen for instance, SZ leads to only one single s-function and for carbon two s-functions and one set of p-functions (1s, 2s, 2p x , 2p y and 2p z ). Moving from SZ to Double Zeta (DZ), the number of all basis functions is doubled which gives: two s-functions (1s and 1s ) for the hydrogen and four s-functions as well as six p-functions for carbon (1s, 1s , 2s, 2s , 2p x , 2p x , 2p y , 2p y , 2p z and 2p z ). Further improvements of the description of bonds for instance is achieved by introducing polarization functions. Usually the first extension (p-functions for the s-functions of hydrogen or d-functions for the p-functions of carbon) describes most of the important charge polarization effects. Chapter 3

Experimental and analytical methods

Outline of the current chapter 3.1 mm-wave spectrometer 52

3.2 Far-IR-FTIR spectrometer 56

Analytical tools 56

The main experiment used during this PhD is a solid state sub THz spectrometer developed in the LPCA Dunkirk described in [82,90]. A schematic presentation is given in Figure 3.2. For the catechol study, the rovibrational spectra were measured using synchrotron based FT-Far-IR spectroscopy with the AILES beamline of SOLEIL [19]. The catechol Far-IR spectra were measured before the begin of this thesis but not analyzed. I participated to a SOLEIL/AILES run in 2020 with the same setup and procedure to measure the furfural Far-IR spectra which will be analyzed soon taking into account additional results obtained very recently in during a new measuring campaign. This work will be not presented in this thesis, only a description of the setup is given in Section 3.2.

The used samples are commercially available molecules purchased from common vendors and used without further purification. The solid or liquid samples are provided in a reservoir attached directly through a valve to the cell. Volatile molecules with a vapor pressure > 50 µbar were chilled by an 52 CHAPTER 3. Experimental and analytical methods ice/ethanol/LN 2 -mixture to reduce their partial pressure.

In this chapter, only the currently used instruments of this thesis are presented. In the last part of this manuscript, I will present the new experimental developments to which I contributed during my thesis which open new perspectives for other spectroscopic studies.

3.1 The versatile solid-state mm-wave spectrometer of the LPCA An oscillating microwave source generator (Rhodes & Schwarz SMA 100 A) synthesizes linear polarized radiation with a frequency in the 7.8 to 12.2 GHz range. The accuracy of the generated frequency is provided by referencing the synthesizer to a GPS signal. The microwaves are then up-converted to the mmwave range by an Amplifier/Multiplier Chain (AMC) from Virginia Diodes Inc. (see Figure 3.1), based on the use of non-linear devices to generate harmonics.

mm-wave spectrometer 53

The current-voltage characteristics of Schottky diodes allow the production of these harmonics.

As illustrated in Figure 3.1 depending on the type and number of used (GaAs) Schottky diode multiplier different spectral ranges are covered. With the first rank of multiplication (×9) and the second rank (×18) the frequency ranges of 70 -110 GHz ("band 1") and 140 -220 GHz ("band 2") are accessed. For the targeted medium-sized molecules catechol and MF these two frequency stages are sufficient. Within this spectral range already high quantum numbers were observed (codes as XIAM and BELGI are usually limited to certain values or the computational efforts get to huge) and the analysis of the rotational spectra led to high precision parameters. The effective ranges for these "band 1" and "band 2" depend not just on the multiplication chain but are also limited by the coverage of the dedicated detectors.

In general there are several detection solutions. In advance to this PhD for for instance a bolometric detector (InSb) was used for some bands [90]. Even though a bolometer is very sensitive, it requires cooling with liquid helium (> 4 K) and therefore the more practical VDI Zero-Bias-Detector (ZBD) operating at room temperature were preferred. These ZBD are again (GaAs) Schottky diodes. These detectors provide high responsivity and extremely fast response time. The VDI ZBD offer full waveguide band coverage adopted to the AMC frequency ranges (bands). A computer-controlled Ametek7230 lock-in amplifier recovered the measured signal as a function of the frequency.

The major drawback of using a multiplication chain to reach higher frequencies is the loss of emission power. While the output power of band 1 is given with 20 mW in the VDI user guide it is only 2 -10 µW for band 6.

As it is illustrated in Figure 3.2 the guided radiation is then launched into free space by a hornet antenna. The diverging radiation is collimated by an off-axis parabolic mirror towards the direction of the absorption cell. Before the beam enters the cell a polarization wire-grid set to transmission is passed. If working with band 1 a second polarization grid is added. By adjusting the emission power with this grid the detector, which is limited to 1 V, is protected and the recorded spectrum does not saturate. The setup contains of a computer to drive the experiment, a frequency generator connected to a multiplication chain, off-axis parabolic mirrors to collimate or focus the beam, a polarization wire-grid to double the interaction path-length, the absorption cell and the Zero Bias Detector connected trough a lock-in amplifier to the computer to record the second harmonic of the frequency modulated signal. During this PhD the experiment was equipped with a heating coat to increase the partial pressure of semi-volatile molecules (see Chapter 8). through a Teflon window. As it is indicated in Figure 3.2 the beam passes the cell a second time after being reflected by a roof-top mirror. Due to this double pass configuration the interaction path-length is doubled. The roof-top mirror rotates the polarization of the beam about 90 • . Thus after passing the cell the second time the beam is reflected by the polarization grid onto another off-axis parabolic mirror focusing the beam into the ZBD unbiased Schottky diode mounted in a wave-guide operating in detection mode. To increase the sensitivity the second harmonic of the frequency modulated signal is recorded removing partially the To remove all the baseline variations caused by stationary waves between the source, the polarization grids, the cell and the detector, as shown in Figure 3.3 a), a post treatment with a Fast-Fourier-Transform (FFT) band-pass filter implemented in Origin 2019b is used. The FFT of a raw spectrum with a sufficiently large frequency range reveals three parts (Figure 3.3 b)). A low-frequency part containing the baseline variations, the middle part containing the molecular absorption lines and the high-frequency part containing just noise. As indicated in Figure 3.3 b) in red, the first and third part are blocked by the band-pass filter, only keeping the part containig the molecular signal. Then the final spectrum is obtained (Figure 3.3 c)).

Synchrotron based Far-IR-FTIR spectrometer

The synchrotron-based FT-far-IR spectra presented in this section were recorded in advance to this PhD and the experimental details given were not executed by me but based on the experience I gained during a similar measuring campaign of Furfural C 5 H 4 O 2 I participated. A first assignment of the measured rovibrational bands were carried out by the two Master interns Hamdi Bayoudh and Thi Thanh Tran in collaboration with the other authors of [21].

The high-resolution FT-far-IR spectrum of catechol was recorded at the synchrotron "Source Optimisée de Lumière d'Énergie Intermédiaire du LURE" (SOLEIL) in Paris/France. Solid catechol of 99% purity purchased from Fisher Scientific was used for the measurements without any further purification. With a vapor pressure of about 1Pa at room temperature the sample was injected directly to the cell. The far-IR radiation is extracted from the synchrotron SOLEIL into the Advanced Infrared beamLine Exploited for Spectroscopy (AILES) THz/far-IR beamline and focused through the entrance aperture beamsplitter into the Bruker IFS 125 FT interferometer equipped with a 6 µm mylar-silicon composite beamsplitter appropriate for THz and far-IR radiation. An absorption path length of 150 m is obtained with the use of a White-type multipass cell, which is isolated from the interferometer by a 50 µm polypropylene window. The signal is then detected by an helium-cooled silicon bolometer equipped with an optical band-pass filter. This experiment explained more in detail in [20] operates in the 10 -700 cm -1 range.

Analytical tools for spectra analysis

To interpret and analyze the obtained spectra different programs and codes were used. The two fundamental programs are part of the Assignment and Analysis of Broadband Spectra AABS package [62]. With the "SVIEW_L" program the recorded spectra given as an ascii file with a frequency and an intensity column can be visualized. "ASCP_L" is used to display predicted lines as a simulated spectrum contained in a ".cat" file. With "SVIEW_L" and "ASCP_L", the two windows showing respectively the observed and the calculated spectra are synchronized. A direct assignment procedure is performed creating a line list (".lin" file) containing the quantum numbers of the predicted transitions and the observed frequencies of the assigned absorption lines.

In cases no specific other codes are required to treat for instance LAM, the two programs from H. M. Pickett can be used to generate the ".cat" and the ".lin" files (see Figure 3.5). With "SPCAT" a list of predicted lines (.cat file) and the order of the rotational energy levels (.egy file) are derived from one file containing the Hamiltonian parameters (.var file) and the dipole moments as well as the temperature required for the line intensities in the ".int" file (see Figure 3.5a)). After assigning some lines in the ".lin" file and providing an initial set of Hamiltonian parameters (.par file) a fit can be run with the "SPFIT" program. A new set of Hamiltonian parameters is obtained in a updated ".par" file and the results of the fit are summarized in the ".fit" file (Figure 3.5b)). The fitting process could be considered as finalised when all the fitted parameters are correctly determined and when the root-mean-square (rms) has reached the experimental accuracy (unitless rms close to 1).

A main advantage of SPFIT/SPCAT is the possibility to treat several states independent but simultaneously. As it will be shown in Section 4 for catechol the GS and five vibrationally ES were treated simultaneously, for instance. After one state which is usually the GS, the initial sets of ES parameters are derived from quantum chemical anharmonic calculations even though they are not precise in absolute values especially for low-frequency modes. Therefore they are scaled by [92]:

[A, B, C] ES est = [A, B, C] ES abinitio × [A, B, C] GS exp [A, B, C] GS abinitio (3.1)
Since it is also possible to include all these states into the simulated spectrum produced by the .cat file in "ASCP_L" it facilitates the assignment of dense or congested spectra.

As already explained in Section 1.3 molecules containing methyl-groups can exhibit a splitting of their rotational lines caused by the internal rotation of the methyl groups. Therefore codes providing a specified Hamiltonian are required. An overview on available codes is summarized at the "Programs for ROtational SPEctroscopy" (PROSPE) [61], managed by Z. Kisiel.

Probably the most commonly used one is the eXtended Internal Axis Method Analytical tools 59 (XIAM) written by Hartwig and Dreizler [47]. Its main advantages are probably its speed and its robustness originated in the use of the co-called "combined axis method" (CAM). Since couplings between the internal and overall rotation lead to large off-diagonal elements in a Hamiltonian matrix setup in the PAM, XIAM transfers each rotor and state into its own rho axis system (RAS). As the Hamiltoninan matrix is diagonal in the rho axis system solving it is fast and efficient. Afterwards everything is transferred back into the PAS. Because XIAM is treating each torsional state separately, with their own set of molecular parameters, by neglecting the off-diagonal coupling terms in the Hamiltonian matrix describing the couplings of different states it is called a "local" approach (see Chapter 7, comparing local and global approaches and discussing it more in detail). XIAM allows to combine up to three internal rotors, to fit up to the sextic rotational centrifugal distortion constants and coupling centrifugal distortion constants between global and internal rotation up to 4 th order.

In contrary to the local approach of XIAM, Hougen and Kleiner developed the BELGI series of codes for asymmetric tops containing one or two internal rotors with ether C s or C 1 symmetry treating all torsional states up to a definable truncation level regardless they are actually assigned and fitted. Therefore it is called a "global" approach, with an unique set of molecular parameters which is particularly successful for low barriers, high excited or strongly perturbed torsional states. The RAM internal-rotation Hamiltonian used in BELGI -C s is based on the work Kirtman [60], Lees and Baker [70] and Herbst et al. [51]. In comparison to XIAM BELGI gives access to numerous higher order parameters but because they are not transferred and therefore given in the PAS. An overview is given in Table 1.2. Since the global approach of the BELGI code is including all torsional states regardless they are observed, assigned and supposed to be fitted and the parameters are given in the RAS the handling is more complex and the fitting more time consuming compared to XIAM. During my thesis, I have been trained in the use of BELGI by Isabelle Kleiner during a stay at the LISA laboratory of Créteil.

For the presented codes and especially to combine those, different small scripts and converter were used. To convert for instance the transition labeling given in the .lin file after assigning with AABS to the form suitable for the BELGI code, a custom made converter was written. Several other converter and scripts for sorting or labeling were provided by Anthony Roucou and Guillaume Dhont enabling the treatment of the large obtained data sets.

Part II

Catechol & Intramolecular Hydrogen bonds

The second part of the manuscript, structured in two chapters, started as a continuation of the work initiated at LPCA by Anthony Roucou's thesis and Atef Jabri's post-doctorate. They were interested in phenol derivatives, which are VOCs identified in CHARME as sources of SOA in the atmosphere. After their studies on methoxyphenols [91,53,11] (I am the second author of [11], carried out during my master internship at the MONARIS laboratory in Sorbonne University) they were confronted to flexible molecules with a complex conformational landscape. Only pure rotational and vibrational spectroscopy experiments at room temperature were successful, thus we decided to focus on a simpler VOC: catechol, the simplest oxygenated ortho-di-substituted phenol derivative.

With catechol, it was possible at room temperature to combine rotational and rovibrational spectroscopy experiments covering the entire THz range. The ozonolysis of catechol was studied in the LPCA-one smog chamber, the forerunner model of CHARME, revealing an efficient SOA formation [26]. Furthermore, catechol exhibits only one conformer populated at room temperature, stabilized by an intramolecular hydrogen bond (IHB).

Hydrogen bonds (HBs) in general and IHBs in particular play a fundamental role in the stability of biomolecules such as proteins. The understanding, investigation and quantification of their strength remains challenging even though the term hydrogen bond was reported for the first time one century ago to describe this specific type of interaction.

The first chapter is dedicated to the pure rotational mm-wave and to the rovibrational far-IR room temperature spectroscopy of catechol, relating the spectroscopic results to the influence of an IHB dynamics as it is reported in our publication "Intramolecular H-Bond Dynamics of Catechol Investigated by THz High-Resolution Spectroscopy of Its Low-Frequency Modes" by Bruckhuisen et al. in Molecules 2021 [21]. The full article is reproduced.

The second chapter reports an extended study of IHBs of several organic planar oxygenated ortho-substituted aromatic molecules by theoretical investigations of their electronic densities. This is a collaborative work with Cecilia Pech, Arnaud Cuisset and Guillaume Dhont from the LPCA, Valérie Vallet and Manuel Goubet from the PhLAM laboratory in Lille and Małgorzata Olejniczak 66 CHAPTER 3. Experimental and analytical methods from the centre of new technologies of Warsaw. It will be the object of a future publication which is in preparation [22].

Chapter 4 Intramolecular H-Bond Dynamics of Catechol Investigated by THz High-Resolution Spectroscopy of Its Low-Frequency Modes

The following article of our work on catechol (1,2-dihydroxybenzene), an organic planar oxygenated ortho-substituted aromatic molecule of formula C 6 H 4 (OH) 2 , combines two topics: (I) the THz spectroscopy of a VOC involved in atmospheric chemistry and the formation of secondary organic aerosols and (II) the investigation of weak intramolecular hydrogen bonds in isolated molecules. The originality of this work is to use both THz rotational and rovibrational spectroscopies to determine some properties related to the influence of the intramolecular hydrogen bond dynamics.

For a lot of biogenic molecules and complex molecules in living matter, structural and physical properties are defined by IHBs. Important biological processes are related to the dynamics, the breaking and reforming of IHBs [95]. Probably the most important examples are secondary and tertiary structures of proteins. These three dimensional structures are mainly stabilized by IHBs [89]. Unfortunately, the investigation of such a system and its IHBs remains challenging due to its complexity, as well as the number of different interactions, 68 CHAPTER 4. Catechol effects and IHBs contributing to its overall structure and properties. Due to its planarity and simplicity of the groups involved in the formation of just one IHB, catechol seems an appropriate candidate for the study of IHBs. Working at low pressure in the gas phase leads to an isolated observation of catechol without any other interactions.

The study on catechol reported in this chapter consists of the investigation of two rovibrational bands in a synchrotron based FT-far-IR (Fourier-transform far infrared) spectrum and the analysis of the vibrational ground state (GS) and the five lowest vibrationally excited states (ES) in a pure rotational spectrum. This work was supported by quantum chemical explorations of the conformational landscape of catechol and an analysis of the IHB through the topology of the electronic density based on the Quantum Theory of Atoms in Molecules (QTAIM) [13] The results of these investigations will be interpreted in the context of the influence of the IHB dynamics to the rotational spectroscopic parameters. A new approach to directly relate spectroscopic results to the IHB will be introduced for this class of planar molecules.

Intramolecular H-Bond Dynamics of Catechol Investigated by THz High-Resolution Spectroscopy of Its Low-Frequency Modes 1. Introduction

To a large extent, complex molecules in living matter have structures and properties that are determined by intramolecular hydrogen bonds (HBs). For understanding biological processes, the dynamics of HB formation and breaking is important [1]. For example, proteins are an important class of biomolecules where intramolecular HBs play a fundamental role in stability [2]. The rovibrational signatures of intramolecular HBs have mainly been studied in the mid-IR by probing the local stretching of the R-H donor and acceptor functional groups [3]. Yet, the vibrational modes directly involved in the dynamics of the intramolecular HB lie at lower frequencies in the far-IR region [4].

Compared to the mid-IR, the far-IR spectroscopy allows exploration of the dynamics of low-energy vibrations involving the full molecular backbone. That explains why far-IR/THz high-resolution spectroscopy is so efficient in discriminating subtle structural differences in particular in aromatic compounds (stable conformers [5], isomers [6], etc.). The low-frequency HB dynamics have been studied directly in the far-IR/THz domain with low or middle resolution vibrational spectroscopy techniques [7][8][9] or indirectly, at high resolution, using electronic excitations [10]. The full potential of high-resolution far-IR/THz gas-phase spectroscopy of isolated (bio)molecules with intramolecular HB remains unexplored today.

The main explanation for this statement is likely the difficulty to find a good molecular candidate and the adapted far-IR/THz spectroscopic technique allowing the detection and resolution of the rovibrational transitions involved in the intramolecular HB dynamics. Ortho-substituted aromatic compounds are probably the most simple and the most commonly cited examples of intramolecular HB. Among them, catechol (1,2-dihydroxybenzene) is an interesting molecule because its two vicinal hydroxy groups can act interchangeably as both hydrogen donors and acceptors in internal HB [11].

Moreover, the gas phase spectroscopic study of catechol is particularly interesting for at least two reasons: (i) catechol is produced in the atmosphere with high yields, around 80%, by the -OH oxidation of the major atmospheric aromatic compounds (benzene, phenol, cresol...) and its ozonolysis contributes significantly to the aerosol loading of the lower troposphere in polluted areas, where ozone concentrations could be high [12]; (ii) catechol moieties are also found widely within the natural world: drugs, hormones/neurotransmitters, poisons found in plants,... Many catechol derivatives have been suggested for therapeutic applications [13].

The microwave spectrum of catechol was studied at the end of the 1980s [11,14], and its assignment revealed a single conformation with a planar structure involving an intramolecular HB. The strength of this HB was discussed from the negative inertia defect, which arises mainly from out-of-plane vibrations of the molecule [15]. Only the ground state (GS) rotational transitions were assigned, and no spectroscopic features connected with the internal -OH rotations were observed.

The vibrations of catechol were also the subject of numerous IR and Raman studies in the gas phase and in the condensed phase. Gas phase investigations are limited to the spectral range above 740 cm -1 , below this, only solid phase studies have been reported so far. The experimental frequencies were compared to the vibrational frequencies obtained from ab initio normal mode calculations at the HF/6-31G(d,p) level of theory [16].

The gas phase far-IR/THz spectra were measured recently by Bakker et al. using the free electron laser FELIX in a more general study of the low-frequency vibrational signatures of intramolecular HB in phenol derivatives [4,7]. The B3LYP-D3 functional provided the best results for the large amplitude anharmonic modes, such as the -OH torsional modes. Three vibrational modes have been identified, which are expected to be diagnostic for the HB strength: HB stretching and HB donating and accepting -OH torsion vibrations. For these measurements, the catechol molecules were expanded in a supersonic jet and probed via low-resolution conformer selective IR-UV ion dip spectroscopy (the REMPI technique).

In the present study, B3LYP and MP2 harmonic and anharmonic calculations using a large basis set were used to predict and interpret the high-resolution rotational and rovibrational spectra of catechol measured respectively by millimeter (mm)-wave and synchrotron-based Fourier-transform (FT)-far-IR spectroscopies. In addition to a fine description of the conformational landscape, a topological analysis of the intramolecular HB was performed.

To the best of our knowledge, the complete rovibrational analysis of the free and bonded torsional modes involved in the intramolecular HB presented in this study is unprecedented. Moreover, in addition to the refinement of GS parameters, the pure rotational transitions in the four lowest energy vibrationally excited modes were assigned in the mm-wave spectra. Finally, splittings due to tunnelling effects are resolved for the rotational transitions excited in the free -OH torsion state.

Results and Discussion

Quantum Chemistry Calculations

Two-Dimensional Scan of -OH Torsional Modes

In order to explore the conformational landscape of catechol, a 2D scan of the two -OH torsional modes was performed and is presented in Figure 1. The dihedral angles D 8 and D 10 used to describe the -OH torsional motions as defined in Figure 1 are different to those introduced in a previous 2D minimal energy torsional surface [17]. The authors in [18] highlighted the need to take care of the symmetry of the molecule in the definition of the angles involved in the description of the internal rotation.

The dihedral angles defined in Figure 1b allow a very convenient use of the symmetry of the catechol molecule, while the coordinates proposed by Bürgi et al. in [17] did not take advantage of it. The molecular symmetry group of catechol is M S4 , which was already used to interpret the structure of the energy levels in phenol [19]. In addition to the identity operation E, it contains the inversion operation E * , the permutation (αβ) which exchanges the nuclei with respect to the dashed vertical plane on Figure 1 and the permutation-inversion (αβ) * . The action of the M S4 group on the two torsional angles is given in Table 1.

E E

* (αβ) (αβ) * D 8 D 8 -D 8 D 10 -D 10 D 10 D 10 -D 10 D 8 -D 8
The 2D scan in Figure 1 shows the electronic energy as a function of the two torsional angles. The surface reveals the existence of two equivalent global minima stabilized by an intramolecular HB. For minimum A 1 (±180 • , 0 • ), the O(5)-H( 11) is the proton acceptor group and the O(7)-H( 13) is the proton donor group, while the roles are reversed for the A 2 minimum (0 • , ±180 • ). The path that starts from the global minimum A 1 and ends at the equivalent global minimum A 2 goes through the saddle points B 1 or B 2 whose energy is approximately 1200 cm -1 above the energy of the global minima. Point C corresponds to a secondary minimum that is significantly higher in energy (around 1300 cm -1 ) compared to minima A 1 and A 2 .

The details of all the identified stationary points are presented in Table 2. Our energy surface depends on two dihedral angles (D 8 , D 10 ) ∈ [-180 • , 180 • [ 2 and is, thus, defined on a two-dimensional torus. Therefore, we can check that the number of each type of stationary point is consistent with the topology of a torus. Using [20] and introducing the numbers c 0 = 3 of the minima (A 1 , A 2 , and C), c 1 = 7 of saddle points (B 1 , B 2 , D, E 1 , E 2 , E 3 , and E 4 ) and c 2 = 4 of the maxima (F 1 , F 2 , G 1 , and G 2 ), the equality c 0 -c 1 + c 2 = 0 indicates that we did not miss any stationary point. The fingerprint of an intramolecular HB was searched in the electron density of the lowest energy conformer A (see Figure 1) of catechol calculated with the B3LYP functional. The topological analysis distinguishes the critical points of the electron density according to their signature. In particular, the nuclei are typically located at the maxima, while the bond critical points suggest the existence of either a covalent bond or a HB. Figure 2a presents the critical points determined with the cc-pVDZ basis set.

This shows the signature of an intramolecular HB. However, this one disappears in Figure 2b when a larger basis set, such as cc-pVTZ is used or when diffuse functions (aug-cc-pVnZ) are introduced. Figure 2a highlights that the cc-pVDZ overestimates the difference in the electron density between the HB and ring critical points. In [21], Mandado et al. noticed the same behaviour concerning the dependence on the size of the basis set. This dependence is due to the weak intramolecular HB of catechol compared to other phenol derivatives as was shown in [4].

Synchrotron-Based FT-Far-IR Spectroscopy

The synchrotron-based FT-far-IR spectrum of catechol, shown in Figure 3, was measured at high resolution ( 0.001 cm -1 ). In this section, we present, first, a vibrational analysis based on the Q-branches observed at medium and high resolutions. Then, we will describe the rovibrational fit of the two intense torsional -OH bands. To the best of our knowledge, it is the first time that a rovibrational assignment was performed on both free and bonded -OH torsional modes involved in the dynamics of the intramolecular HB.

Vibrational Analysis

The catechol molecule belongs to the C s symmetry group with 36 normal modes: 25 A' and 11 A" modes. In this study, we chose to keep the vibrational labelling of Gaussian output files with a classification based on the C s symmetry instead of the labelling based on the C 2v symmetry of monosubstituted benzenes [23] used in previous catechol studies [16,17]. Table 3 presents the low-frequency vibrational modes lying in the far-IR spectral range shown in Figure 3. Ten fundamental vibrations are located below 600 cm * In parentheses, the vibrational labelling used for monosubstituted benzenes [23] and used in previous catechol studies [16,17]. ** Twisting and wagging correspond, respectively, to antisymmetric and symmetric out-of-plane (oop) bending modes; Scissoring and rocking correspond respectively to symmetric and antisymmetric in-plane (ip) bending modes. a REMPI low-resolution gas phase vibrational measurements from [4]. b Solid state IR and Raman measurements from [16].

Considering the theoretical calculations, the two modes associated to the free and bonded -OH torsion have strong intensities (I harm > 70 km.mol -1 ) compared to the other low-frequency modes (I harm < 8 km.mol -1 ). Indeed the FT-far-IR spectrum exhibits two intense rovibrational bands around 222 cm -1 and 415 cm -1 , respectively, for the ν 35 free and the ν 33 bonded -OH torsion. These two bands are pure c-type, and their rotational structures are resolved in the P-and R-branches allowing the rovibrational analysis of catechol (see Section 2.2).

The measured vibrational band centres agree with the REMPI gas phase measurements of [4]. If we consider now the calculated harmonic and anharmonic IR frequencies and intensities at the B3LYP-D3/aug-cc-pVTZ level of theory, which provides us the best global agreement with the experimental ones, we note that the computational method fails to determine the anharmonic contribution of the -OH torsional modes. This could be explained by the large amplitude motions in these out-of-plane (oop) modes involved in the intramolecular HB, which cannot be treated with perturbation methods. These two torsional modes may be better described in a variational calculation with a Hamiltonian model of reduced dimensionality using our 2D PES [24].

Except for the two -OH torsional modes, all low-frequency fundamental vibrations of catechol exhibited poor IR activities with calculated intensities below 8 km.mol -1 . Yet, numerous other intense Q-branches were observed on both sides of the ν 35 and ν 33 band centres (see Figure 3). Considering the calculated frequencies and intensities, these Qbranches were not assigned to fundamental bands but to hot bands of the -OH torsional modes. None of the other modes have been measured yet in a gas phase far-IR spectrum except the ν 25 mode, involving the intramolecular HB stretching, observed in the REMPI experiment of Bakker et al. [4] at 309 cm -1 in good agreement with our calculated values.

In our FT-far-IR spectra, no vibrational signature was visible in this region (see Figure 3). Compared to the c-type bands of the torsional modes, this A' symmetry mode does not induce an out-of-plane variation of the dipole moment leading to a sharp Q-branch, which is easy to identify in the spectrum. The other O-C-C-O bending modes were observed only by solid state Raman measurements [16], and the measured frequencies are in the range defined by our B3LYP-D3 harmonic and anharmonic calculations. Finally, the overtones 2ν 36 and 2ν 35 and the combination band ν 36 + ν 35 were predicted in the 400 cm -1 region by the anharmonic B3LYP-D3/aug-cc-pVTZ calculation. These bands are too weak to be observed and may be masked by the intense ν 33 bonded -OH torsional band. As mentioned previously, the numerous Q-branches, observed in the room temperature FT-far-IR spectra revealed complex vibrational patterns of hot bands on both sides of the ν 35 and ν 33 Q-branches. Their strong intensities reflect the strong c-type transition dipole between the GS and the two -OH torsional oop states. Some of these hot bands are localised far from the ν 35 and ν 33 fundamental vibrational band centres, especially in the blue side of ν 35 . This experimental observation assesses the strong anharmonicity of some modes confirmed by the anharmonic DFT calculations.

In Figure 4, we propose a tentative assignment of the hot bands around the ν 35 free -OH torsional band taking into account the four lowest energy vibrational states ν 36 , ν 35 , ν 34 , and ν 25 that we know to be thermally excited due to the mm-wave analysis described in Section 2.3. First, we attempted to identify the four hot band sequences |v 35 + nv i ← |nv i (with i = 36, 35,34,25), labelled ν 35 ± nν i in Figure 3, starting from the ν 35 vibrational centre at 221.9 cm -1 .

The assignment of the i mode to the ν 35 ± nν i sequence was performed in two steps: (i) according to the Boltzmann factor, the fit of the exponential decay of integrated intensities between successive components of the hot band sequence provides an estimation of the energy difference between consecutive levels; (ii) anharmonic coefficients were deduced from the previous step and are compared with those obtained directly with the frequency progression of the hot band sequence.

Our hot band assignment suggested a large negative diagonal x 35,35 constant of about -12 cm -1 , which constitutes an additional signature of the strong anharmonicity of the free -OH torsion. The off-diagonal anharmonic constants deduced from the three other ν 35 ± nν i hot band sequences were smaller in absolute value with x 35,36 , x 34,35 and x 33,35 estimated, respectively, about +1 cm -1 , +0.2 cm -1 , and -4 cm -1 . As was underlined previously, the anharmonic DFT calculation failed to evaluate the anharmonicity of the -OH torsions, which prevents a reliable comparison between the experimental and computed x i,35 constants. Afterwards, we noticed that the pattern of these hot band sequences observed around the ν 35 band centre was repeating in each component of the strongly blue-shifted ν 35 ± nν 35 sequence. Furthermore, we observed hot band sequences starting from combination levels. An example is given in the red panel of Figure 4 with two sequences, one blue-shifted (ν 35 ± ν 35 ± nν 25 ) and one red-shifted (ν 35 ± ν 35 ± nν 36 ) from the ν 35 ± ν 35 origin.

Finally, for a complete hot band assignment, including ν 33 , a specific study should be performed in a future article in order to confirm and finalize our present work. As was done for thermally excited molecules, such as benzene [25] or naphthalene [26], a suitable treatment based on an anharmonic force field would have to be carried out for the hot bands rovibrational assignment. In the case of catechol with a high number of low-energy states, the possibility of resonances between close-lying states should be considered, and, in addition to the anharmonic force field calculation, the multi-state interaction problem should be solved by considering numerous Coriolis/Fermi/Darling-Dennison couplings to have a better prediction of the hot band sequences.

Rovibrational Analysis

In our rovibrational analysis, we treated the |v 35 = 1 and |v 33 = 1 as isolated vibrational states, i.e., we considered no explicit Coriolis interactions and no vibrational resonances with other close lying states. This turned out to be sufficient considering the accuracy of our data and the range of the observed J values. The fitted parameters in the far-IR analysis of the ν 35 and ν 33 bands are presented in Table 4, and the simulated far-IR spectra with these parameters are compared to the experimental ones in Figure 5. The two experimental rovibrational patterns shown on a spectral range of 50 cm -1 (Figure 5, black curves) exhibit several hot bands, which overlap the P, Q, and R branches of the fundamentals. In this work, the rovibrational lines belonging to hot bands were not included in the fit (see Figure 5, red curves) and numerous rovibrational lines remain unassigned (see Figure 5, zoomed parts). Nevertheless, more than 11,000 rovibrational c-type transitions were assigned in the FT-far-IR spectrum (6937 for ν 35 and 4131 for ν 33 ) highlighting the highly congested far-IR spectrum of catechol.

Numerous rovibrational lines are blended, especially between quasi-degenerate transitions with K a = K a ∈ {0, 1} or K c = K c ∈ {0, 1}. Therefore, the number of fitted transitions is larger than the number of fitted frequencies. A development of the centrifugal distortion up to quartic terms in the effective Hamiltonian was sufficient to reproduce the experimental transition frequencies of the two bands ν 35 and ν 33 at the experimental accuracy with an unitless RMS close to 1.1.

All the molecular parameters for the two torsional bands were determined with a high degree of accuracy. In particular, the vibrational band centres of ν 35 and ν 33 were fitted with an accuracy better than 10 -4 cm -1 , four orders of magnitude better than those obtained with the REMPI technique in [4,7]. The complete set of rotational and centrifugal distortion constants were perfectly determined, and the detailed fit is given in the supplementary materials.

From the results of Table 4, we determined the differences between the GS rotational constants and those in the |v 35 = 1 and |v 33 = 1 torsionally excited states (ES) according to the relation α A i = A GS -A i with i = 32, 35 and similarly for the other rotational constants B and C. The vibration-rotation constants α i allow for estimation of the influence of the two torsional modes on the overall rotation of the catechol molecule.

Table 4. Summary of the fitted parameters in the far-IR analysis of the ν 35 free -OH and ν 33 bonded -OH torsional modes. The GS parameters were fixed to the fitted values obtained by the microwave study of Caminati et al. [11]. 1σ uncertainties are quoted in parenthesis in the units of the last digit. N trans is the number of fitted c-type transitions. N lines is the number of measured lines included in the fit. The table gives also the J max and K a,max quanta and the RMS values (in cm -1 and unitless).

Parameter GS, [11] v 35 v 33

Freq/cm With a bonded -OH almost parallel to the b-axis (see Figure 1, right part), the largest vibration-rotation constant α i was obtained for a rotation around the a-axis (α A 33 8.7 MHz). The free -OH torsion ν 35 also perturbed the overall rotation around the a-and b-axes but with a lesser influence compared to ν 33 (α A,B 35 2.3 MHz). Here, we observe that the free and the bonded -OH torsions differently affected the overall rotation of the catechol molecule.

Millimeter-Wave Rotational Spectroscopy

Using the subTHz spectrometer (see Section 3.2.2), the room temperature Doppler limited mm-wave pure rotational spectra of catechol were recorded in the 70-110 GHz and 140-220 GHz regions. The spectra are highly congested with most of the measured rotational lines blended. Up to eight transitions can be associated to one line. In addition to the GS, four low frequency vibrationally ES were populated sufficiently at room temperature leading to the dense spectrum of Figure 6a. The enlarged 500 MHz region of Figure 6b illustrates how the spectra are composed of these five vibrational states and can be reproduced by our simulation (red curve Figure 6) at the experimental accuracy. Only a negligible number of weak lines remains unassigned.

Ground State Analysis

The analysis of the mm-wave spectra was started with a line-by-line assignment of the GS transitions (see Section 3.2.2). Based on the molecular constants of Caminati et al. [11] and including 171 cm-wave lines of their study, almost 10,000 new transitions were assigned in the present work for the GS, associated with more than 4600 mm-wave lines. Among the assigned transitions, 75.8% were of b-type and 24.2% were of a-type. According to the permanent dipole orientation in the (a, b) plane (see red arrow in Figure 1), the b-type lines were stronger than the a-type ones.

Our results indicate that the ratio µ b /µ a is probably underestimated by the B3LYP-D3/aug-cc-pVTZ calculations µ b /µ a 1.4 and overestimated by the approximation made with the sum of the dipole moments of phenol µ b /µ a 9.2 as was done in [14]. All the determined parameters with their uncertainties are listed in Table 5.

The huge number of catechol GS rotational lines are reproduced at the experimental accuracy with a RMS of 55 kHz and a unitless RMS of 1.17. The fitted spectroscopic parameters include three rotational and nine centrifugal distortion constants. Compared to the previous GS cm-wave analyses [11,14] including GS rotational transitions with J max < 50, the fit of this mm-wave study was extended to J max = 124 requiring to add four sextic centrifugal distortion terms in the asymmetric top effective Hamiltonian: Φ K J , φ J , φ K , φ JK determined for the first time.

The fitted GS rotational constants allow an accurate determination of the inertia defect ∆I, which is a measure of the non-planarity of the catechol molecule. Despite its equilibrium planar structure, the small negative value arises mainly from the quantum zero-point motion of the oop low-energy vibrations detailed in Table 3 [14,15].

Vibrationally Excited State Analysis

A total of 64% of the assigned transitions in the global fit of the mm-wave catechol spectra belong to thermally excited vibrational states. Pure rotational transitions in four different vibrationally ES have been identified, and the Table 5 lists the four sets of fitted molecular parameters. For each of them, rotational and centrifugal distortion constants developed up to quartic terms were determined with a high degree of accuracy. Only a slight degradation of the RMS was observed for the fit of the |v 25 = 1 ES due to the weak intensity of its rotational lines (see Figure 6b). For higher energy far-IR vibrations, such as the bonded -OH torsion ν 33 , the pure rotational transitions were too weak to be observed in the room temperature mm-wave spectra.

The most intense mm-wave lines, which do not belong to the GS, were assigned to the lowest energy |v 36 = 1 ES associated to the O-C-C-O twisting not observed in the far-IR spectrum. As expected, we obtained the largest negative value for the inertia defect for the lowest energy oop vibration (see Table 5).

The ν 35 parameters fitted from the FT-far-IR measurements in Table 4 were used as an initial set of parameters to start the assignment of the rotational transitions in the |v 35 = 1 ES associated with the free -OH torsion. We found doublets separated by around 600 kHz around each predicted line, as depicted in Figure 7. Such doublets were already observed in phenol and associated to the torsion of its single -OH group yielding a double minimum potential. The V 2 tunnelling barrier separating the two symmetrically equivalent structures of phenol was about 1200 cm -1 [19]. In this case, splittings larger than 56 MHz were observed by L. Kolesniková et al. in the phenol mm-wave rotational spectrum both within the GS and within the -OH torsion ES [27] and by S. Albert et al. in the phenol far-IR rovibrational spectrum of the torsional fundamental [19]. In Section 2.1, our results showed that the height of the saddle point B separating the two global minima A 1 and A 2 (see Figure 1a) was calculated to be about 1200 cm -1 , as in phenol. This corresponds to the tunnelling barrier of the -OH torsions separating the two equivalent conformers. The splittings in the |v 35 = 1 torsional state of catechol are two orders of magnitude smaller than in the first excited torsional state of phenol. This can be explained by a higher -OH internal rotation barrier in catechol associated to a path from the minimum A 1 to A 2 requiring a concerted motion of the two hydroxy groups.

Due to the regular splitting, it was possible to analyse both tunnelling sublevels |v 35 = 1 + and |v 35 = 1 -simultaneously following H eff = ∆E + H rot (+) + H rot (-) without implementing any additional terms. Both stacks of rotational sublevels were simultaneously fitted. The resulting sets of parameters were almost identical with differences smaller than the uncertainties (indicated by the blue and red values of Table 5). The splittings of the energy levels created doublets of lines separated by 2∆E. A total of 1651 a-type and 3309 b-type transitions up to J max = 99 were assigned for both sublevels leading to a RMS of 99 kHz, a unitless RMS of 0.93 and ∆E = 312 kHz. This small splitting of about 600 kHz on average was not resolvable in the FT-far-IR of Section 2.2; hence, it was not observed.

Lying in the 300 cm -1 region (see Table 3), the |v 34 = 1 and |v 25 = 1 ES are sufficiently populated to be also observed in the mm-wave rotational spectra. Two independent sets of molecular constants were fitted and non-ambiguously assigned to the antisymmetric O-C-C-O wagging oop ν 34 and symmetric scissoring in-plane (ip) ν 25 vibrations due to the sign of their inertia defects. Indeed, compared to the other A" ES, the fitted rotational constants of the |v 25 = 1 ES yielded a positive inertia defect reflecting the A' symmetry of the ip intramolecular HB stretching. A remarkable agreement between the calculated anharmonic inertia defects ∆I calc and the experimental ones ∆I is observed in Table 5 except for the |v 34 = 1 ES, where the anharmonic calculation underestimates the inertia defect involved by the O-C-C-O wagging.

Finally, Table 6 summarises the vibrational band centres ν and inertia defects ∆I of phenol and catechol provided respectively in [27] and in this study (see Table 5) for the lowest energy oop vibrations. In this table, we calculate a "GS corrected" inertia defect ∆I * i defined by the difference between the inertia defect ∆I i in the vibrationally ES and the inertia defect ∆I GS in the GS. In first approximation, ∆I * i is given by:

∆I * i = ∆I i -∆I GS h 8π 2 ( α C i C 2 GS - α B i B 2 GS - α A i A 2

GS

).

∆I * i indicates the effective contribution of the low-frequency vibrational excitation on the inertia defect of the molecule. Table 6 compares the frequency and the inertia defects of the C-O and -OH oop bending modes in the case of a single hydroxy group and in the case of two hydroxy groups connected by a weak intramolecular HB. From this comparison, three remarks may be made with respect to the HB dynamics: . This statement also applies to the -OH torsions with one blue-shifted frequency (the bonded -OH) and one red-shifted frequency (the free -OH) due to the local anisotropy visible on the 2D PES around A 1 , see Figure 1. The -OH group, which acts as HB donor, leads to a blue-shift of the associated torsional mode frequency in the far-IR domain [7]. It constitutes one of the signatures of the intramolecular HB formation [2].

(ii) The intramolecular HB is preserved in the in-phase wagging of the two hydroxy groups, while it is perturbed in the out-of-phase twisting. This perturbation seems to increase the inertia defect ∆I 36 of catechol compared to the ones of phenol and ∆I 34 of catechol.

(iii) Compared with phenol, ∆I * of catechol was found to be larger (in absolute value) for the free -OH and smaller for the bonded -OH. This is a contrary behaviour compared to the one observed in (i) with the vibrational frequencies. There is a specific effect of stabilization due to the intramolecular HB: the torsion of the -OH group, which acts as HB donor has a smaller contribution to the inertia defect than the torsion of -OH group, which acts as an HB acceptor.

Materials and Methods

Theoretical Methods

Quantum Chemistry Methods

The quantum chemistry calculations were performed with the Gaussian 16 package [28]. The DFT calculations were performed with the B3LYP [29] and B3LYP-D3 [30] functionals with the default ultrafine grid and compared with results from MP2 theory in order to evaluate the efficiency of different functionals and methods for the prediction of the low frequency vibrations. The calculations were performed with the correlation consistent basis set aug-cc-pVTZ [31].

The triple zeta quality is known for its reliability with comparable molecules [15], and the diffuse functions help for the description of the intramolecular HB (see Section 2.1.2). The geometry of the catechol molecule has been represented with a Z-matrix that explicitly makes use of the torsional angle of the two -OH groups. The optimisation of the structures was performed with the tight criterion. The energy landscape of the two torsional modes of the catechol molecule in its electronic GS was determined by quantum chemistry calculations. A two-dimensional scan was obtained after a series of molecular geometry optimizations.

Each optimization released all the internal coordinates except for the two torsional angles 1, which were kept frozen. The scan step is 5 • for both torsional angles. The topology of the electron density was analysed by the Multifunctional Wavefunction Analyzer (Multiwfn) [22]. The harmonic and anharmonic vibrational frequencies and intensities of the lowest energy conformer were computed with the B3LYP and B3LYP-D3 functionals.

We used the anharmonic calculations implemented in Gaussian 16 with the option freq=anharm, which numerically computes the third and fourth derivatives of the electronic energy at the global minimum. The anharmonic calculations provided us an estimation of the rotational constants in the vibrationally ES (see Table 5) and of the anharmonic coupling parameters useful for the hot band assignment (see Section 2.2.1).

Effective Hamiltonians

For the assignment of the high resolution FT-far-IR rovibrational and mm-wave rotational spectra, Pickett's programs SPFIT/SPCAT [32] were used. A Watson quasi-rigid rotor effective Hamiltonian in the A reduction [33] in I r representation was developed up to sextic centrifugal distortion constants for the vibrational GS and up to quartic for the ES.

The initial predictions of rovibrational frequencies were performed using the GS rotational parameters from the microwave study of [11] and the measured band centres of the strongest Q-branches observed in the 222 and 415 cm -1 regions (see Figure 5). The variation of the rotational constants between the GS and the ES ν 35 and ν 33 was evaluated by multiplying the anharmonic B3LYP/aug-cc-pVTZ rotational constants with a scaling factor corresponding to the ratio between the experimental ( [11]) and calculated GS values. This method obtains an initial set of rotational constants with a relative accuracy better than 1% [34]. The rovibrational bands ν 35 and ν 33 of the FT-far-IR spectra were assigned using the Loomis-Wood assignment procedure for asymmetric top molecules with the LWWa software [35].

For the subsequent mm-wave analysis of Section 3.2.2, the fitted GS parameters of [11] were re-evaluated with the mm-wave measurements. The uncertainty of each line was adjusted between 10 and 300 kHz in the weighted fit performed with SPFIT using Equation ( 2) of [36] taking into account the estimated S/N ratio of our measured mm-wave lines. The SVIEW and ASCP software of the AABS package of Kisiel [37] were used to directly assign the measured lines to predicted rotational transitions. The fit procedure for the pure rotational transitions in the low frequency vibrational ES was performed using initial sets of constants determined with the same scaling approach used for the rovibrational analysis.

Experimental Methods

The FT-far-IR rovibrational and the mm-wave rotational spectra were measured, respectively, with the IFS125HR Bruker interferometer coupled to the AILES THz/far-IR beamline of the SOLEIL synchrotron [38] and with the solid state subTHz source of the LPCA in Dunkirk [39]. Solid catechol with a stated purity of 99% was purchased from Fisher Scientific. The room temperature equilibrium vapour pressure (P(300 K) 1 Pa [40]) was directly injected in the absorption cells without further purification. The FT-far-IR and mmwave measurements were performed, respectively, in static and controlled flow conditions.

Synchrotron-Based FT-Far-IR Measurements

The synchrotron radiation was extracted and focused onto the entrance aperture of the Bruker IFS 125 FT interferometer equipped with a 6 µm mylar-silicon composite beamsplitter suitable for the THz/far-IR spectral range. A total absorption path length of 150 m was reached by using a White-type multipass cell, which was isolated from the interferometer by 50 µm thick polypropylene windows. The far-IR/THz signal was detected in the 10-700 cm -1 spectral range with a helium-cooled silicon bolometer equipped with an optical band-pass filter.

The rovibrational spectra shown in Section 2.2 were recorded at the maximum resolution of the instrument (R = 0.00102 cm -1 ), where the rovibrational linewidth is limited by the apparatus function ( 30 MHz). More than 600 scans were co-added allowing the observation of all the far-IR active fundamental vibrational bands (see Table 3).

The corresponding acquisition time was close to 50 h. We estimated that, using a classical source, such as a Hg lamp, 75 days of continuous acquisition would have been required to obtain an equivalent S/N ratio in the ν 35 region (see Figure 5a) [38]. Each spectrum was calibrated using residual water absorption lines, whose wavenumbers were taken from [41], and the experimental error on the rovibrational line wavenumbers included in the fitting procedure was estimated at 0.0002 cm -1 .

Millimeter-Wave Measurements

The mm-wave absorption spectra in the 70-220 GHz shown in Section 2.3 were recorded at room temperature with the solid state subTHz spectrometer developed in the LPCA laboratory and described in detail in [39]. The measurements were performed in flux conditions at P = 1.5 Pa at the Doppler broadening limit of the rotational lines (∆ν Doppler ∼ 150 kHz at ν 100 GHz and T 300 K). The source is an amplified multiplication chain from Virginia Diodes Inc., which up-converts a synthesized microwave frequency.

The guided radiation was launched into free space using a horn antenna and propagated through a 125-cm long and 5.6-cm diameter stainless steel absorption cell closed by two Teflon windows. Using a polarization grid and a roof-top reflector, the interaction path-length was doubled [42]. A pair of off-axis parabolic mirrors were used to collimate the radiation into the cell and to refocus it subsequently onto a Zero Biased Detector, which was an unbiased Schottky diode mounted in a wave-guide operating in detection mode. The spectra have been recorded using 100 kHz frequency steps and a time constant of 100 ms.

The 2F modulation detection scheme was used with a frequency of 13 kHz and depths of 270 kHz and 540 kHz, respectively, in the 70-110 GHz and the 140-220 GHz ranges. A band-pass filter was applied to the spectra cutting off low frequencies and the noisy high frequency part. By this post treatment, the noise level was slightly decreased, and the low frequency baseline variations caused by stationary waves between the source, the polarization grid, the cell, and the detector were removed as was previously done in [6].

Conclusions

The dynamics of an intramolecular HB were investigated through the high-resolution THz rovibrational spectroscopy of the low-frequency modes of catechol in gas phase. In addition to its biological and environmental impacts, catechol is an excellent prototype to study the intramolecular HB dynamics since its two vicinal hydroxy groups can act interchangeably as both hydrogen donors and acceptors. The 2D PES of catechol built by scanning the two -OH torsions showed local anisotropy around the lowest energy equilibrium structures stabilized by a weak intramolecular HB.

We performed synchrotron-based FT-far-IR spectroscopy to explore the influence of the HB on the dynamics of the nuclei. The rovibrational spectrum revealed two far-IR active bands ν 35 and ν 33 associated, respectively, with the -OH free and bonded torsions. Since the spectrum was recorded at room temperature, numerous c-type hot bands were observed around these two fundamental bands, and a proposition of assignment was conducted around ν 35 . Hot bands involving the four lowest energy vibrational states were identified with signatures of strong anharmonicities, which cannot be reproduced by our quantum chemistry calculations based on perturbative methods.

A rovibrational assignment of the two torsional modes involving the -OH groups was performed for the first time. The comparison of the fitted molecular parameters of the |ν 35 = 1 and |ν 33 = 1 states highlights the different influences of the free and bonded -OH torsions on the overall rotation of catechol. Using a solid state subTHz spectrometer, the room temperature Doppler limited mm-wave pure rotational spectrum was also recorded in the 70-220 GHz region. The GS parameters were refined, and pure rotational transitions in the four lowest energy vibrationally ES were assigned. Very small tunnelling splittings were observed in the |ν 35 = 1 ES.

Finally, the inertia defects were determined with a high degree of accuracy, confirming the vibrational assignment to the different ES of the mm-wave transitions. As an example, the experimental inertia defect of the intramolecular HB stretching ν 25 was the only positive one, and this is consistent with the theoretical prediction. For the other ES, the influence of the low-frequency vibrational dynamics on the catechol planarity was discussed by comparing the negative inertia defects.

In particular, a specific effect of stabilization due to the intramolecular HB was observed with the free -OH torsion, which contributes more strongly to the inertia defect compared to the bonded -OH torsion. While the vibrational frequency measurements of the free and bonded -OH stretching and torsion were used in previous low-resolution studies to directly probe the intramolecular HB, high-resolution rovibrational THz spectroscopy provides a new perspective by investigating the influence of the low-frequency vibrational modes on the overall rotation of systems with intramolecular HB. Some molecular parameters accessible by rotational spectroscopy, such as the inertia defect, may be determined with a high degree of accuracy and may be used as an alternative probe of the HB strength [14]. Therefore, we propose, as was done by Bakker et al. in [4,7] with REMPI far-IR low-frequency vibrational measurements and Born-Oppenheimer Molecular Dynamics calculations, a larger study on different phenol derivatives showing intramolecular HB with different HB strengths.

In this aim, a double challenge experimental and theoretical has to be overcome by resolving rotationally the low-frequency vibrational bands involving stronger intramolecular HB and by performing variational calculations that are able to provide better descriptions of the anharmonicities in the large amplitude motions and of the resonances between the different modes.

Conclusion

Introduction

Hydrogen bond (HB) plays a fundamental role in structural chemistry (solvation, molecular geometry) and biology (protein folding, molecular docking) [33]. Its 91 92 CHAPTER 5. Theoretical study of intramolecular H-bonds typical strength is intermediate between the stronger forces involved in covalent bonds and the weaker forces involved in London dispersion forces. HB interactions, dynamics and their directionality are discussed for almost one century. While intermolecular hydrogen bonds can be experimentally studied through various techniques such as X-ray diffraction [102], neutron scattering [102] or IR spectroscopy [50] in solid state, NMR spectroscopy in liquid phase [4] or microwave spectroscopy in gas phase [44], intramolecular hydrogen bonds (IHB) are more difficult to investigate. Lately an analysis of high resolution TeraHertz and IR spectra was performed on catechol [21], revealing a promising new way to study intramolecular HB dynamics of isolated molecules. Quantum chemical tools were used to support these experiments.

Since there are several forces involved in the formation of IHBs making the identification and description not trivial, a rather general definition was given by the IUPAC 2011 [10,9]: "The hydrogen bond is an attractive interaction between a hydrogen atom from a molecule or a molecular fragment X-H in which X is more electronegative than H, and an atom or a group of atoms (Y) in the same or a different molecule, in which there is evidence of bond formation."

To specify this general definition, IUPAC defines six criteria and plenty of characteristics which will not be mentioned all here. Only a few interesting points should be highlighted now:

• . . . the X-H bond is polarized, (and) the HY bond strength (is) increasing with the increase in electronegativity of X.

• The X-HY angle is usually linear (180°) and the closer the angle is to 180°, the stronger is the hydrogen bond and the shorter is the HY distance.

• The length of the X-H bond usually increases on hydrogen bond formation leading to a red shift in the infrared X-H stretching frequency. . .

• The analysis of the electron density topology of hydrogen-bonded systems usually shows a bond path connecting H and Y and a (3,-1) bond critical point between H and Y.

IHB can be theoretically characterized through several quantities derived from the electronic density or the electronic wavefunction. The Quantum Theory of Atoms in Molecules (QTAIM) [13] investigates the electronic density through its critical points.

Presentation of the investigated molecules and their conformers

We looked for IHB in the seven molecules presented in Figure 5.1. All of them are quasi-planar doubly oxygenated benzene derivatives of formula C x H y O z . The potential IHBs are formed between a hydroxy or a methylene group and an oxygen belonging to a functional group in ortho position.

The simplest case is catechol CAT (1,2-benzenediol or 1,2-dihydroxybenzene or pyrocatechol). The two hydroxy groups form a five membered ring through the IHB in the conformer of lowest energy. The hydroxy groups can interchangeably switch their roles as HB donor and acceptor by a concerted torsion of both hydroxy groups. This concerted motion leads to a planar geometry which is undistinguishable from the starting conformer [21]. This effect and the influence of the IHB on the low frequency vibrational modes of catechol have been discussed in Bruckhuisen et al. and Bakker et al. [15,14]. A second stable conformer of higher energy exists for CAT [24,21] but the orientation of the two OH groups prevents in this case the formation of an IHB.

The introduction of a methyl group to the benzene ring of catechol leads to the 3-or 4-methylcatechol 3-mCAT or 4-mCAT (3-methyl-1,2-benzenediol, 4-methyl-1,2-benzenediol) [5]. The same concerted torsions can occur in these two molecules but due to their third substituent, the methyl group respectively in meta or para position, the two resulting rotamers are distinguishable. The energy difference between the two lowest conformers of the 3-mCAT (or the 4-mCAT) is small, see Table 5.1. Both conformers are thermally populated at room temperature and are present in the microwave and mm-wave spectra.

Guaiacol (1-hydroxy-2-methoxybenzene, GUA) is obtained when one hydroxy group of catechol is replaced by a methoxy group (-OCH 3 ). The conformer of lowest energy occurs when the hydrogen of the hydroxy group acts as the HB donor and the oxygen of the methoxy group as the acceptor. The existence of the IHB in guaiacol was discussed in Jabri et al. [53]. This paper mentions other stable conformers of higher energy (> 1000 cm -1 ), but they are not observable in a typical millimeter wave spectrum at room temperature or do not present an intramolecular hydrogen bond. By adding a methylene group in between one hydroxy group and the ring of CAT we produce saligenin SLG (2-hydroxymethyl-phenol). Kumar et al. theoretically identified three conformers, but only one can be seen in a pulsed jet experiment due to the low barrier allowing relaxation towards the conformer of lowest energy [68]. Our results agree with their findings with respect to the relative order of the three conformers according to the energy. They find that the second and third conformers are respectively above the first conformer by 96 CHAPTER 5. Theoretical study of intramolecular H-bonds electronic energies (including Zero Point Energy, ZPE): E(SLG2) -E(SLG1) = 1.37 kcal/mol and E(SLG3)-E(SLG1) = 2.52 kcal/mol, while we found E(SLG2)-E(SLG1) = 0.93 kcal/mol and E(SLG3) -E(SLG1) = 2.29 kcal/mol. Bakker et al. worked with a free electron laser and a supersonic jet expansion [15,14]. The experimental spectrum could be analyzed by just considering the conformer of lowest energy again. However, at room temperature, the three conformers SLG1, SLG2 and SLG3 should be considered.

By exchanging the two protons of the hydroxymethyl group of SLG with an oxygen, the carboxyl group of salicylic acid SAL is obtained. In the cases of SAL1 and SAL2 the hydroxy group is the IHB donor and the carboxyl group the acceptor. For SAL3 it is the opposite. The higher relative energy of SAL3 indicates that the carboxyl group is preferred as acceptor and the hydroxy group as donor. The two rotamers SAL1 and SAL2 have been discussed by [103] and have already been identified in far-IR spectra by Bakker et al. [15,14].

The last considered molecule in the present paper is 1,2-benzenedimethanol (BDM), also named as of α, α -diol-o-xylene [1], which is obtained from catechol by replacing its two hydroxy groups by hydroxymethyl groups. Four internal rotations are possible in this molecule: the two internal rotations along the C -C bonds that connect the hydroxymethyl groups to the benzene ring, and the two internal rotations of each OH group inside the two hydroxymethyl groups. A four dimensional search of the rotamers was carried out. First, we defined guess geometries with the four internal angles defined on a grid with a step size of 45 • . Then, each of these initial geometries was fully optimized by Gaussian with the tight convergence criterion. Reference [1] used the internal rotations of the OH groups to perform a two-dimensional conformational analysis. Their optimized geometry coincides with our fourth rotamer, called BDM4.

Quantum theory of atoms in molecules analysis

The Quantum Theory of Atoms in Molecules (QTAIM) characterizes the topology of the electronic density ρ through its critical points defined as the points in three dimensional space where the gradient of ρ vanishes. Each of these points is characterized by a pair (rank,signature). The rank is the number of non-zero 5.3. QTAIM analysis 97 eigenvalues of the Hessian (matrix of second derivatives) and the signature is the algebraic sum of the signs of the eigenvalues. There are four cases possible:

• (3,-3) → local maximum (all curvatures negative).

• (3,-1) → bond critical point BCP (two curvatures negative and one positive).

• (3,+1) → ring critical point RCP (one curvature negative and two positive).

• (3,+3) → cage critical point, local minimum (all curvatures positive).

Six parameters were used to quantify the IHB in the framework of QTAIM analysis [13]. Besides the difference ∆ρ of the electronic density at the Bond Critical Point (BCP, signature (3,-1)) and at the Ring Critical Point (RCP, signature (3,+1)) involved in an intramolecular hydrogen bond, we introduced the distance L CP between the BCP and RCP, the distance L HB between the oxygen and hydrogen atoms on each side of the IHB, the bond length of the donor group The QTAIM analysis of the electronic density obtained after geometric optimization of the conformers was performed using the Multiwfn program [71]. In this framework, an IHB is identified as a pair of BCP and RCP together with a bond path connecting the hydrogen and oxygen nuclei involved in the IHB. We used the B3LYP exchange-correlation functional with the aug-cc-pVTZ atomic orbital basis set.

However, for catechol, guaiacol, 3-methylcatechol and 4-methylcatechol, no signature of an IHB was observed with the aug-cc-pVTZ basis set, yet it was visible with a smaller basis set such as cc-pVDZ. This basis set dependency was already observed for catechol [72,21] and is illustrated in Figure 5.3. While the electronic density computed with cc-pVTZ exhibits the IHB signature, it is missing for the aug-cc-pVDZ, cc-pVTZ and aug-cc-pVTZ basis sets.

Including empirical dispersion in the form of D3 version of Grimme's dispersion with Becke-Johnson damping [45] does not change this basis set dependency. Therefore, when no signature of an IHB was obtained with the aug-cc-pVTZ calculation for a conformer, it was again investigated with the B3LYP/cc-pVDZ basis set. This basis set dependency occurs in several cases (CAT, 3-mCAT1 and 2, 4-mCAT1 and 2, GUA and BDM4) and may be considered as an indication for weak IHBs.

Rotamer

ring size ∆ρ/a.u. a the BCP and RCP as the signature of the intramolecular hydrogen bond do not exist with neither aug-cc-pvdz, cc-pvtz or aug-cc-pvtz basis sets. b the BCP and RCP as the signature of the intramolecular hydrogen bond do not exist with aug-cc-pvtz basis set. c the donor group is not OH but CH. The values of ∆ρ are consistently increasing along the sequence SLG3 → SLG1 SLG2 → SAL2 → SAL3 → SAL1 and consistently decreasing for L HB . L CP is confirming the trend between SLG1-3 and SAL but L CP does not differentiate the IHB strength of the three SAL conformers.

L CP / Å L HB / Å L D / Å α X-H•••O / • α C-O•••H / • CAT1 a 5 1

1,2-benzenedimethanol

Due to its four internal rotors, the 10 rotamers of the BDM molecule whose ZPE energies are presented in Table 5.1 show different kind of IHB, see Figure 5.6. BDM1, BDM2, BDM6 and BDM10 can be characterized by an IHB closing a seven-membered ring composed of two adjacent carbons of the benzene ring, the two carbons of the methylene groups, the O --H of the donor and the oxygen of the acceptor. The two most favorable rotamers, BDM1 and BDM2, have a seven-membered ring that looks like an open book. An order for the strength of the IHB can be given for these four rotamers according to increasing ∆ρ and decreasing L HB with BDM6 → BDM2 → BDM10 → BDM1. Due to the tilted ring of BDM1 and BDM2, their L CP is shorter compared to BDM6 and BDM10.

Additionally the rotamers BDM3, BDM4, BDM5, BDM7 and BDM8 were identified with the donor not being an OH but a CH group. Consequently the ring size is reduced by one to six. In the case of BDM3 and BDM8 two IHBs are formed simultaneously. Due to its C 2 symmetry the two pairs of (BCP,RCP) are equivalent in BDM3. The IHB in BDM4 is weak and could only be seen with the The situation of BDM9 is rather peculiar, we could not identify an IHB, see Figure 5.7. The donor of the IHB is not clearly identifiable by the IHB bond path.

Conclusion

L d was discarded right away as a parameter to relate the IHB strength due to its missing sensitivity. Within the subgroups defined by the ring size, ∆ρ, L CP and L HB led to consistent results. If we now compare all conformers regardless the ring size several observations can be stated: (I) Figure 5.4 shows that besides SLG3 all other values of ∆ρ are distributed within two ranges, 2 × 10 -5 to 9 × 10 -4 and 1.2 × 10 -2 to 2.5 × 10 -2 . The first range contains the five-membered rings and the conformers with the C -H donor, the second range contains the other six-membered rings (SLG and SAL) and the seven-membered rings.

(II) L CP and L HB are not independent to the ring size. Nevertheless they can be used as reliable indicators of the IHB strength inside one given family (defined by its ring size and the donor group).

(III) L HB is sensitive to the spatial configuration of the ring, as seen in the seven-membered rings of BDM.

Part III Atmospheric reactivity of furan compounds & rotational spectroscopy including internal rotation

So far the targeted molecules were oxygenated, aromatic benzene derivatives. Another family of VOCs emitted significantly by biomass combustion are furan compounds [49]. Furan compounds are heterocyclic, aromatic, five-membered rings with an oxygen as hetero-atom. Furan and its related compounds are primary and secondary pollutants in the atmosphere and are involved in the formation of atmospheric particles such as secondary organic aerosols (SOAs) [55]. Depending on the studied bio-fuel, furan compounds can represent the major fraction of emitted VOCs. Hatch et al. reported in [48] that > 0.4 g/kg furans are produced by wiregrass fires which is the largest fraction. This was explained by the high content of cellulose. The pyrolysis of cellulose or d-Glucose was found to yield in high furan emissions [88].

Methylated furan compounds such as 2-(2MF) and 3-methylfuran (3MF) are emitted directly from biomass burning (first generation), too and they represent a major fraction (20-25%) of the total emission of furan compounds [41]. During the nighttime, the main oxidation processes of these methylated furans occur with the nitrate radical NO 3 [31].

The atmospheric reaction of a series of furan compounds (furan (MF), 2MF, 3MF, 2,5-dimethylfuran (2,5DMF) and 2,3,5-trimethylfuran) with NO 3 has been investigated during the last three years in our laboratory using the ASC CHARME by Fatima Al Ali, Cécile Coeur, Nicolas Houzel and Houceine Bouya in collaboration with Alexandre Tomas and Manolis N. Romanias from the IMT Lille [3]. This work shows that the reaction between furan and methylated furan compounds with NO 3 is the dominant removal pathway during the night with lifetimes between 0.5 and 55 min for the studied molecules and highlights the influence of the methyl group increasing the rate coefficient by its inductive effect into the ring.

Several furan compounds have already been studied by rotational spectroscopy. To just name a few examples, Motiyenko et al. recorded furfural in the range of 7 -21 GHz with a Fabry-Perot cavity, Fourier-transform microwave spectrometer of the Balle-Flygare type in supersonic jet expansion and in the 49-330 GHz region at room temperature using an automated, synthesizer-based, millimeter-wave spectrometer at the Institute of Radio Astronomy of the National Academy of Science of Ukraine at Kharkov [79,78]. In addition to the GS of the two conformers, 15 excited vibrational states (9 for trans-furfural and 6 for cis-furfural) were assigned and analyzed. Accurate values of rigid rotor and quartic centrifugal distortion constants of asymmetric top Hamiltonian have been determined for 13 excited states.

Hakiri et al. recorded the molecular jet Fourier transform microwave spectrum of 5-methyl-furfural in the frequency range from 2 to 40 GHz [46]. And I contributed during an undergraduate student internship to a jet cooled study of 2,5DMF using the FTMW spectrometer located in Aachen, Germany, operating between 2 and 26.5 GHz [100]. Additional measurements were carried out in the LISA laboratory in Paris covering 26.5 to 40 GHz. For the only conformer, a barrier height of approximately 439 cm -1 and accurate molecular parameters were determined from the analysis of the observed spectrum. Their values agree well with the results of quantum chemical calculations.

The GSs of the two mono-methylated furan compounds 2MF and 3MF have been studied in the MW by Norris and Kirsher (2MF) and Ogata and Kozima (3MF) [85,86]. Additionally Finneran et al. investigated the GS and the first torsionally ES of 2MF in the 8.7 -960 GHz region. For 3MF the ES were not investigated so far. [49] the great interest to investigate the atmospheric reactivity and SOA yields for 2MF by: "The best candidates for future smog chamber experiments were identified based on the relative abundance and ubiquity of the understudied compounds, and they included furfural, 2-methyl furan, 2-furan methanol, and 1,3-cyclopentadiene."

Hatch et al. highlighted in

Therefore we chose to accompany with quantum chemical calculations 2MF from the potential candidates experimentally studied by our colleagues (MF, 2MF, 3MF, 2,5DMF and 2,3,5-trimethylfuran). Chapter 6 discusses the first reaction step of 2MF with NO 3 with a focus on the preferred reaction channels.

Chapter 7 presents the mm-wave pure rotational room temperature investigation of the two monomethylated furans 2MF and 3MF. The GS and the first torsionally excited state were analyzed and the line splittings due to the internal rotation of the methyl group was treated using local (XIAM or EHRAM) and Chapter 6

Reactivity of 2-methylfuran in the atmosphere during nighttime Outline of the current chapter 6.1 Reaction mechanisms of furan compounds with NO 3 118

Reaction pathways 120

To investigate the reaction of a VOC with one of the main oxidants in the atmosphere, either reaction simulations under simplified and well defined conditions can be carried out in a ASC or quantum chemical calculations can be performed. By injecting the aimed reactants under well defined conditions (temperature, pressure, concentration, etc.) the VOC will react with the oxidant inside the chamber. By using different types of analytical tools, plenty of different characteristics, products or quantities can be monitored during and after the reaction but nevertheless the actual reaction paths remain unexplored [36].

As it was shown for example by Joo et al. for 3MF reacting with NO 3 , the VOC undergoes multiple reaction steps until a stable product is formed [58]. Since the produced reactive intermediates (IM) and transition states (TS) usually have a short lifetime and only occur in low concentrations, it is not possible to monitor them. Thus only the reactants and the products are examined. At this 118 CHAPTER 6. Reactivity of 2MF in the atmosphere point, quantum chemical calculations can bridge this gap.

Reaction mechanisms of furan compounds with NO 3

In the ASC CHARME of the LPCA in Dunkirk, the reactions with NO 3 of different methylated furan compounds such as 2MF are studied at the moment by my colleagues Fatima Al Ali, Nicolas Houzel and Cécile Coeur. It was shown by Decker et al. that during nighttime the oxidizing of these compounds occurs mainly (≈ 60%) with NO 3 [31]. With their experiments, they aim to qualitatively and quantitatively determine the products in the gaseous and particulate phase. Therefore they use different online and offline analytical tools such as gas chromatography-mass spectrometry (GC-MS), monotraps, proton-transferreaction mass spectrometry (PTR-MS) and FTIR. Furthermore the SOA yields are determined.

To interpret the analytical results and to propose a full reaction mechanism based just on the knowledge on the reactants and some parameters (such as molecular weight, charge, polarity or functional groups) of the products derived from the analytic remains challenging. Quantum chemical calculations can not explore and enlighten the whole mechanism but can direct, support and confirm assumptions.

Before entering in the study of the reaction mechanism of 2MF with NO 3 , a look at what has been done in comparable projects could be used as a guideline. Zhang et al. investigated the reaction of furan with NO 3 in [105]. This process differs from 2MF + NO 3 by the absence of the methyl group linked to the furan cycle on the carbon in alpha position from the oxygen. Two initial reaction steps leading to pathways were highlighted in their paper. The abstraction by the nitrate radical of one hydrogen attached to a carbon of the furan ring was found to be endothermic and negligible. The other channel is the addition-elimination pathway: the nitrate radical addition to a C=C double bond of the furan ring followed by the elimination of one NO 2 molecule. This channel can furthermore explain the experimentally observed formation of cis-butenedial and 3H-furan-2-one [105]. The H-abstraction is assumed to require a coplanar approach of the planar NO 3 towards the plane of the furan molecule. In case of a non planar approach, a drift towards the addition of NO 3 on the furan cycle is expected. As shown in Figure 6.1, the partial atomic charges are directly affected by the methyl group in α position. In particular, the carbon connected to the methyl group stands out with its high positive Mulliken charge compared to the other carbon atoms. For 3MF, Joo et al. found that the 2 and 5 positions are the favored positions for a NO 3 addition due to the stability of the resulting radicals [58].

The geometry optimizations were computed with the Gaussian 16 software [39] using the tight convergence criterion. Frequency calculations were used to check the nature of the obtained stationary points. Because of the high computational cost of MP2 calculations (Figure 6.1 (b)) we tried B3LYP (a) and M06-2X (c), which is supposed to be well adapted to thermochemistry [73] and compared it to the MP2. The calculated Mulliken charges were used as an indicator of the accuracy. Within some uncertainties both calculations reproduced the MP2 results.

The methyl group of 2MF opens another possible reaction pathway. NO 3 can abstract one of the three hydrogen atoms of the methyl group without competing with a possible NO 3 addition on the double bonds C=C of the furan ring. However, Joo et al. did not take this possibility into account when proposing 120 CHAPTER 6. Reactivity of 2MF in the atmosphere a reaction mechanism based on their identified products [58].

Investigation of the NO 3 addition and H-abstraction channels with their reaction pathways

As shown by the time evolution in [58], the first reaction step can define the whole reaction mechanism. With the addition of NO 3 and the hydrogen abstraction, two different reaction channels were investigated. Joo et al. used the stability of the resulting radicals as an argument to favor a pathway. Hence the relative energies of the produced radicals belonging to these two channels can give an indication of the pathways towards the experimentally identified products.

For both channels, the NO 3 addition and the hydrogen abstraction, all potential configurations were investigated and are listed in Table 6.1. The relative energies were calculated by E IN x -E 2MF + E NO 3 for the addition pathways and 3 for the H-abstraction pathways. For the NO 3 addition, five radicals were found (IN1-4 and IN4bis) with the NO 3 added to the four carbon atoms of the furan ring. For the addition at the γ position (2-methyl,4nitrate-furan) two stable conformers IN4 and IN4bis were found. As it was suggested for 3MF and found for furan, the addition to the 2 and 5 positions next to the oxygen (in furan due to symmetry reasons these two positions are equivalent) are preferred [58,105]. Our calculations indicate that the 5 position without the methyl group is the most favored addition site and for B3LYP it is the only exothermic pathway for the addition of NO 3 . On the left side of Figure 6.2 the different structures of the found radicals with their relative energies ∆E B3LYP are illustrated.

E P x + E HNO 3 -E 2MF + E NO
For the H-abstraction, four different first steps were found and are shown in the right side of Figure 6.2. Zhang et al. stated with their results on furan that a H-abstraction from the furan ring is endothermic and unimportant. For the proposed mechanism of 3MF, no H-abstraction was considered even though another channel for NO 3 to abstract a hydrogen is given with the methyl group [58]. Our calculations summarized in Table 6.1 can confirm the high endothermic Surprisingly the H-abstraction of one of the three indistinguishable hydrogens from the methyl group present in our work is the most favorable pathway (P6). With -13.48 kcal • mol -1 for P6 compared to the IN5 with the second lowest relative energy of -1.12 kcal • mol -1 for B3LYP and -21.29 kcal • mol -1 versus -15.05 kcal • mol -1 for M06-2X it represents a non-negligible pathway.

As a matter of fact, two major first generation products were identified experimentally by our colleagues. Cis-4-oxo-2-pentenal (C 5 H 6 O 2 ) and furfural (C 5 H 4 O 2 , furan-2-carbaldehyde). Cis-4-oxo-2-pentenal can be associated to the addition-elimination pathway initiated by the NO 3 The results of M06-2X are generally shifted towards exothermic reactions. The relative energies for B3LYP (black) and M06-2X (red) are compared in Figure 6.3. While only IN5 and P6 are exothermic for the stationary points calculated with B3LYP, all but P3-P5 are exothermic for M06-2X. The same shift is observed for the two transition states TS2-1 and TS3-4 (see appendix) which were not considered so far. One explanation for this behavior could be related to the geometry optimization of NO 3 .

The experimental and theoretical literature on the NO 3 radical now agrees that it has a D 3h structure, with three equivalent N-O bonds [34]. The B3LYP Bibliography of the current chapter 123 calculation with the aug-cc-pVTZ basis reproduces this result, with a bond length of r = 1.232 . However the optimized geometry of NO 3 found with the M06-2X functional has a C 2v symmetry, with two bonds of length 1.193 and one bond of length 1.326 . NO 3 is a molecule known to be difficult to deal with, due to its tendency to exhibit symmetry breaking in theoretical calculations [27]. An optimization at the D 3h symmetry with the M06-2X functional returns a structure with two imaginary frequencies (second order saddle point) [8]. Millimeter-Wave Spectroscopy of Methylfuran Isomers: Local vs.

Bibliography of the current chapter

Global Treatments of the Internal Rotation

While the pure rotational room temperature mm-wave spectrum of 2MF has already been recorded and analyzed for its ground and first torsionally excited states ν t = 1 by Finneran et al. [37], 3MF has not been studied that way, yet. Finneran et al. recorded the spectra from 8.7 to 960 GHz with a chirped-pulse waveguide spectrometer for the cm-waves and a direct absorption flow cell spectrometer for the mm-and sub-mm-wave spectra. To fit the obtained data, containing a splitting of the rotational lines caused by the internal rotation of the methyl group, XIAM and EHRAM were used for the GS. The torsionally excited state ν t = 1 was only fitted with EHRAM because it was not possible for them to fit the first torsionally excited state to an RMS better than 16 MHz with XIAM. Finneran et al. explained this by XIAM forcing the rigid rotor distortion constants to compensate the omission of internal rotor centrifugal distortion parameters, leading to a fit of an overall lower quality.

For 3MF the only rotational spectroscopy was done in 1971 by Ogata and Kozima [87]. They recorded the microwave spectrum between 8.2 and 30 GHz 125 126 CHAPTER 7. Millimeter-Wave Spectroscopy of Methylfuran Isomers and assigned 20 A and 16 E species transitions. Thus they could only provide rather vague rotational parameters. Nevertheless we decided to not record again 3MF in the microwave region but to start the experiment at 70 GHz and instead of going up to 960 GHz as it was done for 2MF, we stopped at 220 GHz. The rotational parameters reported in [87] were sufficient to assign the GS in our new spectra and we did not expect an additional benefit of the higher frequencies because we are limited to J max = 70 with BELGI.

To not consume too much of the rather expensive 3MF, our experiment was adjusted and the measurement parameters were optimized with 2MF because its properties are close to the ones of 3MF. The main difficulty was to adjust a low vapor pressure to reduce the consumption and to work at the Doppler limit. Therefore the sample was cooled with a mixture of ice and liquid nitrogen and the pressure was further adjusted by two micro-valves.

The following study titled: "Millimeter-Wave Spectroscopy of Methylfuran Isomers: Local vs. Global Treatments of the Internal Rotation", was carried out in collaboration with the listed authors. I led the MF mm-wave measurements and analyses during the second part of my thesis. It should be mentioned that the analysis of 2MF based on the reported lines from [37] was mainly done by Sathapana Chawananon and Isabelle Kleiner.

The presented article is part of a more extensive collaboration with Pierre Asselin and Sathapana Chawananon using high-resolution jet-cooled rovibrational IR spectroscopy and Isabelle Kleiner who developed the BELGI code. Besides the pure rotational investigation of the GS and ν t = 1 of the two MF isomers, the same work is certainly under progress for their heterocyclic analogs with a sulfur instead of oxygen methylthiophene (MT) and methylpyrrole (MP), the nitrogen analog. Furthermore several jet-cooled rovibrational high-resolution IR spectra of 2MF, 3MF and furfural were recorded by Sathapana Chawananon and Pierre Asselin using their SPIRALES setup. Recently the rovibrational far-IR spectra were recorded at room temperature at the AILES beamline at the synchrotron SOLEIL.

Introduction

Furan and its derivatives (furans) are heterocyclic organic compounds belonging to the family of oxygenated five-membered aromatic molecules. They are primary and secondary pollutants in the atmosphere emitted from multiple sources such as oil refining, coal mining and gasification, biomass and fossil fuel or waste combustions [1,2]. Furans and other heterocyclic compounds such as pyrroles (with N as the heteroatom in the ring) are produced by the pyrolysis of cellulose and are major components of the emission of wildfire burnings [3]. Such compounds as the volatile furan (C 4 H 4 O) and methylfurans (C 5 H 6 O) (see Figure 1) or the less volatile furaldehyde (C 5 H 4 O 2 ) have emission levels 70 to 120 times higher compared to CO [4]. Once furans are emitted, they will undergo gas phase chemistry and, to an extent, will be photolyzed at actinic wavelengths to produce tropospheric ozone or they will react with the main atmospheric oxidants (OH, Cl atoms, ozone) leading to the formation of secondary organic aerosols (SOA) [5]. A similar process occurs during the night by the oxidation of furans with NO 3 radicals [1][2][3]. These SOA affect the climate both directly and indirectly and large uncertainties still remain on their radiative forcing [6]. For all these reasons, there is a fundamental interest to monitor furans directly in the atmosphere or in atmospheric simulation chambers to characterize their reactivity and their ability to produce SOA. Up today, the monitoring of volatile organic compounds (VOC) involved in biomass burning emissions such as furans is mostly performed off-line with chemical methods based on gas chromatography (GC) and mass spectrometry (MS). A GC-MS instrument provides extensive chemical details of discrete air samples collected in wildfires or during a controlled combustion process in the laboratory. These measurements can be complemented by real-time middle or low resolution measurements with an open-path Fourier transform infrared spectroscopy instrument [4,7]. To the best of our knowledge, high-resolution spectroscopic methods were never used to measure on-line individual signatures of furans at trace level in realistic environment. Trace gas detection in complex chemical mixtures with IR and THz techniques are generally focused on a limited panel of 55 light atmospheric molecules listed in the high-resolution HITRAN database [8]. No high resolution data of furans are present in this database, only vibrational cross-sections of furan, methylfurans (MF) and furaldehyde may be used for quantitative spectroscopy in the IR at middle/low resolution. This might be explained by the difficulty to resolve highly congested room temperature rovibrational spectra of these molecules. To overcome this challenge, one first need to measure the spectra in laboratory and assign pure rotational and low-frequency rovibrational spectra of furans at room temperature. Several groups have performed high-resolution pure rotational spectroscopic studies of furans in millimeter-wave at room temperature. We can cite the furan ground state analysis of Wlodarczack et al. [9]; the ground and first torsional states of trans-furfural and ground and excited state of cisfurfural analyses of Motiyenko et al. [10] assigning in total seventeen states. In 1971 Ogata and Kozima recorded the microwave spectrum of the 3-MF between 8.2 and 30 GHz and assigned 20 A and 16 E species transitions [11] and more recently, the ground and first torsional states of the 2-MF isomer were analyzed by Finneran et al. requiring a specific treatment of the internal rotation of the methyl group [12]. Finally, we can mention the study of furan performed by Tokaryk et al. using FT-Far-IR spectroscopy based on a synchrotron source which constitutes, to the best of our knowledge, the only high-resolution rovibrational study of a furan compound [13].

In this study, new high-resolution millimeter-wave measurements have been performed on 3-MF with a versatile solid-state spectrometer already used for the investigation of other VOC such as methoxyphenol [14] or catechol [15] and gas phase monitoring in an atmospheric simulation chamber [16,17]. As in Ref. [12] with 2-MF, the spectroscopic assignment was complicated by the large amplitude motion associated with the internal rotation of the methyl group. Unlike the work of Finneran et al. where the internal rotation was treated with two local approaches, we have succeeded in this study, using a global treatment, to reproduce the spectra in the ground and first excited torsional states at almost the experimental accuracy with a common set of molecular parameters. Amongst them, the V 3 and V 6 constants of 2-MF and 3-MF are obtained with a high degree of accuracy allowing to characterise finely the internal rotation potential for both MF isomers.

Results

The optimized geometries of 2-MF and 3-MF isomers at the B3LYP/aug-cc-pVTZ level of theory are presented in Figure 1. Both isomers are prolate asymmetric tops with Ray's asymmetry parameter κ 2-MF = -0.69 and κ 3-MF = -0.73. Their permanent dipole moment is oriented in the (a, b) plane with the |µ a |/|µ b | ratio of around 0.6 [18] and 1.9 [11], respectively. Both a-type and b-type transitions are observed in the MF rotational spectra: the most intense transitions are expected to be b-type for 2-MF and a-type for 3-MF. One difficulty in the assignment process, already mentioned by Finneran et al. in Ref. [12], lies in the possible mixing of energy levels arising from comparable asymmetry and internal rotor splitting. Therefore, we were careful to keep only consistent labels for the energy levels. This difficulty which is generally observed in the rotational-torsional spectra of other small organic molecules containing a methyl internal rotor will be discussed more in detail in Section 3.1.

Global Fit of the Vibrational Ground State and First Torsional State of 2-MF

Finneran et al. [12] recorded in 2012 a broad spectrum of 2-MF from 8.7 GHz to 960 GHz. In the 8.7-18.3 GHz range they used a room-temperature chirped-pulse Fourier transform microwave spectrometer. Above 75 GHz, the mm-wave and submm-wave rotational spectra of 2-MF have also been measured by those authors [12] using a direct absorption flow cell spectrometer [19]. The spectra have been obtained in the following spectral ranges: 75-125 GHz, 130-450 GHz, 460-650 GHz, 700-732 GHz, and 760-969 GHz. In the present work, we used a similar spectrometer with an updated technology, a doublepass absorption cell and a room temperature detection based on zero-biased detector (ZBD) [20]. As a test, we decided therefore to measure again the 2-MF spectrum with the first stage of multiplication (×9) covering the 70-110 GHz range. In Figure 2, a part of this spectrum is presented from 86.4 GHz to 86.9 GHz, and we tagged the rotational lines previously assigned in Ref. [12].

Only a few lines remain unassigned. As already mentioned by Finneran et al. [12], apart from the methyl torsion band at 158 cm -1 , two other low frequency modes occur below 400 cm -1 associated with an out-of-plane bending (237 cm -1 ) and an in-plane bending (339 cm -1 ) of the methyl group. Those states are most likely populated at room temperature and thus can be responsible for those unassigned lines. In Ref. [12], Finneran et al. have used the eXtended Internal Axis Method (XIAM) [21] and the Effective Rotationaltorsional Hamiltonian (ERHAM) [22] to fit separately the ground state (v t = 0) and the first excited torsional state (v t = 1) parameters within two "local" approaches. Unlike the XIAM code which failed to fit v t = 1, the ERHAM code succeeded in fitting both v t = 0 and v t = 1 states separately within their experimental accuracy (see Table 1). We plotted in Figure 2b the simulated spectrum with the ERHAM parameters listed in Table 1 of [12] using the prediction published in their supplementary data. Most of the observed rotational lines are predicted taking into account assignments from v t = 0 and v t = 1 states. The remaining unassigned lines belonging to other excited states involving either v t > 1 states or higher frequency vibrational modes are significantly less intense. In this work, we decided to perform a new fit using a global approach with a unique set of parameters for both the v t = 0 and v t = 1 states by means of the BELGI-C s code [23]. 9 GHz frequency range. Blue and red sticks correspond respectively to assigned v t = 0 and v t = 1 lines in Ref. [12]. (b) Simulated spectrum with the v t = 0 (blue) and v t = 1 (red) parameters fitted in Ref. [12] using ERHAM (local approach). (c) Simulated spectrum of the present work with the v t = 0 (blue) and v t = 1 (red) using BELGI-C s (global approach) and the fitted parameters from Table S1.

For XIAM, as shown in Ref. [12], due to the lack of sufficient higher order distortion constants, as well as high order torsion-rotation terms, their fit leads to several difficulties at higher K a values. For this reason, we decided to start the global fit with BELGI-C s using only the assigned transitions from ERHAM for v t = 0 and v t = 1 states. However, the conversion of the quantum numbers used to label energy levels and molecular transitions in ERHAM to the labelling scheme used in the BELGI-C s is not straightforward since the values of K a and K c are approximately determined by the (assumed) order of energy levels for rigid asymmetric rotors. These labels may be incorrect when serious rotational-torsional interactions occur. Thus, for the global fit with BELGI-C s many of the K c values were reassigned. In the range up to J = 70 (limit of the BELGI-C s code), only 14 transitions (which correspond to 7 distinct frequencies) with K a = 53 and 54 used in ERHAM were excluded in our BELGI-C s fit, as we could not find correct labelling for those levels. As for the ERHAM fit, the BELGI-C s fit succeeded to reproduce the experimental 2-MF linelist of Ref. [12] at almost their experimental accuracy.

The complete set of the Rho Axis Method (RAM) parameters including centrifugal distortion and higher order terms used in the BELGI-C s is provided in the supplementary materials (Table S1). In Table 1, we present the fitted rotational constants for both the (v t = 0) and (v t = 1) states, after transforming them into the principal axis method (PAM). In addition, the global approach allows us to fit the height of the internal rotation barrier V 3 and its higher-order correction V 6 with a high degree of accuracy. This is also the case for some structural parameters like the angles between the internal rotation axis and the principal inertia axes. We notice the good agreement of these experimentally derived parameters with those obtained from the B3LYP/aug-cc-pVTZ calculations presented in Section 4.1.1 and discussed in Section 3.2.

Table 1. Torsion-rotation constants of 2-MF for the v t = 0 and v t = 1 states obtained from DFT calculations (this work), from the fits of microwave and mm-wave data with local XIAM and ERHAM approaches (Ref. [12]) and global BELGI-C s approach (this work). The complete set of parameters obtained for XIAM and ERHAM can be found in Tables 1 and2 of Ref. [12]. The complete set of parameters obtained for BELGI-C s is given in the supplementary Table S1. The numbers in parentheses represent 1 σ standard deviation in units of the last significant digit. All parameters are in the Principal Axis System (PAS).

Unit B3LYP a XIAM v t = 0 ERHAM v t = 0 b ERHAM v t = 1 b BELGI-C s v t = 0; 1 c Present Work
Ref. [12] Ref. [12] Ref. [ a Calculation with the aug-cc-pVTZ basis set. b The complete set of higher order tunneling terms used in ERHAM are listed in Tables 1 and2 of Ref. [12]. c Parameters in the PAS after transforming them from the RAM. The complete set of RAM parameters including centrifugal distortion and higher order terms used in our fit are listed in Table S1 of the supplementary data. d In XIAM F is a derived parameter from F 0 , see supplementary data in Ref. [12]. In BELGI-C s F was fixed to the best value obtained by fitting it. e Standard error of the analytical fit based on Equation ( 5) as given by Gnuplot [24]. f Reduced barrier height: s = 4V 3 /(9F). g N corresponds to the number of assigned transitions for v t = 0 and v t = 1. In the BELGI-C s fit 14152 and 3742 correspond to the number of transitions fitted. h In XIAM only 8006 unblended lines were included in the fit. i In the ERHAM fit 11,793 and 2580 correspond to the number of distinct frequencies used for the fits of Ref. [12]. j WRMS is the weighted unitless root mean square deviation of the fit:

1

N ∑ i f obs. i -f calc. i ∆ i 2
with N the total number of observed ( f obs. ) and calculated ( f calc.

i

) frequencies and ∆ i the estimated error on the frequency measurement. k RMS is the Root mean square deviation of the fit in kHz.

Figure 2c shows 500 MHz of a 2-MF spectrum simulated with the unique set of molecular constants obtained from the BELGI-C s fit (The complete line list is provided in Table S3 of the supplementary material). As for Figure 2b, a simulated spectrum based on the ERHAM fit, the rotational lines belonging to the v t = 0 and v t = 1 states are plotted respectively in blue and in red. A direct comparison between the local ERHAM and global BELGI-C s fits may be performed. Both predictions are able to reproduce reasonably the measured line positions of the 2-MF spectrum. Nevertheless, some differences are observed between these two simulated spectra especially when considering the relative intensities. Indeed the Figure 2b,c exhibit a few line intensities which are not in agreement with the experimental ones (e.g: the v t = 1 line centered around 86,620 MHz for the ERHAM prediction or the v t = 0 line centered around 86,786 MHz for the BELGI-C s prediction). The differences between local (XIAM and ERHAM) and global (BELGI-C s ) are discussed in more details in Section 4.1.2. As shown in Figure 3, a simulated spectrum (red) consisting of the v t = 0 A-(green) and E-species (blue) as well as v t = 1 A-(magenta) and E-species (brown) rotational lines predicted with our BELGI-C s fit reproduces the experimental spectrum (black) well. For the frequency range of 70 -220 GHz, J max = 50 and K a,max = 31 for v t = 0 and v t = 1 was sufficient to assign the most intense lines. Remaining unassigned weaker lines are probably associated to the out-of-plane and in-plane methyl bending modes predicted respectively at 267 cm -1 and 321 cm -1 with anharmonic B3LYP/aug-cc-pVTZ frequency calculation. To compare the efficiency of local and global approaches (see Section 3.1), the same data set (excluding one line) was fitted using the XIAM code for the v t = 0 and v t = 1 states separately. The results of these fits are given in Table 2 along with the theoretical B3LYP/aug-cc-pVTZ calculation. Again, as for the 2-MF, our PAM values fitted by the BELGI-C s code agree reasonably well with the theoretical calculations. The complete set of constants (19 parameters) obtained from the BELGI-C s global fit in the RAM axis system is presented in Table S2 and the line list deduced from our global BELGI-C s fit is given in Table S4 of the supplementary materials.

Global

Table 2. Torsion-rotation constants of the 3-MF obtained from the mm-wave (70-220 GHz) analysis using the XIAM code for v t = 0 and v t = 1 separately, and BELGI-C s with a global fit analysis. These values are compared with quantum chemistry calculations (B3LYP method) and with the microwave analysis performed by Ogata et al. [11]. The numbers in parentheses represent 1 σ standard deviation in units of the last significant digit. All parameters are in the principal axes system.

Unit

B3LYP a

Ref. [11] XIAM a Calculation with the aug-cc-pVTZ basis set. b The complete set of RAM parameters including centrifugal distortion and higher order terms used in our fit are listed in Table S2 of the supplementary data. Parameters were transformed from RAM to PAM system. c Taken from the v t = 0 XIAM fit. d Derived from F. e In XIAM F is derived from F 0 , fitted to 159.6895 (10) GHz for v t = 0 and 159.8645(13) GHz for v t = 1. f Standard error of the analytical fit based on Equation ( 5) as given by Gnuplot [24]. g Reduced barrier height: s = 4V 3 /(9 × F) h N corresponds to the number of assigned transitions for v t = 0 and v t = 1. i WRMS is the weighted unitless root mean square deviation of the fit:

v t = 0 XIAM v t = 1 BELGI-C s v t = 0,
1

N b ∑ i f obs. i -f calc. i ∆ i 2
where N b is the number of distinct observed ( f obs.

i

) and calculated ( f calc.

i

) frequencies, for v t = 0 N b = 1845, for v t = 1 N b = 1538 and ∆ i is the measurement uncertainty. j RMS is the root mean square deviation of the fit in kHz. k Previous fit of Ogata et al. [11] using only A species transitions and refined from A-E splitting analysis with A A -A = 2.33 MHz and B A -B = 0.00 MHz.

Discussion

"Local" versus "Global" Approach

A "local" method treats separately each torsional v t state, whereas a "global" method explicitly takes into account all the interactions between the different v t states. Both XIAM and ERHAM programs adjust the parameters of each torsional state separately: they belong to "local" approaches. BELGI-C s on the other hand allows, for a given vibrational state, the fit of several torsional states together within the same rotation-torsion Hamiltonian matrix, see Section 4.1.2. A comparison of the results obtained with a "local" approach with those issued from a "global" approach has already been introduced in several papers [23,25,26]. Local approaches have shown their efficiency and high speed, especially in the first steps of assignments, but they sometimes fail when the potential barrier is low or when reaching higher excited torsional states. Finally one of the differences between XIAM and ERHAM is that the potential barrier does not appear explicitly in the ERHAM method. The information about the barrier is thus hidden in the tunneling coefficients of the internal rotation energy.

For 2-MF, as mentioned by Finneran et al. [12], ERHAM computes very quickly and accurately the line positions and intensities up to J = 120 and provides much better RMS deviations (108 kHz for v t = 0 and 113 kHz for v t = 1) than XIAM (263 kHz and 16 MHz respectively). ERHAM used five and ten tunneling parameters, (the Bkpr q parameters listed in Tables 1 and2 of Ref. [12] and defined in Ref. [22,27]) to fit v t = 0 and 1 respectively. The XIAM fit stays of rather poor quality, even after they added four sextic centrifugal distortion, and three rotation-torsion parameters, (see third column of Table 1 [12]). On the other hand, XIAM provides a direct value for the potential barrier [21].

Our global fit for 2-MF with BELGI-C s simultaneously includes both the v t = 0 and 1 rotational transitions and achieves a similar quality as ERHAM. The reserved memory by the BELGI-C s program allows the construction of the Hamiltonian matrix for J up to 70 with an Hamiltonian matrix dimension is (2J + 1) × 9. Even though we only assigned transitions of v t = 0 and 1, we take into account interactions within the lowest nine torsional states, a truncation usually allowing for the best lowest states energy calculation. The RMS deviations obtained by BELGI-C s are 107 and 114 kHz for v t = 0 and 1 respectively. As shown in our supplementary Table S1, we use in total 21 parameters (plus F which is fixed): the three rotational constants A, B and C, the off diagonal inertia moment, D ab , the five fourth order centrifugal distortion terms, and only one sextic centrifugal constant (H K ). We also fit V 3 and V 6 , ρ the coupling term between internal and global rotation, seven fourth order and one six order rotation-torsion terms.

Compared to the XIAM values, our values, after transforming them into the PAM, are in reasonable agreement, considering the difference between the two methods (see Table 1). One of the differences between XIAM and BELGI-C s is that XIAM fits the three angles ∠(i, x), ∠(i, y) and ∠(i, z) between the internal axis of the methyl group and the principal axes, whereas BELGI-C s fits the D ab term. We have to diagonalize the inertia tensor, using a procedure described in [25], to get the eigenvalues which are the A, B and C values in the PAM. The eigenvectors generated by this diagonalization of the tensor of inertia are related to the angles ∠(i, x), ∠(i, y) and ∠(i, z) reported in Table 1. Compared to XIAM our A, B, C parameters in the PAM only differ by 0.0002, 0.05, 0.01 % to XIAM. The ∠(i, x), ∠(i, y) and ∠(i, z) angles have also close values, showing that XIAM does well with determining the structure, even with a poor quality of fit. Compared to the theoretical B3LYP calculation, the agreement of our PAM values A, B, C from the BELGI-C s code is 0.9, 0.2, 0.4 %. The V 3 from BELGI-C s only differs by 1.8 % with its value from XIAM, and by 11.8 % with the B3LYP calculation, which is also satisfying. We note that a good order of magnitude is obtained as well for V 6 by the theoretical method compared to the BELGI-C s value. The angle between the PAM axis and the RAM z axis is listed in Table 1 as "β" to be coherent with ERHAM notation. We called this angle θ RAM in our previous paper [28] (see Equation ( 6) of the theoretical section). Its order of magnitude is conserved between BELGI-C s and ERHAM, but ERHAM has two distinct values for v t = 0 and 1. Finally we note that in Table 1, we do not indicate centrifugal distortion terms for BELGI-C s . Indeed, their values are fitted in the RAM system, but there is no way to easily convert them into PAM values.

For 3-MF, our global BELGI-C s fit includes 19 parameters (see Table S2 of the supplementary materials): like for the 2-MF fit, we performed a fit on A, B, C, D ab , the five quartic and one sextic (H K ) centrifugal distortion constants, the parameter ρ, and the two first Fourier expansion coefficients V 3 and V 6 of the potential barrier. For 3-MF, we were able to also fit the F parameter and four higher order interaction terms between internal and global rotation. Our RMS deviations (181 kHz and 174 kHz for v t = 0 and 1 respectively) are slightly above the averaged measurement accuracy estimated to 150 kHz. Near 4500 rotational transitions involving energy levels up to J = 50 have been assigned in the 70-220 GHz scanned range. The 30 lines with low J values (18 A species lines and 12 E species lines) from Ogata and Kozima [11] with a weight of 100 kHz were also included to the fit. For those lines, the RMS deviation was 116 kHz. Sixteen lines from [11] showed large observed-calculated values of more than three times the measurement accuracy and we decided to discard them. As indicated in Table 2, for 3-MF the XIAM fit was of rather poor quality, with RMSs of 200.6 kHz and 1500 kHz for v t = 0 and v t = 1 respectively. However our BELGI-C s values for A, B, C transformed in the PAM only differ by 0.005, 0.04, 0.02% with those of XIAM in v t = 0. The ∠(i, a) angle differs by 0.2%. The V 3 values differs by 6% and 8% with XIAM v t = 0 and v t = 1, respectively. Again, as for the 2-MF, our PAM values fitted with the BELGI-C s code agree reasonably well with the B3LYP theoretical calculations.

For both the 2-and 3-MF, the threefold torsional potential barrier is rather high (V 3 ≈ 420 cm -1 and 358 cm -1 respectively), and the value of the reduced height s = 4V 3 /(9F) (with the internal rotation constant F ≈ 5.64 cm -1 for 2-MF and F ≈ 5.32 cm -1 for 3-MF) is 33 and 30, respectively. Torsional splittings reach values of 15 MHz in v t = 0 and 380 MHz in v t = 1 states. This classifies them as rather good candidates to apply "local" approaches at least in the v t = 0 state. Using the global approach, small internal rotation splittings may result into correlation between the parameters. As it was already observed in other small organic molecules (such as for methyl formate HCOOCH 3 [29]), the assignment was complicated by two main factors: (i) 2-MF and 3-MF have two small-amplitude vibrations [12]: the out-of-plane bendings of the methyl group at 237 and 267 cm -1 , respectively and the in-plane bending mode at 339 and 321 cm -1 , respectively. These modes are lying below the barrier and therefore are expected to cause some perturbations on the rotationtorsional energy levels. (ii) The value of the ρ parameter which represents the coupling term between internal rotation and global rotation in the kinetic energy operator is only 0.056. This low value does not allow us to get much information about the torsion-rotation coupling. In this complicated and rich room-temperature spectra of internal rotors, it is thus very useful to have various tools to first analyze the spectra (using the "local" codes which are very efficient and easy to use), and then fit globally the torsional manifold (with the "global" codes which are very powerful in predicting higher torsional states that can be populated). It is clear that so far no automatic procedure can really handle the complicated torsional-rotational manifold, and even more the vibrational-rotational-torsion manifold. A new code is currently built by Ilyushin and collaborators towards that goal [30].

Influence of the Isomerism on the Internal Rotation of the Methyl Group, Comparison with Other Heterocyclic Compounds

The hindered internal rotation of the methyl group in 2-MF and 3-MF is due to the one-dimensional torsional potential. The first two terms of its threefold Fourier series, see Equation ( 5), introduce a V 3 and a V 6 parameter. Quantum chemistry calculations based on Density Functional Theory (DFT) B3LYP method and the single reference Møller-Plesset perturbation theory at second order (MP2) method give the dependence of the energy of the electronic ground state on the torsional angle α. Figure 4 indicates that B3LYP and MP2 methods provide nearly identical barriers with slightly higher value with B3LYP. Furthermore, the barrier is lower in 3-MF than in 2-MF. This lowering of the barrier might be interpreted by the larger distance between the oxygen atom and the methyl group which slightly flattens the torsional potential. While the fits with just the V 3 parameter already qualitatively reproduce the data, the fits are improved by adding the V 6 term in the series expansion, in particular near the top of the barrier as it can be seen in the insets of Figure 4a,b and confirmed by the differences between the computed electronic energies and the fitted ones in Figure 4c,d.

The values of V 3 and V 6 obtained from quantum chemical calculations can be compared with the spectroscopic parameters of Table 1 for 2-MF and Table 2 for 3-MF obtained by Table 3. V 3 and V 6 barriers for 2-and 3-methylfuran (MF), methylthiophene (MT) and methylpyrrole (MP) calculated with B3LYP/aug-cc-pVTZ as the function of the methyl groups torsional angle α. Uncertainties are the standard error given by Gnuplot [24] for the fit of the DFT potential based on Equation (5). The experimental values determined in this work for MF or in the literature for MT and MP are mentioned in square brackets.

Molecule

V 3 /cm -1 V 6 /cm -1 100 V 6 /V 3 The internal rotation potential and particularly the V 3 parameter is sensitive to both steric and electronic effects. In heterocyclic compounds, electronic effects are usually dominant [32,34]. When we compare the V 3 values of the three heterocyclic compounds, we can observe that: first, the variation of V 3 is stronger when the methyl group is substituted to the second position (2-MF, 2-MT and 2-MP) compared to its third position (3-MF, 3-MT and 3-MP); second, V 3 is larger for MF compared to MT and MP ((V 3 ) MF > (V 3 ) MP > (V 3 ) MT for the 2-position and (V 3 ) MF > (V 3 ) MP (V 3 ) MT for the 3-isomers) since a larger electronegativity of the oxygen which creates an electronic environment hindering the internal methyl rotation.

Concerning the V 6 term listed in Table 3, we observe larger values for the 3-isomers compared to the 2-ones as if the electronic effects tend to reduce the anharmonicity of the potential. Moreover we can observe negative V 6 values for the three 3-isomers where |V 6 /V 3 | > 3%. These negative V 6 are generally observed for internal rotation potential with significant anharmonicity, we can cite as example molecules such as acetaldehyde [35], methyl ketene [36] or meta-cresol [37].

Materials and Methods

Theoretical Methods

Quantum Chemistry Calculations

The quantum chemical investigations on 2-MF and 3-MF were performed with the Gaussian 16 package [38]. The B3LYP [39] functional was used in the DFT calculations with the default ultrafine grid. We also performed molecular orbital based calculations with MP2 [40]. All our results were obtained with the correlation consistent basis set aug-cc-pVTZ [41]. The convergence criteria of the geometry optimisations of both 2-MF and 3-MF isomers were set to the tight option. The one dimensional energy curves describing the electronic energy as a function of the internal rotation of the methyl group are presented on Figure 4 and all results are listed in Table 3. Each energy value is the result of a geometry optimization on all the coordinates except the frozen angle describing the internal rotation. A step size of 5 • was chosen between two successive angles.

Internal Rotation Hamiltonian

There exist several approaches and codes to treat rotational spectra of molecules containing one or two internal rotor(s). Codes are available at the "Programs for ROtational SPEctroscopy" (PROSPE) [42], managed by Z. Kisiel. Among them, the three codes we are using in the present work, i.e., the program XIAM written by Hartwig and Dreizler [21] which can handle up to three internal rotors, the program called the "ERHAM" (ERHAM) developed by P. Groner for one or two-tops [22,27] and the BELGI series of codes developed by Hougen and Kleiner for asymmetric tops containing one or two internal rotors, with C s [43] (BELGI-C s ) and C 1 (BELGI-C 1 ) [29] symmetries. Finally, Ilyushin has developed the RAM36 code for one-top in the same RAM approach [44].

The Hamiltonian used in the BELGI-C s code is the RAM internal-rotation Hamiltonian based on the work of Kirtman [45], Lees and Baker [46], and Herbst et al. [47]. XIAM and ERHAM can be qualified as "combined axis methods" (CAM) because they set up the Hamiltonian (or parts of it) in the Rho-Axis-System (RAS) but then apply a transformation back to the PAS. ERHAM and XIAM allow to fit each torsional state separately (neglecting thus matrix elements off-diagonal in the torsional quantum number v t ). We thus classify these two methods as "local" ones because they fit each torsional state by itself, even though they treat the A and E states together. In the BELGI code, all the torsional states, up to a given truncation level are taken into account and fit together, so we call it a "global" method. This global approach is particularly successful for low barriers or high excited torsional states.

Since rather complete descriptions of these methods already exist in the literature [48], we will not repeat here such a general description. We only emphasize here the various characteristics that the three methods and programs had to face for the present study.

The RAM is a choice of an axis system which eliminates in the rotation-torsion Hamiltonian the Coriolis type terms (the x, y, z axis are related to b, c, a for prolate molecules. For an asymmetric top with a plan of symmetry as the case here, the Coriolis cross term -2Fρ y p α J y does not exist because of symmetry restrictions.) -2Fρ x p a J x and -2Fρ y p α J y , where J x and J y designate the components of the rotational angular momentum in the molecular axis system, p α is the internal rotational angular momentum, F is the internal rotation constant and ρ is the coupling constant. The RAM Hamiltonian may be written as [47]:

H RAM = H T + H R + H cd + H int (1)
where H T is the torsional Hamiltonian, H R the rotational Hamiltonian, H cd the usual centrifugal distortion Hamiltonian, and H int contain higher order torsional-rotational interaction terms:

H T = F(ρ a -ρJ z ) 2 + V(α) (2)
H R = A(cos θ RAM J z -sin θ RAM J x ) 2 + B(sin θ RAM J z + cos θ RAM J x ) 2 + CJ 2 y (3)
For this prolate asymmetric top, the reduction A and the representation I r were chosen. By grouping the terms and if x, y, z → b, c, a we get:

H R = A RAM J 2 a + B RAM J 2 b + C RAM J 2 c + D ab (J a J b + J b J a ) (4)
The potential function which hinders the internal rotation of the methyl group is described by a threefold Fourier series depending on the torsional angle α:

V(α) = V 3 2 (1 -cos 3α) + V 6 2 (1 -cos 6α) + . . . (5)
The relation between the rotational constants A, B, C in the principal axis system and the constants in the Rho Axis system is given by the angle θ RAM which turns the PAS into the RAS:

tan 2θ RAM = 2D ab A RAM -B RAM (6)
From a fit of the spectrum, the following parameters are derived from the BELGI-C s code: V 3 , F, A RAM , B RAM , C RAM , D ab and ρ (plus higher-order parameters).

In the ERHAM code [22,27], the overall rotation-internal rotation Hamiltonian is set up in a product basis of symmetric rotor eigenfunctions with eigenfunctions of the internal rotation Hamiltonian set up in a Rho Axis system. It is assumed that the internal rotation Hamiltonian has already been solved. In the matrix elements of the effective Hamiltonian, the integrals over the internal rotation variables are expressed as Fourier series. Their coefficients are called "tunneling coefficients", and they are the fitting parameters of the effective rotational Hamiltonian in ERHAM.

In the XIAM code [21], the Hamiltonian is set up in the principal axes system of the entire molecule but then the internal rotation operator of each top is set up in its own Rho Axis system (RAS) and after diagonalization, the resulting eigenvalues are transformed (rotated) back into the principal axis system. The fitted parameters are the rotational constants A, B, C, the centrifugal distortion constants up to the 6th order, and for each methyl top the direction of the top axis in the PAM system ∠(i, x), ∠(i, y), ∠(i, z) the internal rotation constant F and the potential barrier height V 3 . Only some higher (4th order) coupling terms between internal rotation and overall rotation are sometimes implemented, and each torsional state is fit by itself.

Room Temperature Millimeter-Wave Spectroscopy

The Doppler limited room temperature mm-wave absorption spectra of 2-and 3-MF in the range of 70-110 GHz and 170-220 GHz were recorded at the LPCA laboratory using the solid state THz spectrometer described in detail in Ref. [20]. The measurements were performed in flux conditions with a low pressure of about P = 5 Pa allowing to limit the consumption of MF and to reduce the collisional broadening up to the Doppler broadening limit (∆ν Doppler ∼ 150 kHz (FWHM) at ν 100 GHz and T 300 K). Due to the high volatility of MFs (P vap 200 hPa for 2-MF and P vap 100 hPa for 3-MF at 300 K), the samples of 2-MF and 3-MF were cooled with a mixture of ice and liquid nitrogen and the flows were regulated with a micro-valve. The spectra were recorded using a combination of a frequency multiplier chain (Virginia Diodes, Inc., Charlottesville, VA, USA) exciting the molecule and a ZBD, which was an unbiased Schottky diode mounted in a wave-guide operating in detection mode.

After up-converting the synthesized microwave frequency by the multiplication chain the guided radiation is launched into free space using a horn antenna, collimated by an off-axis parabolic mirror, passing a polarization grid and propagated through a 125 cm long and 5.6 cm diameter stainless steel absorption cell closed by two Teflon windows. The interaction path-length is doubled [49] with a roof-top reflector positioned at the output of the gas cell. The reflected beam is returned to the output parabolic mirror which ensures the focusing onto the detector. The second harmonic of the frequency modulated signal were recorded in 100 kHz steps with a time constant of 100 ms using a modulation depth of 50 kHz and a modulation frequency of 43 kHz delivered by the frequency synthesizer.

A post treatment with a FFT band-pass filter cuts off lower frequencies and the noisy higher frequency parts of the spectra reducing the noise level and removing the low frequency baseline variations caused by stationary waves between the source, the polarization grid, the cell, and the detector [28].

Conclusions

2-MF and 3-MF isomers are oxygenated VOCs emitted from multiple sources in the atmosphere especially natural or industrial biomass combustion processes. Their atmospheric reactivity leads to the formation of SOAs which directly or indirectly affect the climate. Mm-wave spectroscopy is an interesting approach to monitor them but it requires a prior determination of reliable rotational-torsional line lists. In this study, we propose a global approach using the BELGI-C s code providing a unique set of fitted parameters able to reproduce, at the experimental accuracy, the 2-MF and 3-MF observed mm-wave lines belonging to the ground v t = 0 and the first torsional v t = 1 states up to high J and K values. Unlike 2-MF for which our assignment was based on previous measurements performed by Finneran et al. in Ref. [12], the mm-wave spectrum of 3-MF has been measured in this study in the 70-220 GHz frequency range with the mm-wave spectrometer developed at the LPCA [20]. For both isomers we compared our global approach using BELGI-C s with local approaches based on the XIAM and ERHAM codes. Two advantages of the BELGI-C s global approach are highlighted: (i) the ability to fit at the experimental accuracy the A and E components involving both v t = 0 and v t = 1 states (XIAM failed to fit correctly rotational lines of 2-MF and 3-MF in v t = 1); (ii) the possibility to determine with a high degree of accuracy the V 3 and V 6 parameters of the internal rotation potential (in the ERHAM method, the potential barrier does not appear explicitly and V 6 could not be determined). Based on DFT calculations, these (V 3 , V 6 ) parameters are discussed considering other sulfur and nitrogen heterocyclic analog in order to better understand the influence of the electronic environment on the internal rotation barrier and its higher-order correction term. To confirm experimentally the identified trends, we propose to investigate in the mm-wave domain the rotational-torsional spectroscopy of MP and MT already studied in the microwave domain [31][32][33][34]. Finally, in order to assign the remaining mm-wave lines of 2-MF and 3-MF, a rovibrational analysis of the lowest energy vibrational modes will be undertaken by means of synchrotron-based FT-Far-IR high-resolution spectroscopy as it was done recently by our group on the catechol molecule [15]. Part IV

GS

Experimental developments for future prospects

So far our room temperature pure rotational THz spectroscopy setup is limited to volatile molecules with a vapor pressure of > 10 µbar. Unfortunately, a lot of the especially more complex compounds emitted by biomass burning have lower vapor pressures, the so called semi-volatile organic compounds (SVOCs). To be able to monitor molecules as in the Chapters 4 and 7 non-invasive, in realtime and in-situ during reactions in the atmosphere the presented spectroscopic results are an important foundation but additional technical improvements are necessary.

We have chosen a straightforward solution by developing a heated coat, integrated in the solid state mm-wave spectrometer described in Section 3.1. We aimed to increase, in a homogeneous way, the temperature of the targeted SVOC and therefore its equilibrium vapor pressure in the absorption cell by avoiding any recondensation. I contributed to this experimental development, described in chapter 8, by participating in the supervision of a Master 2 trainee Manuel Roca. The tests were carried out on methylcatechol, the mm-wave spectrum of which was measured for the first time.

The second technical improvement constitutes the final goal of this thesis: The application of THz spectroscopy in a controlled environment in which it is possible to study atmospheric reactions, in our case, the ASC of the LPCA CHARME. My contribution to this project consisted in the installation of a solid state mm-wave spectrometer (and a near-IR diode-laser) into the ASC CHARME to enable non-invasive, real-time and in-situ measurements inside the ASC with a modified Chernin-type multi-pass cell called "MULTICHARME", developed by the LPCA engineers and our collaborators from Chinese Academy of Sciences, Anhui, China, under the lead of my thesis director Anraud Cuisset. To the best of our knowledge, for the first time, THz radiation was propagated over a distance of more than 200 m [29] and was used for a direct monitoring of polar species in an ASC. This work is described in Chapter 9 via the article published in 2022 in Atmospheric Measurement Techniques [30].

Chapter 8

Measurements of semi-volatile compounds in a heated cell

Outline of the current chapter Measuring VOCs with the solid state mm-wave spectrometer of the LPCA, described in Section 3.1, two limitations regarding the pressure are given. To preserve the selectivity of the THz rotational spectroscopy, the pressure needs to be lowered up to the value at which the line width is mainly defined by Doppler broadening, so called Doppler limit (see Equation 1.53). In case of higher pressures the molecular signal is higher but due to the collisional broadening the SNR would not be improved and the selectivity is deteriorated. At lower pressure the molecular signal is further reduced but the line width remains the same leading to a reduction of the SNR. For the previously presented molecules the ideal working pressure, the so-called "critical pressure" (transition in a Voigt profile from the Doppler limit to collisional broadening when ∆ν Doppler = ∆ν coll ), is in the range of 10 -50 µbar.

CHAPTER 8. Measurements of semi-volatile compounds

The other limitation is given by the setup itself. The minimum pressure reachable with the secondary vacuum produced by the turbo vacuum pump within the absorption cell with its Teflon windows and connections to the reservoir, the vacuum pump and the pressure gauge is ≈ 2 µbar.

As mentioned already before there are plenty of interesting molecules with lower vapor pressures at room temperature called semi-volatile organic compounds (SVOCs). To measure these SVOCs either the sensitivity of the experiment or the vapor pressure of the molecule need to be increased. Of course their are steady efforts of many scientists to contribute to the first option as example by increasing the THz interaction pathlength (e.g. by Cuisset et al. in [29]) but the more straightforward way to achieve it, is by increasing the vapor pressure. Therefore raising the temperature seems to be the simplest way.

An increased temperature on the other hand influences the partition function as it is explained in Section 1.3.2. At higher temperature the molecular signal will be increased in total due to the higher vapor pressure but at the same time it will be distributed over more energy levels. The line intensity is inversely proportional to the partition function Q(T ) (see Equation 1.45) with a rotational contribution proportional to T 3/2 (see Equation 1.49). In case all required parameters for the partition function and the vapor-pressure-curve are known, the two oppositional effects could be weighted against each other. As our interest to enable the studies of these SVOCs is derived from the absence of the precise spectroscopic parameters, required to evaluate their impact, we gave it a trial by heating and investigating 3-mCAT (introduced already in Section 5.2).

Unfortunately, no data of the vapor pressure are available for 3mCAT in the literature [40]. Only the melting point (T m = 68 • C) and the boiling point (T B = 241 • C) are listed in the PubChem database [59]. Since these values are close to those of 4-mCAT (T m = 65 • C and T B = 251 • C) the vapor pressure curve of 4-mCAT can be used in first approximation (see Figure 15 in the appendix). According to that curve an aimed minimal pressure of P min ≈ 10 Pa is achieved at ≈ 340 K. At about 370 K, being slightly above T m , a vapor pressure of 1 mbar is given.

Heatable absorption cell 151

8.1 Implementation of a heating system for the solid state mm-wave spectrometer of the LPCA To ensure the increase of the molecular signal by a higher vapor pressure it is of major importance to heat the whole setup homogeneously. Inhomogeneous heating causes temperature gradients or cold points. The molecule would condensate and lowering the vapor pressure. Over the time depositions at cold points would cause problems by impeding the pressure control or even blocking connections. As indicated in Figure 8.1 four different parts of the setup therefore need to be heated: (I) The sample reservoir with a valve and the connecting tube T S , (II) the second/right Teflon window with the inlet and one mount T R , (III) the central tube of the absorption cell T C and (IV) the first/left window with the connections to the pressure gauge, the outlet to the vacuum pump and the second mount T L .

The sample reservoir and the connection part is heated by a manually controlled heating wire covered with an aluminum foil to keep a homogenized temperature. To have potential condensation in the sample reservoir and not in the absorption cell, its temperature is set lowest. The cell is heated by a custom made heating coat purchased from DBM Technologie composed of three parts covering the absorption cell (in total 1275.3 mm long and 99 mm in diameter) T L , T C and T R (see Figure 8.1). Each part of the heating coat has its individual dimensions and length (T L = 42 cm, T C = 60 cm and T R = 30 cm) adopted to the size, the connections and mounts.

The heating system is controlled by two proportional-integral-derivative (PID) controllers. Because the three thermal coatings are of different size the required power to obtain a certain temperature is not equal. When driven by just one PID controller and set to 50 • C a gradient of about 20 • C is produced. Therefore two PID controllers are used, one for T C and another one for T L and T R leading to a offset temperature of 1 • C.

In principal the heating system is capable to reach 400 • C. However with the windows of the cell made of Teflon which is generally rated for us up to 260 • C [75] T max is even lower. Indeed we did not exceed 150 • C because not 152 CHAPTER 8. Measurements of semi-volatile compounds all components of the current setup (especially the pressure gauge) are made for high temperatures. In case temperatures greater than 150 • C are needed these parts just need to be exchanged by commercially available heat resistant components.

First mm-wave measurements of a SVOC in the heated cell: the 3-methylcatechol

A molecule combining all the presented topics of the Chapters 4, 5, 6 and 7 is 3-methylcatechol (3-mCAT):

• 3-mCAT contains a IHB as investigated in Chapter 5.

• it is a derivative of catechol and could be investigated in a similar way to verify our approach to relating spectroscopy to IHB.

• the methyl group can undergo similar internal rotation as the one of methylfuran.

8.2. First mm-wave measurements of a SVOC in the heated cell 153

• Sun et al. determined its reactivity in the atmosphere to be higher than catechols [98].

A general description of 3-mCAT in given in Section 5.2 and a theoretical investigation of its IHB is given in Section 5.4.1. Table provides some additional parameters of the two stable conformers expected to be observable in the room temperature spectra. The parameters are computed with B3LYP and the aug-cc-pVTZ basis set.

ν < 500cm -1 b 9 - 9 -
a Derived from potential energy curve of Figure 8.2. b A detailed list of all the vibrational modes potentially visible in the room temperature mm-wave spectra of Figure 8.4 is given in the appendix.

Table 8.1 -Parameters relevant for room temperature rotational mm-wave spectroscopy of the 3-mCAT1 and 3-mCAT2 (see Section 5.2). The parameters were obtained by B3LYP calculations with the aug-cc-pVTZ basis set and fitted from a jet-FTMW sprectrum in the 5 -20 GHz region provided by Xiujuan Wang and Dr. Qian Gou of the School of Chemistry and Chemical Engineering, Chongqing University, China. Besides the rotational constants A, B, C and the dipole moments µ a , µ b , µ c the relative energies with Zero-point correction of the two conformers, their V 3 barriers of the internal rotation of the methyl group, the number of potentially observable vibrationally ES is given.

Additionally to the geometry optimization, determining the rotational constants and dipole moments and the anharmonic frequency calculations to obtain the frequencies and intensities of the IR active vibrations, one dimensional scans were performed (see Figure 8.2). Therefore the dihedral angle defining the torsion of the methyl group was rotated in 5 • steps and kept constant during the optimization step. For the lowest energy conformer 3-mCAT1 a barrier of V 3 = 288.0 cm -1 and for 3-mCAT2 V 3 = 468.6 cm -1 was found. The almost 200 cm -1 higher barrier of the second conformer might be explained with the hydroxy group in the 2 position being orientated towards the methyl group. Due to sterical hindering and interactions between these two substituents the rotation is impeded. To estimate the optimal temperature for recording the 3-mCAT spectra in the mm-wave region, spectra were recorded at different temperatures with an example illustrated in Figure 8.3. Due to the competing effects of increasing vapor pressure and the number of populated energy levels the temperature will need to be optimized for each measured molecule individually. Because the spectra of Figure 8.3 show a high density of rotational lines the increasing broadening with temperature and consequently overlapping/merging of lines need to be taken into account, too.

Due to its highest SNR of the dense spectra of XIAM for the GS spectra of both conformers. Figure 8.4 compares these simulations (in black for 3-mCAT1 and in red for 3-mCAT2) with the experimental spectra. The zoomed part highlights the good agreements of the simulation with the experimental spectra.

The analysis of these spectra is currently under progress managed by Anthony Roucou. Extending the XIAM fits provided by Xiujuan Wang and Qian Gou, GS lines of both conformers were identified. The methyl internal rotation splitting of conformer 1 is resolved in the MW and mm-wave regions. For conformer 2 the A-and E-species were only identified in the MW spectra, so far. Besides the GS lines of both conformers, additional intense lines remain unassigned leading to the assumption that the spectra also contain ES lines. But before to assign and analyse these potential ES, reliable GS fits are required. The obtained results are furthermore a proof of concept. It is possible to not just increase the vapor pressure of a given compound but also improve the molecular signal and the line intensities of the rotational lines. The main limitation is given by the partition function, therefore especially the investigation of SVOCs with less conformers and low frequency modes will benefit from this heating system.

Another approach, not discussed so far, could be the heating of VOCs, already studied at room temperature, to populate higher frequency vibrational modes or maybe even higher energy conformers.

Abstract. We have developed MULTICHARME, a modified Chernin-type multi-pass cell especially designed for IR and THz long-path absorption measurements in the CHamber for Atmospheric Reactivity and Metrology of the Environment (CHARME). By measuring the output power using a near-IR diode-laser and a THz amplified multiplication chain, we have established that the effective reflectivity of MULTICHARME is better than 94 % over approximately three decades of frequency. Absorption measurements of N 2 O have been performed by probing highly excited rovibrational transitions in the near-IR and ground state rotational transitions at submillimeter wavelengths. In each case the linearity of the absorbance with the path lengths was verified. Finally, we demonstrate that THz spectroscopy is able to study the isotopic composition of greenhouse polar gases such as N 2 O and to absolutely quantify stable (N 2 O) and reactive (O 3 ) species at trace levels. At low pressure the ozone concentration was continuously monitored and its decay characterized. The deduced ozone lifetime of 3.4 ± 0.1 h is shorter compared with previous measurements performed in CHARME at atmospheric pressure. For the first time, the ability of THz rotational spectroscopy to monitor, with a very high degree of selectivity, stable and reactive polar compounds at trace level in an atmospheric simulation chamber is demonstrated. However, the sensitivity of the THz monitoring needs to be improved to reach atmospheric trace levels. For this purpose, it is necessary to fully understand the origin of the observed baseline variations caused by the complex multiple standing waves present in MULTICHARME.

Introduction

Atmospheric simulation chambers (ASC) have been developed to study atmospheric physicochemical processes under controlled conditions. Beside small Teflon bags of a few hundred liters, approximately 35 chambers are currently in operation around the world. All these reactors are equipped with a large variety of instruments dedicated to the monitoring of gases and particles, ranging from commercially available apparatuses to specialized custom-designed set-ups offering in situ measurement of chemical species by optical techniques.

Various spectrometers based on photonic sources from UV to mid-IR have been coupled to different ASC allowing the stable and unstable reactants to be monitored along with the gas and particle phase products involved in key atmospheric reactions [START_REF] Barnes | An FTIR product study of the photooxidation of dimethyl disulfide[END_REF]Bloss et al., 2005b;Rohrer et al., 2005;[START_REF] Wagner | Chamber Simulations of Cloud Chemistry: The AIDA Chamber[END_REF][START_REF] Ren | Investigation of the reaction of ozone with isoprene, methacrolein and methyl vinyl ketone using the HELIOS chamber[END_REF]Massabò et al., 2018). The identification of critical intermediate species and the time-resolved quantification of kinetic parameters are of upmost importance for atmospheric models. The optical components used to couple the probe beam with the ASC are selected depending on the nature of the light source employed, the detection scheme and the geometry of the reac-Published by Copernicus Publications on behalf of the European Geosciences Union.

tor. The trace gas monitoring requirement in an ASC makes it necessary to reach sub-ppm limits of detection (LOD) by maximizing the interaction path length between the light and the probed species. Nowadays, most of the ASCs, using optical spectrometers as analyzers, are equipped with an optical system enabling multiple passes of the probe light back and forth across the ASC, thus increasing the absorption path length and consequently improving the LOD.

For example, several ASCs are coupled to commercially available Fourier transform infrared (FTIR) spectrometers for volatile organic compound (VOC) detection at low resolution (> 0.5 cm -1 ) in the mid-IR (typically 400-4000 cm -1 ) using a White-cell multi-pass mirror configuration reaching several hundreds of meters of interaction path lengths with a broadband black-body IR source [START_REF] White | Long Optical Paths of Large Aperture[END_REF]. The following ASCs are well known examples in the EUROCHAMP 2020 network (EUROCHAMP 2020, 2021): (i) the 4.2 m 3 CESAM chamber in Paris uses a globar source inside a Bruker interferometer with a 192 m path length White-cell (Wang et al., 2011); (ii) the quartz reactor QUAREC in Wuppertal also employs a White-cell configuration to achieve an optical path length of 484.7 ± 0.8 m and is entirely mounted inside the photoreactor for sensitive in situ long path IR absorption monitoring of reactants and products [START_REF] Barnes | An FTIR product study of the photooxidation of dimethyl disulfide[END_REF]; (iii) the EUPHORE photoreactor in Valencia makes it possible to intercompare 1 cm -1 resolution FTIR data (L = 616 m) with differential optical absorption spectroscopy measurements in the 389-469 nm UV range with a dedicated White cell (W-DOAS) which can reach km path lengths (Bloss et al., 2005a, b).

The highly instrumented reactor for atmospheric chemistry (HIRAC) chamber in Leeds is coupled to a laserinduced fluorescence-fluorescent assay by gas expansion (LIF-FAGE) analyzer and to a multiple pass FTIR system. In contrast to the previous examples of traditional White-type arrangements, the HIRAC team chose a modified multiple pass matrix system developed by [START_REF] Chernin | Optical multipass matrix systems[END_REF] and [START_REF] Chernin | Development of optical multipass matrix systems[END_REF]. This solution retains the focal properties of the original White cell and perfectly conserves optical throughput over a range of matrix arrangements. In practice, the Chernin cell is very easy to align and shows very good stability to vibrations, with the FTIR giving good LODs over short acquisition times. For observation times as short as 1 min, LODs below 100 ppbv are obtained for ozone and VOCs, such as acetaldehyde, methane and formaldehyde with the FTIR interferometer coupled to the 128.5 m Chernin cell (Glowacki et al., 2007b). Finally, the Chernin multi-pass cell optimizes the recirculation of the beam over many focused lines on the field mirrors and minimizes overlapping between adjacent refocusing points, thus facilitating the control of the propagation of more divergent beams over long distances.

Due to the lack of reliable and sufficiently powerful sources and due to the difficulty to control the propagation of more divergent beams over long distances, far-IR/terahertz (THz) spectrometers have never been used for trace gas monitoring in ASCs; however, in 2013 Kwabia-Tchana et al. ( 2013) have demonstrated the ability to perform FT-far-IR spectroscopy in a large cryogenically cooled Chernin cell (Kwabia-Tchana et al., 2013). This cell is coupled to the AILES beamline of the SOLEIL synchrotron (Brubach et al., 2010) and allows mid-IR and far-IR measurements with variable path lengths from 3 to more than 141 m thanks to exceptional properties of brightness and small divergence especially in the THz domain.

In this study, we present and characterize a multiple pass system developed for the CHamber for Atmospheric Reactivity and Metrology of the Environment (CHARME) (Fayad, 2019). Based on a Chernin type arrangement, the so named MULTICHARME has been dimensioned for the CHARME ASC and allows the monitoring of stable and reactive atmospheric species at trace levels over three decades of frequencies by probing long path rovibrational and rotational molecular absorbances respectively in the IR and in the THz domains. To the best of our knowledge, this is the first time that a THz spectrometer has been used for in situ measurements of atmospheric species in an ASC. The results obtained in this study highlight a new approach based on pure rotational spectroscopy for rapid and highly selective detection of stable and reactive atmospheric compounds in a simulated atmospheric environment. The first part of the article is dedicated to the description of CHARME, MULTICHARME and its coupling with IR and THz sources. The results are presented and discussed in the second part of the article with a special focus on the THz measurements which are unprecedented in the ASC community. The CHARME is the new atmospheric simulation chamber designed in the LPCA (Laboratoire de Physico-Chimie de l'Atmosphère) laboratory in Dunkirk (France). CHARME is described in detail in Fayad (2019). Briefly, it consists of a 9.2 m 3 evacuable cylinder (length ≈ 4 m; internal diameter ≈ 1.7 m) made of electropolished stainless steel (304 L). The inner surface of the reactor is mechanically polished in addition to an electrochemical treatment, which enhances the light reflectivity and also reduces the interaction of gases and particles with the walls. There are four stainless steel fans (diameter 50 cm) located at the bottom of the chamber to assure a fast homogenization of the reactive mixtures and can be activated only at atmospheric pressure.

The rigid walls with a thickness varying from 4 to 40 mm permit the reactor to guarantee vacuum and nondeformation of the flanges. Consequently, CHARME is considered as vacuum compatible and it is capable of support-ing most of the mechanical constraints when it is under vacuum. The range of pressure under which it can operate is: 0.05 mbar < P < 1000 mbar. CHARME is pumped with a vacuum pump (Cobra NC0100-0300B) and is filled with purified and dried air at the required pressure using a generator (Parker Zander KA-MT 1-8). The pressure within the chamber is measured using 2 MKS BARATRON (626B13MDE (1000 mbar) and 626B01MDE (1 mbar)) and a pressure reader (MKS PR4000B) and the relative humidity and temperature are monitored by a combined probe (Vaisala HUMICAP, HMT330).

CHARME has 9 different circular access ports ranging from 45 to 20 cm in diameter (see Fig. S1 in the Supplement), which are used for various tasks: accommodate the MULTICHARME optical set-up for a Chernin cell described in this article; to provide physical access to the inside of the chamber for any cleaning and alignment operations; for in situ monitoring of gases and particles by incoherent broad band cavity enhanced absorption spectroscopy (IBBCEAS, Fiedler et al., 2003;[START_REF] Meng | Incoherent broadband cavity enhanced absorption spectroscopy (IBBCEAS)-based strategy for direct measurement of aerosol extinction in a lidar blind zone[END_REF] to introduce gases and/or particles into the chamber.

MULTICHARME (MULTI-pass cell specially

designed for CHARME)

General design

In order to ensure a sufficient optical throughput at THz frequencies the MULTICHARME Chernin cell configuration employed uses two rectangular field mirrors (266 × 310 mm and 222 × 50 mm), and three circular objective mirrors (diameter 130 mm). As shown in Fig. 1b, we have opted for the modified version of the Chernin cell with the input and output windows on both sides of the field mirrors [START_REF] Chernin | Development of optical multipass matrix systems[END_REF]. MULTICHARME has been designed in order to maximize the size of the mirrors to account for the large size of the beams and the strong divergences at longer wavelengths in the THz domain. We were nevertheless limited by the size of the flanges coupled to the DN 450 circular ports of the CHARME ASC. All mirrors have the same radius of curvature (ROC = 5000 mm) corresponding to the MULTI-CHARME base length. Fused silica substrates were used for the field mirrors, K9 for the objectives. To optimize the reflectivity from near-IR to THz domain, i.e. three frequency decades from 300 to 0.3 THz, a coating of 500 nm silver protected by 10 nm of Al 2 O 3 was used. These relatively large mirrors were manufactured by the Anhui Institute of Optical and Fine Mechanics over a period of several months to build the substrates and to deposit the coatings. This institute has already successfully developed a Chernin cell for the detection of atmospheric radicals with Faraday rotation spectroscopy in the mid-IR (Fang et al., 2020). The two optical mounts, equipped with the three objective mirrors and the two field mirrors, constitute the Chernin cell presented in Fig. 1. Using the DN 450 access ports (A1 and A2 in Fig. S1) and custom-made vacuum enclosures, they are located on opposite ends and placing the mirrors inside of the cylindrical chamber. Two aluminum optical mounts were constructed to hold the mirrors. The mass of the additional components added to CHARME was 160 kg for each of the two DN 450 ports located at opposite ends.

The total deformation of the Chernin cell and the corresponding mounting flanges were analyzed under static conditions. The forces that were considered were their own gravity and the atmospheric pressure on the outer surface of the flanges when the chamber was in a vacuum state. The maximum displacements have been estimated to be less than 30 µm. A picture of the five mirrors is given in Fig. S2. The characterization of their reflectivity in the IR and in the THz domains is described in Sect. 2.2.2 and 2.2.3, respectively. In order to accurately and easily control the optical alignment and the path length, both the field and objective mirrors are equipped with computer-controlled micrometric screws: MULTICHARME can be aligned with 18 compact linear motorized actuators TRA25PP from the MKS/Newport company (6 actuators are fixed on the field mount to adjust the 3 degrees of freedom of the 2 field mirrors; 12 actuators are on the objective mount: 9 to control the position of the 3 objective mirrors and 3 to adjust the relative orientation between field and objective blocks). The actuators are controlled by a home-made Arduino-based system located outside the cell (see Fig. S3). This system allows each actuator to be selected independently and to control their movement. The "5-mirror configuration" is easy to align, forms a matrix with an adjustable number of rows and even columns on the field mirrors and provides good vibration stability. Different spot patterns obtained with a He-Ne alignment laser are shown in Fig. S4 highlighting our ability to adjust matrix arrangement on the field mirror for different path lengths in MULTICHARME from 120 to 540 m.

Coupling with IR tunable diode laser

The characterization in the near-IR has been performed using a continuous-wave external cavity diode laser (ECDL, Toptica DL pro) tunable from 1340 to 1450 nm with an output https://doi.org/10.5194/amt-15-1201-2022 Atmos. Meas. Tech., 15, 1201-1215, 2022 power of 80 mW, a spectral width of 100 kHz and a modehop free tuning range of 20 GHz. The ECDL source, the photodetector and the transfer optics were placed on an optical breadboard fixed to the field flange. The IR input and output were coupled to the CHARME ASC by two 76.2 mm diameter ZnSe windows with a 1 • wedge giving a theoretical transmission of about 70 % at 1.4 µm.

The IR optical configuration is presented in Fig. 2b, an additional mirror was inserted into the beam path to coaxially inject a red MKS/Newport He-Ne laser (5 mW) with the IR beam axis in order to facilitate the alignment of the Chernin cell. This enables the IR path length in MULTICHARME to be evaluated by the observation of the matrix arrangement of the He-Ne spots on the field mirrors observed from a BK7 window placed on the objective transfer flange. All adjustments and path length changes can be made in situ, without venting CHARME, with the computer-controlled actuators. Once the laser was adjusted for the desired operating range, a wavelength calibration was performed (Burleigh WA-1500) with an accuracy better than 4 × 10 -3 cm -1 . An InGaAs detector (Thorlabs PDA400) with a typical bandwidth of 10 MHz was used for the detection. Spectra were obtained by applying a voltage ramp to the piezo actuator allowing an excursion of 0.17 cm -1 around the line center at a frequency of 1.3 Hz. The received photodiode signal was averaged by a digital oscilloscope (DSO-X 2002A Agilent Technologies, maximum frequency 70 MHz). The signal was typically accumulated over 16 ramp cycles with a sampling of 12.5 kHz (10 bits of vertical resolution).

To characterize the performance of MULTICHARME in the near-IR, we have examined the optical throughput in the modified Chernin multi-pass cell by measuring the output IR power for several different matrix arrangements (Glowacki et al., 2007a). It corresponds to 12 matrix configurations from 24 to 108 passes, for path lengths from 120 m (3 rows × 4 columns) to 540 m (9 rows × 6 columns), respectively. The output powers shown in Fig. 3 were measured with a PDA400 power-meter from Thorlabs with an accuracy of 1.2 µW. The variation of the output power with the number of reflections was modeled by a power law P = A×R n eff , where A is a constant corresponding to the received power with no reflection, R eff is the effective mirror reflectivity at 1.4 µm and n is the number of reflections. An effective reflectivity of the mirrors at 1.4 µm was adjusted to 95.98 ± 0.06 % (error given by the fit) with a weighted fit using the estimated error bars taking the accuracy of the IR photodetector into account. This value is relatively good considering the expected decrease of the IR reflectance at shorter wavelengths.

Coupling with THz source

Several compact and versatile solid-state sub-THz sources are currently used in our laboratory for trace gas monitoring using high resolution rotational signatures of atmospheric pollutants in realistic media, e.g. industrial combus-tion (Mouret et al., 2013) or gas emitted in food packaging [START_REF] Hindle | Monitoring of food spoilage by high resolution THz analysis[END_REF]. In this study, a commercial Virginia Diode Inc amplified multiplication chain (AMC) driven by a microwave synthesizer (Rhodes & Schwarz SMA 100B) was used (see Fig. 2c). Two Menlo systems TPX lenses of 50.8 mm diameter and 100 mm focal length were used to collimate the beam at the entrance of the chamber and refocus the output beam onto the detector. The propagation of the THz radiation in MULTICHARME was modeled as a Gaussian beam using a program developed by Lightmachinery inc. [START_REF] Williams | Gaussian Beam Propagation[END_REF] showing that the use of f = 100 mm lens provides the best results taking into account the beam properties (waist and divergence), the dimension of MUL-TICHARME and the different losses (transmission through the window & reflections on the field and objective mirrors). Two different AMC multiplication stages were used, the first (multiplication × 18) to cover the 140 to 220 GHz frequency region with an average power of 3 mW and the second (multiplication × 54) to cover the 440 to 660 GHz region with an output power of around 50 µW. To detect the MULTI-CHARME output THz signal, two VDI Schottky zero biased detectors (ZBD) WR5.1 and WR1.5 were chosen with typical responsivities of 1000 and 2400 V W -1 , respectively for the first and the second stages. The typical noise equivalent power (NEP) of these Schottky diodes is estimated to be 10 pW √ Hz -1 . Both amplitude modulation (AM) and frequency modulation (FM) schemes were employed. The simultaneous use of AM and FM as a function of frequency proved useful to minimize the effects of the standing waves in the baseline, (see Sect. 3). A computer-controlled Ametek 7230 lock-in amplifier recovered the measured signal as a function of the frequency. High resistivity float zone silicon windows with a theoretical transmission of more than 50 % were used for the entry and exit of MULTICHARME during the THz measurements. This material is opaque at the He-Ne laser wavelength, so the THz beam alignment in MULTI-CHARME was performed by superimposing the THz beam onto the IR beam at the entrance of MULTICHARME and on the objective mirrors.

As done with the IR radiation, we have measured the THz output power for different path lengths. These measurements presented in Fig. 3b were performed around 190 GHz corresponding to the maximum output power at the rank × 18 of the AMC. With a lower input power and a more divergent beam, only 5 matrix configurations corresponding to path lengths from 120 m (24 passes) to 280 m (56 passes) were accessible at this frequency. If we consider just the detector NEP, 50 pW should be detectable with a time constant of 1 s, i.e. four orders of magnitude below the power level measured for a 280 m path length. Here the strong limitation to reach larger path lengths is the divergence of the THz radiation and the size of the THz waist on the field mirrors. Reaching a path length of 280 m with an amplified frequency multiplication chain which is a highly divergent source, is a significant im- provement compared to commonly used set-ups. Extending the path length further should be possible for higher frequencies or with more powerful THz sources. An overview of the best performance reached by rotational sub-mm-wave/THz long-path absorption spectroscopy is provided (Cuisset et al., 2021): the maximum THz path length in a White-cell was obtained with a weakly divergent and bright synchrotron source but it never exceeded 200 m (Brubach et al., 2010); longer interaction path lengths are accessible only in Fabry-Perot resonators with intracavity spectroscopic techniques [START_REF] Hindle | Terahertz gas phase spectroscopy using a high-finesse Fabry-Pérot cavity[END_REF]. By fitting, with the power law, the THz output power, an effective THz reflectivity of 94.2 ± 0.4 % (error given by the fit) has been found for MULTICHARME. This value is only slightly lower than the near-IR value found in Fig. 2a. Therefore, MULTICHARME guarantees a reflectivity better than 94 % on more than 3 decades of frequencies. With a unique modified Chernin type multi-pass cell, long path absorption spectroscopic measurements are now possible from the THz to the near-IR domain in an ASC such as CHARME.

3 Results and discussion

Absorption linearities

The first spectroscopic measurements were carried out to verify the linearity of the absorption over three decades of frequencies from mm-wave to near-IR domains. With the aim to characterize the performances of MULTICHARME, we have chosen nitrous oxide N 2 O as test molecule for three main reasons: (i) N 2 O is a powerful and very stable greenhouse gas which can be considered now as the dominant ozone-depleting substance emitted in the 21st century in our atmosphere [START_REF] Ravishankara | Nitrous Oxide (N 2 O): The Dominant Ozone-Depleting Substance Emitted in the 21st Century[END_REF]. The monitoring of its chemical activity during transport from the troposphere to the stratosphere is crucial to control the ozone depletion; (ii) N 2 O is actually monitored in the troposphere and in the stratosphere by probing its rovibrational IR and rotational THz transitions with sounders such as the infrared atmospheric sounding interferometer (IASI) (Clerbaux et al., 2009) or THz atmospheric limb sounder (TALIS) [START_REF] Meng | Incoherent broadband cavity enhanced absorption spectroscopy (IBBCEAS)-based strategy for direct measurement of aerosol extinction in a lidar blind zone[END_REF] respectively; (iii) the molecular rotational and rovibrational line parameters (line frequencies, line widths, line intensities) of N 2 O were measured and calculated from the mm-wave to the near-IR domains and are listed in the international spectroscopic databases such as JPL [START_REF] Pickett | Submillimeter, Millimeter, And Microwave Spectral Line Catalog[END_REF] or HITRAN [START_REF] Gordon | The HITRAN2020 molecular spectroscopic database[END_REF].

The absorption linearity was first checked in the near-IR by probing the R(17) rovibrational transition of N 2 O in the highly excited (3, 2, 0, 1) ← (0, 0, 0, 0) vibrational band. From the HITRAN database [START_REF] Gordon | The HITRAN2020 molecular spectroscopic database[END_REF], this line is predicted with a weak intensity (S = 7.1 × 10 -25 cm molecule -1 ) and is expected at 7149.45 cm -1 , where the ECDL performs optimally. As shown in Fig. 4a, the near IR rovibrational absorbance has been obtained for 8 different paths in MULTICHARME covering interaction distances from 120 to 480 m at a pressure of 20 mbar. In order to avoid any saturation of the absorption signal, a calibrated mixture of χ = 1000 ppmv of N 2 O diluted in N 2 was used. In order to deduce the absorbance given by A(ν) = ln I 0 (ν) I (ν) , baseline variations I 0 (ν) were measured systematically with the signal variations I (ν). The wavenumber calibration was performed with the measurements of the WA-1500 wavelength-meter with an accuracy better than 4 × 10 -3 cm -1 . The integrated absorbances, converted in cm -1 units, are determined by fitting the Doppler broadened near-IR lines with Gaussian profiles. They have been plotted in Fig. 4b according to the associated path lengths. A linear regression weighted with the error bars (3σ ) deduced from the Gaussian fits yields an R 2 of 0.998 and a slope s = 1.17(7)×10 -5 cm -1 m -1 . The linearity observed ensures the absence of saturation and guarantees that the IR photons introduced into MULTICHARME have traveled the same optical path before they reach the detector (Kwabia-Tchana et al., 2013). From the measured slope in Fig. 4b and the averaged linewidth estimated to be ν = 0.014 cm -1 (HWHM), we can deduce, according to the equation α 0,exp = 2 ln 2 π s ν [START_REF] Sigrist | Air monitoring by spectroscopic techniques[END_REF], an experimental value of the maximum absorption coefficient of the line α 0,exp = 3.92 × 10 -6 cm -1 , around 50 times bigger than the expected value α 0,th = 7.26×10 -8 cm -1 given by the equation α 0,th = Sχ k B T γ air (Hindle et al., 2018), where the line intensity S and the airbroadening coefficient γ air are the tabulated values in the HI-TRAN database. The variation between α 0,exp deduced from our measurements and α 0,th could be partially explained by significant uncertainties of the tabulated near-IR parameters S and γ air from a very weak rovibrational line which was, to the best of our knowledge, never measured before this study.

The absorption linearity was also checked in the THz domain by probing the pure R( 22) rotational transition of N 2 O in its ground state expected at 577 578.215 MHz with a line intensity estimated to be S = 2.9×10 -22 cm -1 (molecule cm -2 ) -1 from the HITRAN database [START_REF] Gordon | The HITRAN2020 molecular spectroscopic database[END_REF], 400 times stronger than the previously probed near-IR rovibrational line and experimentally measured [START_REF] Rohart | N 2 -and O 2 -broadening coefficients and profiles for millimeter lines of 14 N 2 O[END_REF]. For the THz measurement, the mixing ratio in air was 400 ppmv and the rotational lines were measured at a total pressure of 4 mbar. Unlike IR rovibrational bands, with only a few mbar of pressure, the collisional broadening is dominant compared to the Doppler broadening and a Lorentzian profile was assumed to fit these THz lines. The measured absorbances for five different path lengths from 120 to 280 m are presented in Fig. 5a. Compared to the IR lines, strong baseline oscillations due to standing THz waves affect the line profile especially for the longest THz paths. In Fig. 5b, we have determined the integrated absorbances by determining the area of the rotational lines shown in Fig. 5a. Compared to the IR results, larger uncertainties are deduced from the integration process due to the baseline variations. Nevertheless, a linear behavior is estimated with the different path lengths at least up to 240 m which already constitutes a record for a THz radiation in a multi-pass cell (Cuisset et al., 2021). With s = 5.1(4) × 10 -7 cm -1 m -1 , the slope obtained with the four THz measurements from 120 to 240 m is smaller than the IR slope. The THz rotational linewidth is estimated to be 3.4×10 -4 cm -1 (HWHM), around 300 times smaller than the IR rovibrational linewidth highlighting the excellent selectivity of the THz spectroscopy compared to IR due to a weaker Doppler broadening. An associated value of α 0,exp = 4.77 × 10 -6 cm -1 is deduced from the relation α 0,exp = s π ν assuming pressure-broadened lines [START_REF] Sigrist | Air monitoring by spectroscopic techniques[END_REF]. Unlike the near-IR results, the measured maximum absorption α 0,exp is in good agreement with the calculated value from the tabulated intensity S and the air-broadening coefficient γ air yielding α 0,th = 1.23 × 10 -5 cm -1 . There is no doubt that in this case, the rotational parameters of N 2 O are more reliable and here the slight differences between the two values are due to an absorbance averaged on the full line profile compared to an absorption α 0,th calculated for the maximum of the rotational line.

Specificity of the THz measurements

Compared to IR rovibrational spectroscopy, rotational THz spectroscopy presents several advantages and disadvantages for the monitoring of atmospheric compounds in an ASC such as CHARME.

The main advantage deals with the selectivity of the technique at low pressure. Indeed, THz rotational linewidths have two main contributions: the temperature-dependent Doppler broadening and the pressure and temperature-dependent col-lisional broadening. The first contribution is the residual source of broadening at low pressure (below 1 mbar), the associated linewidth never exceeds a few MHz at THz frequencies giving rotational spectroscopy a much better selectivity than that obtained in IR gas phase rovibrational spectroscopy, especially for the light stable and reactive polar atmospheric compounds (De Lucia, 2010). Moreover we have demonstrated the ability of gas phase THz rotational spectroscopy to perform absolute quantification without any calibration step of targeted gaseous pollutants in complex chemical mixtures including both gases and particles [START_REF] Bigourd | Detection and quantification of multiple molecular species in mainstream cigarette smoke by continuous-wave terahertz spectroscopy[END_REF](Bigourd et al., , 2007;;Mouret et al., 2013). Several measurements performed in realistic gas phase media contaminated with particles demonstrate that THz spectroscopy with submillimeter and mm-wavelengths is less sensitive to scattering than shorter wavelength IR and UV spectroscopy. Finally, due to the capabilities of the RF synthesizer driving the AMC THz source, the acquisition times (typically hundreds of ms) are short and a time-resolved quantification providing kinetic parameters is also possible and simplified by using the THz electronic sources [START_REF] Omar | Continuous Monitoring of Formaldehyde Photolysis Products by THz Spectroscopy[END_REF].

Despite these different advantages, some difficulties have to be underlined concerning THz monitoring of trace gases in ASC: (i) first, the output power level of the THz sources are significantly smaller than those of optical IR sources: as shown in Fig. 3, the THz measurements are performed at the µW level, at least two orders of magnitude lower than the power available in the near-IR measurements that inevitably affects the sensitivity of the detection scheme; (ii) the price to pay for maintaining an excellent selectivity is to carry out measurements at low pressures representative of the pressure levels of the upper atmosphere and a selective detection of rotational lines at tropospheric pressures is difficult to imaghttps://doi.org/10.5194/amt-15-1201-2022 Atmos. Meas. Tech., 15, 1201-1215, 2022

Analysis of isotopic composition

The THz rotational spectroscopy is a powerful technique for detection at low pressure due to its great selectivity allowing discrimination between: (i) polar compounds in complex chemical mixture [START_REF] Bigourd | Detection and quantification of multiple molecular species in mainstream cigarette smoke by continuous-wave terahertz spectroscopy[END_REF](Bigourd et al., , 2007 ). For the four isotopomers, the differences between the observed and the JPL frequencies never exceed 500 kHz. In Fig. 6a, for each path length the absorption of the R(23) rotational transition of the most abundant 14 N 14 N 16 O isotopomer is saturated. Nevertheless, the equivalent transition for the 14 N 15 N 16 O expected to be only 43 MHz (1.4 × 10 -3 cm -1 ) lower in frequency with an intensity around 260 times weaker is clearly observed and re-solved. The other monosubstituted isotopomers 15 N 14 N 16 O and 14 N 14 N 18 O are also observed with the shortest path length L = 120 m at a pressure close to 1 mbar (Fig. 6b). An isotopic ratio [ 15 N 14 N 16 O] / [ 14 N 14 N 18 O] of 1.87 is deduced from the intensities of the two absorption lines plotted in Fig. 6b. This value is sufficiently close to the expected value of 1.83 deduced from the natural abundances in Table 1 to suggest the possibility to use THz spectroscopy with MUL-TICHARME for the analysis of the isotopic composition of atmospheric trace gases and to detect anomalous isotopic signatures, a powerful approach to identify sources and sinks of pollutants and/or greenhouse gases [START_REF] Röckmann | The origin of the anomalous or "mass-independent" oxygen isotope fractionation in tropospheric N 2 O[END_REF]. Finally the discrimination of the N 2 O isotopomer rotational lines (especially the lines of 14 N 15 N 16 O and 14 N 14 N 16 O on Fig. 6a) highlights the exceptional selectivity of the THz rotational spectroscopy. Indeed, when the measurements are performed at low pressure (typically stratospheric pressures) the line widths converge to the Doppler limit. For molecules such as N 2 O, the Doppler line widths, proportional to the line frequencies, typically vary from hundreds of kHz in the THz domain to hundreds of MHz in the IR and to several GHz in the UV visible domains. There is no doubt that THz high-resolution monitoring exhibits a significantly better selectivity compared to the IR/UV. In complex chemical mixtures studied in ASC, the THz method allows individual molecular signatures to be observed and resolved even for compounds with close molecular structures (isomers, conformers, isotopomers etc.). Moreover, the highresolution THz method strongly limits the problem of interference substances in the gas monitoring. With photon detection in the IR/UV spectral domain, it is generally not possible to resolve individual rovibrational or rovibronic transitions with the typical instrumental resolutions (e.g resolutions of FTIR spectrometers coupled to ASC are limited to few GHz) and some corrections due to interferences with other species

Isotopomer

Natural abundance Line intensity Line frequency obs-calc (%) (cm -1 (molec.cm -2 ) -1 ) (MHz) (MHz)

Absolute quantification of stable and reactive atmospheric traces

A priori all the polar compounds may be detected and quantified from their rotational signatures. In practice, for THz atmospheric monitoring at trace levels, we must opt for the lighter and the more strongly polar compounds with intense and resolved rotational transitions generally listed in the international databases. For these molecules, rotational line frequencies, line widths and line intensities are known with a good degree of accuracy allowing, if the line profile is pre-served during the measurement, an absolute quantification without any standard of calibration.

In the present article, we demonstrate this statement in Fig. 7a by fitting the absorbance of the R( 22) rotational line of N 2 O diluted in N 2 at 1000 ppmv with a Voigt profile . Prior to the fit, two baseline treatments have be done in order to reduce the oscillations due to standing waves occurring in MULTICHARME: first of all, due to the capacities of the RF synthesizer, we have applied simultaneously to the amplitude modulation (AM) a rapid frequency modulation (FM) with a depth exceeding the FSR of the interaction length allowing a partial minimization of the effects of the standing waves. Next, during the posttreatment of the recorded signal leading to the absorbances shown in Fig. 7, an FFT filter was used https://doi.org/10.5194/amt-15-1201-2022 Atmos. Meas. Tech., 15,[1201][1202][1203][1204][1205][1206][1207][1208][1209][1210][1211][1212][1213][1214][1215]2022 to further reduce the rapid oscillations of the baseline. This treatment is described in Fig. S5. We have been careful that the postprocessing does not affect the line shape and hence the error of the resulting number density. The number density of absorbing N 2 O molecules in molec. cm -3 is directly deduced from the relation: N = A(ν)dν S×L with the numerator A(ν)dν corresponding to the integral, in cm -1 units, of the fitted absorbance by a Voigt profile and for the denominator the product of the line intensity S in cm molecule -1 tabulated in HITRAN [START_REF] Gordon | The HITRAN2020 molecular spectroscopic database[END_REF] with the path length L in cm. Finally the mixing ratio χ is deduced by: χ = N P k B T with P and T , the pressure and the temperature in CHARME during the measurement.

In Fig. 7a, an integrated absorbance of 2.4 ± 0.3 MHz was fitted giving a N 2 O number density of N = (1.4 ± 0.2) × 10 13 molec. cm -3 and a mixing ratio 1140 ± 160 ppmv. Taking into account the uncertainty of the fit, mainly due to the remaining baseline oscillations, the density number estimated by the absolute quantification procedure is in agreement with the value of the standard gas used. Based on the previous method, another example is given in Fig. 7b with the quantification of unknown quantity of ozone in CHARME. Ozone is a key compound in atmospheric chemistry, both in the troposphere and stratosphere (Finlayson-Pitts and Pitts Jr., 1999) and a real time in situ monitoring of reactive ozone is very interesting for numerous ozonolysis reactions occurring in our atmosphere especially with VOCs. In our study, ozone was produced at atmospheric pressure by a generator (Air Tree Ozone Technology C-L010-DTI), which converts O 2 into O 3 from zero air exposed to a high voltage corona discharge. Based on the calibration of the ozone generator, performed with a photometric O 3 analyzer, and the injection time (90 min), the ozone volume ratio introduced in CHARME was estimated to be around 500 ppmv. Then the ASC was pumped down (in 45 min) to 1.5 mbar and the THz spectrometer was used to detect and quantify O 3 traces from individual rotational transitions. The O 3 wall losses occurring during the ozone introduction as well as during the pumping procedure contribute to reduce the ozone mixing ratio to an unknown lower value which is measured by THz spectroscopy. Ozone is an asymmetric top with a large number of rotational transitions in the THz domain and its rotational frequencies and intensities have been determined with accuracy in the THz domain [START_REF] Colmont | Microwave Fourier transform, millimeterwave, and submillimeterwave spectra of ozone in its vibrational ground state[END_REF][START_REF] Birk | Experimental Linestrengths of Far-Infrared Pure Rotational Transitions of Ozone[END_REF]. The 25 1,25 ← 24 0,24 transition centered around 610 GHz with a tabulated intensity of S = 4.035 × 10 -22 cm molecule -1 , the most intense on the source's band emission, was chosen for this reason. A mixing ratio of 258 ± 22 ppmv was deduced from the fit of a Voigt profile to the line presented in Fig. 7b. This value is around two times lower than the initial concentration injected in the ASC at atmospheric pressure. This difference is due to the losses on the chamber walls during the ozone injection and the pumping times from atmospheric pressure to 1.5 mbar (135 min). In Sect. 3.2.3, we show how to characterize at low pressure the kinetics of the O 3 losses on the CHARME walls by THz monitoring.

In order to determine the limit of detection (LOD), we have considered the baseline oscillations as our detection noise and the LOD as the concentration obtained with a signal to noise (S/N ) ratio equal to 1. Both for N 2 O and O 3 , the S/N of Fig. 7 are estimated to 15 by taking the maximum amplitude of the rotational line as signal and the maximum of the amplitude of the residual away from the line as noise. Therefore, an LOD of around 75 and 15 ppmv may be estimated respectively for N 2 O and O 3 . These LOD are slightly lower than the mixing ratio errors obtained with the uncertainties on the fitted area. For N 2 O, the LOD obtained by THz spectroscopy in this study are more than three orders of magnitude larger than the LOD on the strongest mid-IR rovibrational bands by tunable diode laser spectroscopy (TD-LAS) even with measurements at low pressure [START_REF] Hoor | Intercomparison of airborne N 2 O measurements using tunable diode laser absorption spectroscopy and in situ gas chromatography[END_REF]. With the THz method, for instance the LOD is limited to 15 ppmv. Using incoherent broad band cavity-enhanced absorption spectroscopy in the visible domain, an LOD of 120 ppbv was obtained in the Dunkirk ASC at atmospheric pressure [START_REF] Wu | Simultaneous monitoring of temporal profiles of NO 3 , NO 2 and O 3 by incoherent broadband cavity enhanced absorption spectroscopy for atmospheric applications[END_REF]. In order to improve the sensitivity of the THz method, we have to correctly model the baseline and to remove its variations due to multiple interfering stationary waves in MULTICHARME. Work is under progress to this goal.

THz monitoring of the ozone decay in CHARME

In Fig. 8, we demonstrate the ability of the THz source coupled to MULTICHARME to monitor the ozone reactivity at low pressure in CHARME. To achieve the same O 3 25 1,25 ← 24 0,24 rotational transition centered at 610 365. 35 MHz was targeted and measured during 12 h, over a frequency range of 60 MHz, every 3 min. Then 240 absorbance spectra were obtained and their time evolution as a 3D plot is shown in Fig. 8a. For each spectrum, we have repeated the baseline treatment and the line profile fit described in Fig. 7b. Then the data treatment to obtain the 240 absorbances of Fig. 8a and the 240 mixing ratios of Fig. 8b has been batch processed with the Origin Software. As shown in Fig. 8b, the ozone concentration decreases exponentially from 230 to 15 ppmv in 12 h. We have considered the first-order kinetics of the ozone decay due mainly to the ozone losses on the chamber walls. The concentration decrease was fitted using the exponential law [O 3 ] t = [O 3 ] 0 e -t/τ O 3 . A lifetime τ O 3 of 3.4 ± 0.1 h was deduced from a fit weighted on the instrumental errors corresponding here to LODs estimated with the same method as explained in the previous subsection with the Fig. 7b. In the present case, we can see that for ozone concentrations lower than 50 ppmv, the lower error bars point to zero or negative values indicating that the LOD is reached at this level of concentration. The losses of ozone in CHARME have already been investigated at atmospheric pressure with a UV-photometric analyzer (Thermo Scientific 49i; λ = 254 nm). Using several initial concentrations, from 0.7 to 4.8 ppmv, the O 3 lifetimes τ O 3 were deduced from the first-order kinetics O 3 wall loss reactions and varied from 6.2 to 13.8 h (Fayad, 2019), depending on the cleanliness of the chamber walls, which can change for different initial concentrations of ozone. Compared to the previous measurements performed in CHARME with a UV photometry analyzer, a shorter lifetime was determined by our low pressure THz measurements. Itoh et al. (2004[START_REF] Itoh | Surface Loss Rate of Ozone in a Cylindrical Tube[END_REF] have developed and experimentally verified a physical model enabling understanding of the pressure and the wall material dependencies of the ozone-to-wall loss rate in a cylindrical tube (Itoh et al., 2004[START_REF] Itoh | Surface Loss Rate of Ozone in a Cylindrical Tube[END_REF]. They showed that the variation of the ozone lifetime with the pressure due to wall losses can https://doi.org/10.5194/amt-15-1201-2022 Atmos. Meas. Tech., 15, 1201-1215, 2022 be reproduced by the Eq. ( 1):

1 τ O 3 ∼ D e P f (α, l, β) + kNP , (1)
where P is the pressure, N is the molecular density, f (α, l, β) is a function depending on geometrical and surface properties of the chamber (a and l are the radius and the length of the cylinder, respectively and β is a surface parameter), D e is an equivalent diffusion coefficient giving the magnitude of the surface loss rate of ozone according to the material and k is a loss rate coefficient due to collisions with oxygen [START_REF] Itoh | Surface Loss Rate of Ozone in a Cylindrical Tube[END_REF]. The pressure measurement conditions in THz rotational high-resolution spectroscopy are typical for chamber cleaning activities. Under these conditions it is known that the O 3 loss in the chamber is dominated by wall reactions and not by reactions with O 2 . It corresponds to the first term of Eq. ( 1) and, therefore, as it is shown by our results, a decrease of the lifetime at low pressure was expected due to the reinforcement of the losses by the ozone diffusion on the chamber wall. That is why these conditions are chosen to get rid of impurities, such as VOCs, on the chamber wall.

Conclusions

We have developed for the Dunkirk ASC CHARME a Chernin-type multi-pass cell allowing performance of spectroscopic measurements over approximately three decades of frequencies from the submillimeter-wave spectral domain to the near-IR. In this study, the performances of MULTI-CHARME have been characterized in the near-IR region using a diode laser source oscillating around 1.4 µm and in the THz region around 600 GHz with a compact and versatile AMC. Benefiting from a base dimension of 5 m, MULTI-CHARME enables very long optical paths to be reached for absorption spectroscopy from 120 to 280 m in the THz domain and to 480 m. in the IR. The output powers have been measured for the different path lengths and an effective mirror reflectivity better than 94 % has been measured both in the THz and in the near-IR. By targeting rovibrational and rotational transitions of the N 2 O greenhouse gas, the linearity of the integrated absorbances has been checked and experimental values of the maximum absorption coefficient were deduced and compared to the expected values deduced from the tabulated spectroscopic parameters. The THz monitoring of atmospheric compounds presents some specificities in comparison with other spectroscopic techniques: as an example, the measurements of the rotational lines of the most abundant isotopomers of N This work demonstrates that THz monitoring is able to quantify gaseous compounds in an ASC such as CHARME and will allow the determination of kinetic rate coefficients as well as reactional pathways for targeted atmospheric processes. In the future, we plan to couple a Fourier transform interferometer to MULTICHARME allowing study of the tropospheric reactivity of VOCs at medium resolution (0.5 cm -1 ) using vibrational spectroscopy on a broadband spectral range from the far to the near-IR domains (20-8000 cm -1 ). Moreover, THz high-resolution rotational spectroscopy will be used in CHARME for the study of the stratospheric processes at low pressures (few mbars) and low temperatures (T < -20 • C obtained by cryocooling). In particular the chemistry of stable and unstable halogenated species involved in the catalytic destruction of stratospheric ozone are good candidates for these future experiments as the rotational transitions of the stable HX, CH 3 X and unstable OX (X = F, Cl, Br, I) compounds lie in the THz domain and are sufficiently intense for monitoring at trace levels [START_REF] Pickett | Submillimeter, Millimeter, And Microwave Spectral Line Catalog[END_REF].

Data availability. Data are available upon request to the corresponding author.

Supplement. The supplement related to this article is available online at: https://doi.org/10.5194/amt-15-1201-2022-supplement.

Author contributions. AC was involved with the supervision and conceptualization. JD, ÉF, PK, WZ, BF and AC contributed to the conception of MULTICHARME. The measurements in CHARME were performed by: JD, ÉF, JB, NH, FH and AC. JD, JB, RB, GD and AC contributed to the data curation. AC wrote the paper with some contributions from JD, FH, NH and CC. The figures were plotted by JD, JB, PK, BF and AC. All the authors contributed to the paper discussion and revision. AC, ÉF, GM and CC were involved in the funding acquisition.

Competing interests. The contact author has declared that neither they nor their co-authors have any competing interests.

Disclaimer. Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. CHAPTER 9. THz monitoring in an atmospheric simulation chamber

General conclusion and outlook

The introduction of my PhD thesis presented the combination of THz spectroscopy and quantum chemistry as an effective approach to investigate the gas phase properties of VOCs emitted by biomass burning. The obtained spectroscopic parameters of rotational effective Hamiltonians are an essential step towards the monitoring of these compounds in the atmosphere. Furthermore, this combination of experimental technique and quantum chemistry calculations was introduced as a helpful tool to investigate and understand the complex atmospheric reaction mechanisms these VOCs can undergo.

During my PhD I aimed to implement this objective and to cover the entire bandwidth of application. The full capacity of the THz spectral range was exploited by the pure rotational mm-wave spectroscopy done for catechol, methylfuran and 3-methylcatechol etc. and the rovibrational synchrotron based FT-far-IR spectroscopy of catechol. Its sensitivity on geometrical changes was used to distinguish and identify conformers and vibrationally excited states. Working at room temperature led to populated vibrationally excited states of low energy: the spectra were dense and difficult to analyze, but gave access to the rotational constants of these excited states.

For catechol the inertia defects of all analyzed states were determined with a high degree of accuracy, confirming the vibrational assignment of the mm-wave transitions. The influence of the low-frequency vibrational dynamics on the catechol planarity was shown by comparing the negative inertia defects.Therefore high-resolution rovibrational THz spectroscopy provides a new perspective by investigating the influence of the low-frequency vibrational modes on the overall rotation of systems with intramolecular hydrogen bonds.

Large amplitude motion as an important effect in the context of rotational spectroscopy was studied by the tunneling splitting of ν 35 = 1 catechol and the internal rotation of the methyl group of methylfuran. By applying the global approach of the BELGI -C s code instead of a local one, two advantages are highlighted: (I) the ability to fit both v t = 0 and v t = 1 at the experimental accuracy while XIAM failed to fit correctly v t = 1 of 2-methylfuran and 3methylfuran; (II) the possibility to determine the V 3 and V 6 barrier heights of the internal rotation potential with high accuracy.

With the implementation of the heating system, the scope of application was enlarged to SVOCs. The mm-wave spectra of 3-methylcatechol were recorded and the analysis is currently under progress. After installing a THz spectrometer into an atmospheric simulation chamber CHARME, its ability to monitore atmospheric compounds was demonstrated on the stable greenhouse gase N 2 O and reactive O 3 . This work demonstrates that THz monitoring is able to quantify gaseous compounds and can allow the determination of kinetic rate coefficients as well as reaction pathways for targeted atmospheric processes. I used quantum chemistry not just to support the THz spectroscopy by predicting conformers and their spectroscopic relevant parameters. By examining the electronic density, intramolecular hydrogen bonds were studied where analytical approaches face serious difficulties. Its potential to investigate molecules of short lifetimes was used to estimate the first reaction step of 2-methylfuran with the NO 3 radical leading to unstable and experimentally hardly observable intermediates.

It can be concluded that the combination of THz spectroscopy and quantum chemistry is very valuable to investigate VOCs and provide chemo-physical parameters helpful for other techniques and applications. It can be used to study fundamental effects such as intramolecular hydrogen bonds or Large amplitude motions. To present an independent approach for atmospheric science however the constraint of low pressure needs to be overcome.

In continuation to this PhD, several projects are already currently under progress or planned. For catechol, an extensive theoretical investigation of the hot bands observed in the FT-far-IR spectrum is planned and the two isomers resorcinol (benzene-1,3-diol) and hydroquinone (benzene-1,4-diol) are now ready to be measured due to the heating system. A publication about the theoretical intramolecular hydrogen bond study is under progress including non-covalent interaction and natural bond orbital investigations. .9 -The two intense far-IR rovibrational bands of 3-methylfuran recorded at the synchrotron SOLEIL. In the upper panel in black is the c-type v 27 methyl out-of-plane bending mode. It was recorded at room temperature with a pressure of 140 µbar at 0.001 cm -1 resolution. In the lower panel in blue the c-type v 29 symmetric out-of-plane ring bending mode, recorded under the same conditions but with a pressure of 40 µbar.

The calculations of the reaction of 2-methylfuran with NO 3 will be part of a joint publication with the experimentalists and a complete theoretical study inspired by [105] is under progress. Concerning the spectroscopy of furan related compounds, several things were already done, are currently ongoing or are planned. Some rovibrational IR-spectra of 2-methylfuran, 3-methylfuran and furfural were recorded, resolving the methyl internal rotation. Two weeks in november 2022 at the AILES beamline of the synchrotron SOLEIL were allocated for the measurements of these molecules in the far-IR. The two sulfur and nitrogen analogs MT and MP will be examined as MF was in [23].

To benefit from the new possibility to heat the setup, different candidates are ready to be measured: resorcinol, hydroquinone and 4-methylcatechol. Additionally the analysis of the 3-methylcatechol spectrum, based on the initial constants provided by Xiujuan Wang and Dr. Qian Gou, is currently under progress. To improve MULTICHARME, we put a lot of efforts in the simulation of the baseline. The problem is assumed to be originated in the overlapping beam spots on the mirrors and we are now seeking for a solution. Furthermore we think about coupling a THz cavity ring-down spectrometer as the one described in [35] to CHARME and to measure at low temperature obtained by cryocooling. In the context of this work, measurements of the ozonolysis of catechol and the oxidation of methylfuran with NO 3 would put the finishing touch to it. Pour valider l'étude théorique de la liaison hydrogène intramoléculaire du catéchol, une étude théorique plus approfondie de plusieurs autres molécules apparentées a été exécutée. Sept molécules avec de nombreux conformères différents présentant une liaison hydrogène intramoléculaire ont été étudiées théoriquement avec des techniques et des outils de chimie quantique mettant en évidence le potentiel, les limites et les difficultés de ces approches traitant des liaisons hydrogène intramoléculaires particulièrement faibles. L'influence de la taille de l'anneau formé par la liaison hydrogène intramoléculaire sur la force de la liaison hydrogène intramoléculaire a été étudiée et la capacité de représenter la force de la liaison hydrogène intramoléculaire avec des paramètres géométriques tels que les longueurs et les angles de liaison impliqués ainsi que les paramètres liés à la topologie de la densité électronique ont été testés. Une publication comprenant des techniques supplémentaires de chimie quantique est actuellement en cours d'écriture [22].

La deuxième partie de cette thèse a été consacrée à l'étude des composés furanes méthylés. Ces COVs hétérocycliques ont également été identifiés comme des précurseurs gazeux d'AOS notamment pendant la nuit avec le radical NO 3 . Deux voies de réaction différentes, l'addition de NO 3 sur le cycle furanique et l'abstraction d'un atome d'hydrogène du groupe méthyle ont été étudiées. Pour les deux canaux, une voie réactive a été identifiée. Ces résultats sont en bon accord avec les résultats expérimentaux de nos collègues qui ont simulé ces réactions dans la chambre de simulation atmosphérique CHARME du LPCA à Dunkerque. Par conséquent, un article commun, en cours de soumission, combinera les deux approches dans [2].

De plus, les spectres d'ondes millimétriques à température ambiante du 3-méthylfurane ont été enregistrés. Les raies rotationnelles observées sont dédoublées en composantes A et E en raison de la rotation interne du groupe méthyle. Un traitement spécifique de ce mouvement de grande amplitude est donc nécessaire. L'état fondamental a été analysé avec l'approche locale couramment utilisée du code XIAM. En raison de difficultés liées à la rotation interne du groupe méthyle induisant des motifs non triviaux dans les spectres de rotation, le code XIAM n'était pas suffisant pour traiter le premier état excité par vibration. Par conséquent, l'état fondamental et le premier état excité de torsion ont été analysés avec l'approche globale du code BELGI-Cs. De plus, les transitions rotationnelles mesurées dans les domaines centimétriques et millimétriques du 2-méthylfurane ont été réanalysées avec le code BELGI-Cs. L'approche globale reproduit les raies rotationnelles observées du 2-méthylfurane et du 3-méthylfurane dans la région des ondes millimétriques à la précision expéri- La dernière partie de cette thèse est consacrée aux récents développements techniques auxquels j'ai pris part et qui vont ouvrir de nouvelles perspectives. Tout d'abord, un système de chauffage a été mis en place sur le spectromètre à chaîne de multiplication de fréquences THz. En augmentant la température, la pression de vapeur de composés semi-volatils est augmentée, et le signal moléculaire peut être optimisé. Des tests à différentes températures ont été réalisés et ont montré l'existence d'une température optimale caractérisée par une quantité suffisante de molécules absorbantes et une fonction de partition rotationnelle limitée. L'illustration a été faite pour le 3-méthylcatéchol, une molécule où aucun signal n'avait été obtenu à température ambiante. Le meilleur compromis en matière de signal/bruit a été obtenu en chauffant à 50 • C. Ce nouveau système de chauffage élargit le champ des molécules potentielles aux composés organiques semi-volatils. Pour ce travail, j'ai eu l'occasion d'encadrer avec Anthony Roucou, Manuel Rocca, un stagiaire du M2 international « Atmospheric Environment » adossé au LaBEX « Chemical And Physical Properties of the Atmosphere » (CAPPA). Mon manuscrit de thèse est structuré en quatre parties. Après avoir rappelé le contexte scientifique et la motivation de ces études, je vous fournirai, dans une première partie, un bref résumé des principes théoriques et des méthodes expérimentales employées. La deuxième partie présente les études spectroscopiques THz rovibrationnelles et rotationnelles du catéchol et l'emploi des calculs de chimie quantiques dans cette analyse. Une liaison hydrogène intramoléculaire particulièrement faible a été identifiée pour le catéchol, ce qui a conduit à une étude théorique approfondie des liaisons hydrogène intramoléculaires de diverses molécules apparentées. La troisième partie contient une étude de chimie quantique de l'étape de réaction initiale du 2-méthylfurane avec le radical de la chimie atmosphérique nocture NO 3 ainsi qu'une analyse rotationnelle des spectres d'ondes millimétriques des deux isomères du méthylfurane. Un traitement spécifique de la rotation interne du groupe méthyle a été réalisée avec des codes dédiés à ces mouvements de grande amplitude La dernière partie du manuscrit ouvre de nouvelles perspectives expérimentales via deux innovations techniques de notre spectroscopie THz : un système de chauffage pour mesurer les composés organiques semi-volatils et l'implémentation de notre spectromètre pour des mesures in situ dans une chambre de simulation atmosphérique.

Operator a All constants refer to a rho-axis system, therefore the inertia tensor is not diagonal and the constants cannot be directly compared to those of a principal axis system. P a , P b , P c are the components of the overall rotation angular momentum, P γ is the angular momentum of the internal rotor rotating around the internal rotor axis by an angle γ.

{u,v} is the anti commutator uv + vu. b The product of the parameter and operator from a given row yields the term actually used in the vibration-rotation-torsion Hamiltonian, except for F, ρ and A, which occur in the Hamiltonian in the form F(P γ -ρP a ) 2 + AP 2 a . N νt=0 /N νt=1 /N tot are the numbers of ν t = 0 transitions, νt = 1 transitions and the total number of transitions. a All constants refer to a rho-axis system, therefore the inertia tensor is not diagonal and the constants cannot be directly compared to those of a principal axis system. P a , P b , P c are the components of the overall rotation angular momentum, P γ is the angular momentum of the internal rotor rotating around the internal rotor axis by an angle γ.

{u,v} is the anti commutator uv + vu. b The product of the parameter and operator from a given row yields the term actually used in the vibration-rotation-torsion Hamiltonian, except for F, ρ and A, which occur in the Hamiltonian in the form F(P γ -ρP a ) 2 + AP 2 a . c Values of the parameters from the present fit. Statistical uncertainties are shown as one standard uncertainty in the last digit. d N νt=0 /N νt=1 /N tot are the numbers of νt = 0 transitions, νt = 1 transitions and the total number of transitions. In the fit 1845 and 1538 distinct frequencies were taken into account for ν t = 0 state and 1 respectively. 30 transitions from Ogata et al. [87] were weighted 100 kHz and fit with an rms of 116 kHz. Present data was weighted 150 kHz and fit with an rms of 178 kHz. σ νt=0 /σ νt=1 /σ tot are the respective standard deviations. Table 3 -Molecular constants of Chapter 7 in the RAM system of 3-methylfuran obtained by a global fit using program BELGI-C s .

Quantum chemical study and THz spectroscopy of biogenic oxygenated volatile organic compounds precursors of secondary organic aerosols in the atmosphere Abstract

The main objective of this PhD thesis was to investigate oxygenated volatile organic compounds (VOCs) identified to be involved in the chemistry of the atmosphere especially in the formation of secondary organic aerosols (SOA). Taking advantage of the molecules being isolated in the gas phase it was possible to investigate intramolecular hydrogen bonds (IHBs) stabilizing some chosen quasi-planar oxygenated aromatic orthodisubstituted organic compounds. The main molecule investigated by room temperature mm-wave pure rotational, synchrotron based FT-Far-IR spectroscopies, and quantum chemical (QC) calculations is catechol. For catechol, two vicinal hydroxyl groups form this IHB and by a concerted rotation about 180 • they can switch their roles as donor and acceptor. Spectroscopical parameters were fitted for the ground and four lowest energy vibrationally excited states. It was possible to directly relate the IHB dynamics to these spectroscopic parameters. Several other related molecules were investigated theoretically with different QC techniques and tools highlighting the potential, limitations and difficulties of these approaches treating especially weak IHBs. Another main objective of the thesis was the study of methylated furan compounds. These heterocyclic VOCs were also identified as gaseous precursors of SOA. To estimate the contribution of especially 2-methylfuran (2MF) QC calculations were carried out showing the potential of 2MF to react with NO 3 which is the major reactant in the atmosphere during the night. Room temperature mm-wave spectroscopy of 3MF and the analysis of the obtained spectra were carried out. Due to the splitting of the rotational lines caused by the internal rotation of the methyl group, this analysis required a specific treatment for this large amplitude motion. As the commonly used local approach of the XIAM code was not sufficient to encode the first vibrationally excited state the global approach of the BELGI code was used not just for 3MF but also applied to the reported assignment of 2MF taken from the literature. As possible next steps in the use of mm-wave spectroscopy in atmospheric science the implementation of a heating system to the used setup and the installation of the spectrometer into an atmospherical simulation chamber (ASC) are described in this thesis. With the heating system the pressure of the studied molecule can be increased, enlarging the field of potential molecules to semi-volatile VOCs. First spectra were obtained for methylcatechol with an optimized temperature of 70

  and processes that can result from the combustion of biomass. . . . . . . . . . . . . . . . . . . . . . . . . . 2 Cooling and warming radiative forces of the main influences since 1750. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 General procedure of THz spectroscopic studies combined with quantum chemical calculations. . . . . . . . . . . . . . . . . . . 1.1 Energy level diagram for an asymmetric top with assignment J K a K c . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Schematic model of an energy diagram for two vibrations. . . . 1.3 Parabolic potential energy curve for harmonic oscillator and Morse potential taking into account anharmonicity. . . . . . . . . . . . 1.4 Potential energy curve V for large amplitude motions as a function of torsional angle α. . . . . . . . . . . . . . . . . . . . . . . . . . 1.5 Simulated rotational spectra at 300 K and 500 K. . . . . . . . . 1.6 Gauss, Lorentzian and Voigt line profiles. . . . . . . . . . . . . 2.1 Typical motions in a molecule. . . . . . . . . . . . . . . . . . . . 3.1 VDI multiplication chain . . . . . . . . . . . . . . . . . . . . . . 3.2 Schematic illustration of the solid state mm-wave spectrometer of the LPCA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Fast-Fourier-Transform band-pass filter treatment of measured spectra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Interferometer used at the AILES beamline of the synchrotron SOLEIL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Prediction of transitions and energies by SPCAT and Fitting of assigned lines by SPFIT. . . . . . . . . . . . . . . . . . . . . . . . 4.1 Potential energy surface of the two -OH torsions. . . . . . . . . 4.2 Topological analysis with basis set dependency of the IHB signature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

[ 4 ]

 4 Ibon Alkorta et al. "Are resonance-assisted hydrogen bonds 'resonance assisted'? A theoretical NMR study". In: Chemical Physics Letters 411.4 (2005), pp. 411-415. doi: 10.1016/j.cplett.2005.06.061.

Figure 3 -

 3 Figure 3 -The general procedure of the room temperature THz spectroscopic studies of this work combined with quantum chemical calculations. During several steps, different spectroscopic techniques and quantum chemical calculations are required. The color code defines in green: literature/bibliography research; in red: quantum chemical (QC) calculations; in blue: experimental measurements; in yellow: data analysis; in purple: valorization of results.

1 22 1. 2 . 2 25 1. 3

 12222253 Fundamental bands . . . . . . . . . . . . . . . . . . Hot bands . . . . . . . . . . . . . . . . . . . . . . . . Large Amplitude Motions/Internal rotation 26 1.3.1 Hamiltonians to describe LAM . . . . . . . . . . . . 26 1.3.2 Intensities . . . . . . . . . . . . . . . . . . . . . . . . 31

Figure 1 . 2 -

 12 Figure 1.2 -Schematic model of an energy diagram for two vibrations. (I) fundamental transitions, (II) overtone, (III) combination band, (IV) hot band, (V) hot band.

  Figure 1.3 -a) Parabolic potential energy curve derived from the harmonic oscillator model (red) and Morse potential taking into account the anharmonicity (blue). b) Rovibrational energy levels. Due to the anharmonicity of the potential, the vibrational levels are not equally spaced as in an harmonic oscillator. Two consecutive levels get generally smaller as they are getting closer to the dissociation energy. The arrows are examples for a rotational (red), vibrational (green) and rovibrational (blue) transitions.

Figure 1 . 4 -

 14 Figure 1.4 -Potential energy V scheme for large amplitude motions as a function of the torsional angle α. a) 3-folded potential of the internal rotation of a methyl group leading to the splitting of the rotational levels into A (σ = 0) and E (σ = 1) species. b) Splitting rotational lines into a (+) and (-) species caused by a 2-folded potential of the inversion tunneling in catechol.

1. 3 .

 3 Large Amplitude Motions/Internal rotation 31 ∆E t change to: • sign does not change (µ g ↔ µ g ): (+) ↔ (+) and (-) ↔ (-) -→ ∆ν = ∆E • sign changes (µ g ↔ -µ g ): (+) ↔ (-) and (-) ↔ (+) -→ ∆ν = 2∆E with g = a, b, c.

Figure 1 . 5 -

 15 Figure 1.5 -Simulated rotational spectra using the ASCP software [62, 64] of catechol GS and four lowest vibrationally ESs. a) At room temperature 300 K and b) 500 K. The additional 200 K of b) are leading to a shift of the intensity maxima from ∼ 350 GHz to ∼ 450 GHz. The frequency of each transition remains the same, only the relative intensities are influenced.

5 Figure 1 . 6 -

 516 Figure 1.6 -Typical line profiles produced with the implemented line profiles of Origin 2019b. In black is the Gauss, in red the Lorentzian and in blue the Voigt profiles for the given parameters.

Figure 3 . 1 -

 31 Figure 3.1 -Schame of the Virginia Diodes Inc. (VDI) multiplication chain. Depending on the used type (doubler or tripler) and the number of used multiplier, different spectral ranges are covered.

Figure 3 . 2 -

 32 Figure3.2 -The schematic illustration of the solid state mm-wave spectrometer of the LPCA. The setup contains of a computer to drive the experiment, a frequency generator connected to a multiplication chain, off-axis parabolic mirrors to collimate or focus the beam, a polarization wire-grid to double the interaction path-length, the absorption cell and the Zero Bias Detector connected trough a lock-in amplifier to the computer to record the second harmonic of the frequency modulated signal. During this PhD the experiment was equipped with a heating coat to increase the partial pressure of semi-volatile molecules (seeChapter 8).

Figure 3

 3 Figure 3.3 -a) The 100-101 GHz range of the raw spectrum of 3-methylfuran (see Chapter 7). b) Fast-Fourier-Transform (FFT) of the raw-spectrum. The first red part containing the baseline variations and the second one containing noise are excluded by using a band-pass filter. c) The obtained spectrum without baseline variations and less noise.

Figure 3 . 4 -

 34 Figure 3.4 -Taken from the synchrotron SOLEIL hompage (https://www.synchrotron-soleil.fr/en/beamlines/ailes 22.09.2022 10.53pm): Schematic view of the long pass White cell with the interferometer. The modulated beam represented in red is undergoing multiple reflections before being redirected toward the detector.

Figure 3 .

 3 Figure 3.5 -a) Prediction of transitions and energies of rotational levels by SP-CAT derived from an initial set of Hamiltonian parameters and a file containing the dipole moments and the temperature. b) Fitting of assigned lines with an initial set of Hamiltonian parameters by SPFIT providing a new set of updated parameters and a result file.

Figure 1 .

 1 Figure 1. (a) 2D scan of the -OH torsional angles of catechol calculated with the B3LYP functional and the aug-cc-pVTZ basis set. The left and upper borders must be respectively identified with the right and lower borders. Contour curves are drawn every 200 cm -1 . The points A to G correspond to stationary points of the two-dimensional surface, sorted by increasing energy, see Table 2. Symmetry equivalent points share the same letter and are distinguished by a subscript. Squares, triangles, and diamonds, respectively, indicate the minima, saddle points, and maxima. (b) Labelling of the nuclei of catechol and definition of the two torsional angles as the dihedral angles D 8 (green sequence of nuclei) and D 10 (blue sequence). This structure corresponds to the saddle point D (central point in the right figure) with D 8 = D(H(11)-O(5)-C(1)-C(3)) = 0 • and D 10 = D(H(13)-O(7)-C(3)-C(1)) = 0 • . (c) Conformation A 1 corresponding to one of the two global minima. The permanent dipole moment in the (a, b) principal inertia plane is indicated by the red arrow.

Figure 2 .

 2 Figure 2. Topological analysis of the electron density of the global minimum A of catechol analysed by the Multifunctional Wavefunction Analyzer (Multiwfn) [22]. Purple, orange, and yellow dots are, respectively, the local maxima localized on the atoms, bond critical points, and ring critical points of the electron density. The B3LYP functional and different basis sets were used: (a) the intramolecular HB is visible with a cc-pVDZ basis set; (b) with diffuse functions and/or a larger basis set (aug-cc-pVDZ/cc-pVTZ/aug-cc-pVTZ), no intramolecular HB is visible.

- 1 :

 1 the antisymmetric ν 36 and symmetric ν 34 out-of-plane O-C-C-O twisting and wagging modes; the antisymmetric ν 24 and symmetric ν 25 in-plane O-C-C-O rocking and scissoring modes; the free ν 35 and the bonded ν 33 -OH torsion; and four low-frequency ring deformations, ν 32 , ν 31 , ν 23 , and ν 22 .

Figure 3 .

 3 Figure 3. The FT-far-IR spectrum of catechol in the 100-600 cm -1 range measured at high-resolution (10 -3 cm -1 ) at the AILES beamline of the SOLEIL synchrotron (630 scans co-added, P 10 µbar and T = 300 K). ν 35 and ν 33 label the bands associated with the free and bonded -OH torsional modes involved in the intramolecular HB. Artefacts due to bad compensations with the background spectrum are marked with an asterisk.

Figure 5 .

 5 Figure 5. Left: rovibrational band of the ν 35 free -OH torsional mode. Right: rovibrational band of the ν 33 bonded -OH torsional mode. Experimental synchrotron-based FT-far-IR spectra are shown in black. Simulated spectra with the fitted constants of Table4are presented in red. Two zoomed parts highlight the quality of the rovibrational fit in the P-branches of the two fundamental torsions.

Figure 6 .

 6 Figure 6. (a) Experimental (black) and calculated (red) rotational spectrum of catechol in the 160-210 GHz frequency range. (b) Zoom on a 500 MHz range highlighting the GS and the different low-frequency vibrationally ES contributions to the calculated spectrum.

  (i) Instead of a single oop C-O bending in phenol, we observed, in catechol, one blueshifted vibration (the O-C-C-O wagging) and one red-shifted vibration (the O-C-C-O twisting)

Figure 7 .

 7 Figure 7. Tunnelling splittings observed in the pure rotational mm-wave spectrum within the |v 35 = 1 ES. Each doublet associated with J K a ,K c ← J K a ,K c rotational transitions represented by their blue and red components.

  D 8 = D(H(11)-O(5)-C(1)-C(3)) and D 10 = D(H(13)-O(7)-C(3)-C(1)) of Figure

Chapter 5 4

 54 Intramolecular hydrogen bond formation in five, six, and seven membered rings Influence of ring size 5.4.1 Five-membered rings . . . . . . . . . . . . . . . . . . 5.4.2 Six-membered rings: SLG and SAL . . . . . . . . . . 5.4.3 BDM . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 5 . 1 -

 51 Figure 5.1 -The studied molecules: catechol (CAT), saligenin (SLG), 3methylcatechol (3-mCAT), 4-methylcatechol (4-mCAT), guaiacol (GUA), salicylic acid (SAL), and benzenedimethanol (BDM). The number of studied rotamers is given in parenthesis for each molecule.

LFigure 5 . 2 -

 52 Figure 5.2 -Definition of the three distances L CP , L HB , L d , and the two angles α X-H•••O and α C-O•••H related to the IHB (dashed line).

Figure 5 . 3 -

 53 Figure 5.3 -QTAIM analysis of CAT using the optimized geometries with B3LYP and different basis sets: a) cc-pVDZ. b) aug-cc-pVDZ. c) cc-pVTZ. d) aug-cc-pVTZ. Introducing empirical dispersion leads to the same behavior.

Table 5 . 2 - 100 CHAPTER 5 . 101 5. 4

 5210051014 QTAIM: difference ∆ρ = ρ (BCP)ρ (RCP) between the electronic density at the Bond Critical Point (BCP, signature (3,-1)) and at the Ring Critical Point (RCP, signature (3,+1)) involved in an intramolecular hydrogen bond, distance L CP between the BCP and RCP, distance L HB between the two atoms on each side of the intramolecular bond, bond length of the chemical bond L OH , angle α X-H•••O and angle α C-O•••H . Theoretical study of intramolecular H-bonds 5.4. Influence of ring size Influence of the ring size to the IHB strength

Figure 5 . 4 -

 54 Figure 5.4 -Upper figure: distance L CP (black) and bond length L HB (red) as a function of ∆ρ for five-membered rings (squares), six-membered rings (circles), and seven-membered rings with OH donor (up triangles), and six-membered rings with C -H donor (down triangles). Lower figure: angle α X-H•••O (black) and α C-O•••H (red) as a function of ∆ρ. Same symbol code.

5. 4 . 1 Figure 5 . 5 - 5 . 4 .

 415554 Figure 5.5 -The rotamers of SLG1-3 and SAL1-3.

Figure 5 . 6 -

 56 Figure 5.6 -The first ten lowest energy rotamers of BDM exhibiting an IHB. For BDM3 and 8 two coexisting IHBs were found. The QTAIM analysis of BDM9 indicates an IHB with cc-pVTZ but the IHB bond path is rather peculiar.

Figure 5 . 7 -

 57 Figure 5.7 -The QTAIM IHB signature of BDM9. The starting point of the IHB bond path is rather peculiar.

Figure 6 . 1 -

 61 Figure 6.1 -The Mulliken charges of 2MF computed with (a) B3LYP, (b) MP2 and (c) M06-2X. For all three calculations the aug-cc-pVTZ basis set was used.

Figure 6 . 2 -

 62 Figure 6.2 -The potential first reaction steps of 2MF with NO 3 . On the left side is the NO 3 addition channel and on the right side the hydrogen abstraction channel shown. The B3LYP relative energies indicate two exothermic reactions for the NO 3 addition leading to IN5 and the H-abstraction from the methyl group giving P6. IN2 is in comparison to the others only slightly endothermic and should be considered therefore as well.

Figure 6 . 3 -

 63 Figure 6.3 -The energy diagram of the first reaction step between 2MF and NO 3 calculated with two functionals: B3LYP (black) and M06-2X (red). (a) The reactants. (b) The NO 3 addition products and transition states. (c) The H abstraction products.

[ 8 ]

 8 Josep M. Anglada, Santiago Olivella, and Albert Solé. "Atmospheric formation of the NO 3 radical from gas-phase reaction of HNO 3 acid with the NH 2 radical: proton-coupled electron-transfer versus hydrogen Chapter 7

Figure 1 .

 1 Figure 1. Optimized geometries of the 2-MF and 3-MF isomers determined at the B3LYP/aug-cc-pVTZ level of theory. The axes are the principal axes of inertia. The blue arrow is the permanent electric dipole moment.

Figure 2 .

 2 Figure 2. (a)Experimental mm-wave spectrum of 2-MF measured in this work (black) in the 86.4-86.9 GHz frequency range. Blue and red sticks correspond respectively to assigned v t = 0 and v t = 1 lines in Ref.[12]. (b) Simulated spectrum with the v t = 0 (blue) and v t = 1 (red) parameters fitted in Ref.[12] using ERHAM (local approach). (c) Simulated spectrum of the present work with the v t = 0 (blue) and v t = 1 (red) using BELGI-C s (global approach) and the fitted parameters from TableS1.

  i

  Fit of the Vibrational Ground State and First Torsional State of 3-MF Concerning 3-MF, a microwave study was performed in 1971 by Ogata et al. [11] in the 8.2-30 GHz range, providing a first estimation of the rotational constants for the vibrational ground state. This study allowed them to determine the permanent dipole moment from Stark measurements (1.03 D) and constants associated to the CH 3 internal rotation like the V 3 barrier height (381 cm -1 ) from the observed A-E splittings of 16 transitions. In our present work the mm-wave spectral analysis of 3-MF allowed us to identify 2463 new transitions in the v t = 0 state and 2017 in the first excited v t = 1 state up to J = 50.

Figure 3 .

 3 Figure 3. (a) Experimental (black) and calculated (red) rotational spectra of 3-MF in the 170-220 GHz frequency range. (b) Zoom on a 1 GHz range highlighting the different species contributing to the calculated spectrum: v t = 0 A (green) and E (blue) species; v t = 1 A (magenta) and E (brown) species.

8. 1

 1 Heatable absorption cell 151 8.2 First mm-wave measurements of a SVOC in the heated cell 152

Figure 8 . 1 -

 81 Figure 8.1 -Scheme of the heatable absorption cell including the sample reservoir of the solid state mm-wave spectrometer of the LPCA. The absorption cell is covered by three thermal coats with the middle part and the two outer parts each controlled by PID. The reservoir is heated by a manually controlled heating wire.

Figure 8 . 2 -

 82 Figure 8.2 -The internal rotation barrier V 3 for the methyl groups of the two lowest energy conformers of 3-mCAT.

Figure 8 .

 8 3 a temperature of 50 • C was chosen to record the spectra in the 70 -110 GHz and 140 -220 GHz

Figure 8 .

 8 Figure 8.3 -3-mCAT spectra recorded at different temperatures to define the optimal temperature. The presented spectra in the 90440 -90790 MHz range were recorded with the same conditions except the temperature.

Figure 8 . 4 -

 84 Figure 8.4 -Upper part: The 3-mCAT spectra of the first two stages of multiplication (70 -110 GHz and 140 -220 GHz) compared to the simulation obtained by XIAM using the experimental parameters of Table 8.1.Lower part: Zoomed spectrum to verify the good agreement between experimental and simulated spectra.

2

  Experimental setup and methodology 2.1 CHARME (CHamber for Atmospheric Reactivity and Metrology of the Environment)

Figure 1 .

 1 Figure 1. Schemes of the two mirror assemblies of MULTI-CHARME: the objective block (a) and the field block (b).

Figure 2 .

 2 Figure 2. (a) 3D plot of MULTICHARME in CHARME performed with the FreeCad software and the Optics Workbench. (b) Near-IR coupling to MULTICHARME via ZnSe windows using an external cavity diode laser (ECDL), a standard photodiode (PD), a He-Ne laser for alignment and a wavelength meter (λ-meter). (c) THz coupling to MULTICHARME via high resistivity float zone-silicon (HRFZ-Si) windows using an amplified multiplication chain (AMC) driven by a RF synthesizer and a zero-biased detector (ZBD) connected to a lock-in amplifier.

Figure 3 .

 3 Figure 3. Attenuation of the IR (a) and the THz (b) output power (linear scale in red, log. scale in blue) vs. the number of the reflections in MULTICHARME. The effective IR and THz reflectivities are deduced from the fit of the measurements with the power law: P = A × R n eff (power law fit in red, linear fit in blue). The fits are performed with an instrumental weighting ω i = 1/σ 2 i with σ i being the error bar sizes taking into account: the IR sensor uncertainty (5 %) and the accuracy of the controller sensor (3 %) for (a); the THz power fluctuations measured on the lock-in amplifier for (b). See Fig. S4 for spot matrix illustrations.

Figure 4 .

 4 Figure 4. (a) Absorbance of the R(17) rovibrational line of N 2 O in the (3, 2, 0, 1) ← (0, 0, 0, 0) vibrational band measured with the ECDL IR source in the 7149.5 cm -1 region for 8 different path lengths in MULTICHARME (χ N 2 = 1000 ppmv and P = 20 mbar). The shoulder observed at low frequency is assigned to the ECDL source which is not perfectly monomodal in this region. (b) Linear fit of path length dependence of the integrated absorbances, instrumentally weighted on the error bars deduced from the Gaussian fits of the absorbances shown in (a).

Figure 5 .

 5 Figure 5. (a) Absorbance of the R(22) rotational line of N 2 O in its ground state measured with the AMC THz source in the 577.58 GHz region for 6 different path lengths in MULTICHARME (χ air = 400 ppmv, P = 4 mbar). (b) Linear fit of the of path length dependence of the integrated absorbances instrumentally weighted on the error bars deduced from the Lorentzian fits of the absorbances shown in (a).

Figure 6 .

 6 Figure 6. THz absorptions of four different N 2 O isotopomers in MULTICHARME measured without baseline treatment. (a) R(23) rotational transition measured at P = 0.36 mbar for the most abundant 14 N 14 N 16 O and the less abundant 14 N 15 N 16 O isotopomers; measurements are performed for four optical path lengths between 120 to 240 m (in each case the 14 N 14 N 16 O absorption is saturated). (b) Measurements at P ∼ 1 mbar and L = 120 m, lower in frequency, of the same rotational transition for the 15 N 14 N 16 O and 14 N 14 N 18 O isotopomers.

Table 1 .

 1 Natural abundances of the four most abundant isotopomers of N 2 O (Gordon et al., 2022). Tabulated line intensity and frequency of the R(23) rotational transition from the JPL (Pickett et al., 1998) and the HITRAN (Gordon et al., 2022) databases, respectively. Differences between tabulated and measured frequencies in Fig. 6.

Figure 7 .

 7 Figure 7. THz trace gas quantification of stable N 2 O and reactive O 3 in MULTICHARME. (a) Red circles: R(22) transition of 1000 ppmv N 2 O diluted in N 2 measured at P = 0.5 mbar (AM: f mod = 4.5 kHz + FM: f mod = 50 kHz, ω depth = 1.44 MHz); red solid line: fit with a Voigt profile ( A(ν)dν = 2.4(3) MHz; ν = 577 578,36 MHz). (b) Blue circles: 25 1,25 ← 24 0,24 transition of an unknown quantity of O 3 diluted in air produced by an ozone generator measured at P = 1.5 mbar (AM: f mod = 4.5 kHz + FM: f mod = 50 kHz, ω depth = 1.08 MHz); blue solid line: fit with a Voigt profile ( A(ν)dν = 2.3(2) MHz; ν = 610 365,35 MHz). The residuals between the Voigt fit and the experimental points are given for both lines.

Figure 8 .

 8 Figure 8. THz monitoring of the ozone decay in CHARME measured for 12 h at P = 1.1 mbar. (a) 3D plot of absorbance spectra measured every 3 min of the O 3 25 1,25 ← 24 0,24 rotational transition as a function of frequency (in MHz) and time (in min). (b) First-order exponential fit of the ozone concentration decay in CHARME deduced by batch processing of the absorbances shown in (a). A lifetime τ O 3 of 3.4 ± 0.1 h is deduced from a weighted fit using the LODs as instrumental errors.

  e n u m b e r / c m -1

Figure 9

 9 Figure9.9 -The two intense far-IR rovibrational bands of 3-methylfuran recorded at the synchrotron SOLEIL. In the upper panel in black is the c-type v 27 methyl out-of-plane bending mode. It was recorded at room temperature with a pressure of 140 µbar at 0.001 cm -1 resolution. In the lower panel in blue the c-type v 29 symmetric out-of-plane ring bending mode, recorded under the same conditions but with a pressure of 40 µbar.

Figure 10 -

 10 Figure10-Résumé graphique de l'article[21] rapportant notre étude du catéchol. Cette étude contient des calculs de chimie quantique, des mesures de spectroscopie rovibrationnelle IRL-TF et des mesures de spectroscopie de rotation pure dans la gamme millimétrique, à température ambiante.

Figure 11 -

 11 Figure 11 -Résumé graphique de l'article "Millimeter-Wave Spectroscopy of Methylfuran Isomers: Local vs. Global Treatments of the Internal Rotation" [23].

Figure 12 -

 12 Figure12-Résumé graphique de l'article présentant MULTICHARME et les premières mesures THz réalisées dans une chambre de simulation atmosphérique[30].Ensuite, j'ai contribué à l'installation du spectromètre THz dans la chambre de simulation atmosphérique CHARME du LPCA. Mon travail consistait à coupler le rayonnement issu de la source submillimétrique dans le système MUL-TICHARME spécialement conçu pour atteindre de longs trajets d'interaction dans les domaines THz et IR. Pour la première fois, un spectromètre à ondes submillimétriques a été couplé dans une chambre de simulation atmosphérique. En utilisant une cellule multi-passage de type Chernin, la sensibilité a été améliorée pour la détection de molécules polaires à l'état de traces. Le potentiel de ce spectromètre pour effectuer une surveillance submillimétrique en ligne et in situ des réactions atmosphériques est démontré en surveillant la dégradation de l'ozone avec le temps. En ajustant le signal moléculaire de l'ozone, sa durée de vie a été déterminée. Ce projet, nommé "MULTICHARME", a été publié dans la revue Atmospheric Mesurement Techniques, sous le titre : MULTICHARME: a modified Chernin-type multi-pass cell designed for IR and THz long-path absorption measurements in the CHARME atmospheric simulation chamber

  σ νt=0 /σ νt=1 /σ tot are the respective standard deviations. c Values of the parameters from the present fit. Statistical uncertainties are shown as one standard uncertainty in the last digit.

Table 1 -

 1 List of abbreviations.

	Abbreviation
	AABS	Assignment and Analysis of Broadband Spectra (program)
	AILES	Advanced Infrared beamLine Exploited for Spectroscopy
	AMC	Amplifier/Multiplier Chain
	ASC	atmospheric simulation chamber
	BELGI	belgian internal rotor program
	BCP	bond critical point
	CHARME CHamber for Atmospheric Reactivity and Metrology of Environment
	CAM	combined axis method
	cc	correlation consistent
	DFT	density functional theory
	DZ	Double Zeta (basis set)
	ES	excited state
	FTIR	Fourier-transform infrared spectroscopy
	FSR	free spectral ranges
	GS	ground state
	GTO	Gaussian-Type Orbital
	HITRAN high-resolution transmission (molecular absorption database)
	HF	Hartree-Fock
	HB	Hydrogen-bond
	ip	in-plane (vibration)
	IR	infrared
	IHB	intramolecular hydrogen bond
	JPL	jet propulsion laboratory
	LAM	large amplitude motion
	LPCA	Laboratoire de Physico-Chimie de l'Atmosphère
	LOD	limit of detection
	MW	microwave
	MMW	millimeterwave
	MO	molecule orbital
	MP2	Møller-Plesset second-order
	NCI	Non-Covalent Interaction
	NBO	Natural Bond Orbital
	oop	out-of-plane (vibration)
	PAS	principle axis system
	PAM	principle axis method
	PES	potential energy surface
	PROSPE	Programs for ROtational SPEctroscopy
	PID	proportional-integral-derivative

  1) e -

	34	CHAPTER 1. Basics of molecular spectroscopy
	In case the molecule contains a methyl group undergoing internal rotation
	Q tor is given with Equation 1.50. E	(tor) (ν t ,A) and E	(tor) (ν t ,
	E i (rot) kT		π A P AM B P AM C P AM	k B T h	3	(1.49)

Table 2 .

 2 2 -Some properties derived from derivative perturbations of the external electric n F or magnetic n B fields, the nuclear n I or electron n s magnetic moments and the nuclear geometry n R .

	The basis sets used in this work are the correlation consistent (cc) basis
	sets introduced by Dunning, Peterson and coworkers. They aim to recover
	the correlation energy of valence electrons and the primitive functions are

Table 1 .

 1 The transformation properties of the dihedral angles D 8 and D 10 under the elements of the M S4 molecular symmetry group.

Table 2 .

 2 Stationary points of the energy surface of Figure1. The B3LYP and MP2 relative energy calculations were performed with the aug-cc-pVTZ basis set. The position of the other points labeled on the Figure1acan be deduced from symmetry arguments and Table1.

	Point	D 8 / •	D 10 / •	Stationary Point	∆E B3LYP /cm -1	∆E MP2 /cm -1
	A 1 B 1 C D E 1 F 1 G 1	180.00 39.74 180.00 0.00 178.97 104.69 -96.05	0.00 39.74 180.00 0.00 103.95 104.69 96.05	global minimum saddle point local minimum saddle point saddle point local maximum global maximum	0 1274 1302 2197 2230 3197 3566	0 1219 1353 2307 2284 3208 3585
	2.1.2. Topological Analysis of the Intramolecular H-Bond

Table 3 .

 3 Description of the low-frequency vibrational bands in the FT-far-IR spectral range. The vibrational frequencies and intensities are given in cm -1 and km/mol, respectively.

	Mode *	Description **	Symmetry	This Work	ν exp Prev. Work	B3LYP-D3/aug-cc-pVTZ ν harm ν anharm I harm
	ν 36 (17a) ν 35 (τ 2 ) ν 34 (17b) ν 25 (9a) ν 33 (τ 1 ) ν 24 (18a) ν 32 (16b) ν 23 (6b) ν 31 (16a) ν 22 (6a) 2ν 36 2ν 35 ν 36,35	O-C-C-O twisting free -OH torsion O-C-C-O wagging O-C-C-O scissoring bonded -OH torsion O-C-C-O rocking sym oop ring deformation antisym ip ring deformation antisym oop ring deformation sym ip ring deformation O-C-C-O twisting overtone free -OH torsion overtone combination band	A" A" A" A' A" A' A" A' A" A' A' A' A'	-221.9 --415.0 --------	202 b 220 a 295 b 307 a 414 a 449 b 456 b 564 b 555 b 581 b ---	190 240 296 309 432 451 463 557 576 591 382 498 441	204 74 385 305 339 442 502 547 550 583 385 411 403	1.1 120.5 3.2 4.9 75.0 7.1 0.1 8.5 0.2 2.5 ---

  Hot band assignment proposition around the ν 35 free -OH torsional band at middle resolution (10 -2 cm -1 ). The assigned hot band progressions ν i ± nν j and ν i ± ν i ± nν j are marked with blue arrows. Two spectral zones are zoomed: the blue panel shows the hot band sequence red shifted from the ν 35 fundamental vibrational centre; the red panel highlights the hot band substructure around the |2v 35 ← |v 35 vibrational transition.

												0 1 2 3
												𝜈 "# ± 𝑛𝜈 "&
	𝜈 "# ± 𝑛𝜈 "#	2		1			0				2 1	𝜈 "# ± 𝑛𝜈 "'
											218	219	220	221	222	223	224	225	226	227	228
												wavenumbers˚/˚cm -1
							𝜈 "# ± 𝑛𝜈 (# 1 2				0 1 2 3 𝜈 "# ± 𝜈 "# ±𝑛𝜈 "&
	150	160	170	180	190	200	210	220	230	240	250
					wavenumbers˚/˚cm	-1
										192	193	194	195	196	197	198	199	200	201	202
												wavenumbers˚/˚cm -1

2 𝜈 "# ± 𝜈 "# ±𝑛𝜈 (# 1 Figure 4.

  While the rotation of catechol in the ring plane around the c-axis is almost not affected by the -OH torsional modes, we observed significant decreasing of the A 35 , B 35 , and A 33 rotational constants.

	-1 ∆ JK /kHz A/MHz B/MHz C/MHz ∆ J /kHz ∆ K /kHz δ J /kHz δ K /kHz	3387.5939(1) 2246.1882(1) 1350.9738(1) 0.091(15) 0.57(1) 0.043(8) 0.027(1) 0.126(7)	221.9125852(643) 3385.3793(48) 2243.7576(32) 1350.96712(240) 0.08983(47) 0.5712(33) 0.04329(244) 0.026704(270) 0.12374(190)	415.0091367(613) 3378.9268(88) 2246.0999(36) 1350.40579(106) 0.09726(44) 0.5790(91) 0.0416(36) 0.026348(218) 0.15957(159)
	N trans N lines J max K a,max RMS/cm -1 Unitless RMS		6937 3978 97 51 0.00022 1.10	4131 2455 199 41 0.00023 1.17
	From the fitted values of Table 4 for the free -OH torsional mode, we obtained 35 = 2.2146 MHz, α B α A 35 = 2.4306 MHz, and α C 35 = 0.0063 MHz. Similarly, for the bonded -OH torsional modes, the values were α A 33 = 8.6671 MHz, α B 33 = 0.0883 MHz, and α C 33 = 0.56801 MHz.

Table 5 .

 5 The spectroscopic constants and fit results of the mm-wave spectrum of catechol in the GS and in the lowest frequency vibrationally ES. For the rotational constants and the inertial defects∆I = h 8π 2 ( 1 C -1 B -1 A), the experimental fitted values are compared to the calculated values. In the lower part of the table, the number of measured lines N lines , the number of fitted transitions N trans , the maximum J, and K a values and the RMS highlighting the quality of the fit are given.

	Parameter Freq/cm -1 A calc /MHz ** B calc /MHz ** C calc /MHz ** A/MHz B/MHz C/MHz ∆ J /kHz ∆ K /kHz ∆ JK /kHz δ J /kHz δ K /kHz Φ K J /mHz φ J /µHz φ K /mHz φ JK /mHz ∆I calc /amu.Å 2 ** -0.064923 GS -3370.42487 2239.43737 1345.69441 3387.585698(280) 3379.64380(36) |v 36 = 1 202 3362.27296 2238.44835 1346.53357 2246.182094(175) 2245.18108(34) 1350.967110(157) 1351.797832(248) 1350.96338/6(91) * |v 35 = 1 221.9125852(643) 3369.43585 2236.82996 1345.87423 3385.374399/7(130) * 3394.8332(32) |v 34 = 1 295 3365.29996 2240.06675 1346.59351 2243.75593/1(124) * 2240.35362(184) 2255.98280(207) |v 25 = 1 307 3370.30499 2241.95487 1344.13595 3372.6254(35) 1351.92941(74) 1349.34535(68) 0.0796982(194) 0.080140(39) 0.079639/7(149) * 0.095688(150) 0.068570(200) 0.549465(151) 0.538075(118) 0.55185/4(50) * 0.26194(196) 0.53505(157) 0.057612(78) 0.062049(116) 0.056538(48) 0.13356(65) 0.05032(86) 0.0280925(161) 0.0282030(141) 0.028002/3(53) * 0.036035(73) 0.023006(105) 0.114669(101) 0.110693(96) 0.11245(32) 0.16456(35) 0.10445(52) -0.0810(214) ----2.55(130) ----0.2445(253) ----0.0260(140) -----0.76222 -0.42217 -0.4806 0.6186 ∆I/amu.Å 2 -0.09344(5) -0.77422(8) -0.43314(29) * 0.67186(31) -0.62657(8) N lines 4744 2694 926 */888 395 367 N trans a-type 2437 1077 840 */811 384 598 N trans b-type 7609 4689 1687 */1622 * 670 814 J max 124 129 99 */96 * 110 85 K a,max 72 74 66 */66 * 53 53 RMS/MHz 0.055 0.077 0.093 0.070 0.19 Unitless RMS 1.17 1.18 0.93 1.15 1.40

* Blue numbers correspond to the transitions σ = 1 ← σ = 0 between sublevels of the splitting caused by -OH torsion tunnelling in the v 35 = 1 state and red numbers to the transitions σ = 0 ← σ = 1. ** Rotational constants determined by anharmonic calculations at the B3LYP/aug-cc-pVTZ level of theory.

Table 6 .

 6 Comparison of the vibrational band centres ν and the inertia defects ∆I for the C-O oop bending and -OH torsional modes of phenol and catechol. The relative variations ∆ν ν = ∆I catechol -∆I phenol ∆I phenolfrom the phenol parameters issued from[27] are given in %. ∆I * = ∆I ES -∆I GS corresponds to the inertia defect corrected by the GS value, i.e., induced by the oop vibration.

	ν catechol -ν phenol ν phenol	and	∆(∆I) ∆I	=

* /amu.Å 2 ∆(∆I * ) ∆I *

Table 5 .

 5 ZPE /E h ∆E ZPE /kcal • mol -1 ∆E ZPE /cm -1 1 -Electronic energies E ZPE , including Zero-Point Energy correction, of the conformers with intramolecular hydrogen bond. All the data was computed with the B3LYP functional and the aug-cc-pvtz basis set.

	5.2. Presentation of molecules

Table 6 .

 6

	addition to position 2,

1 -Summary of the calculated energies of the first reaction step between 2MF and NO 3 . The B3LYP and M06-2X calculations were performed with the aug-cc-pVTZ basis set. The upper part of the table is dedicated to the NO 3 addition, the middle part to the H-abstraction and the lower part to the transition states found. The total energy E in Hartree is the sum of electronic and thermal free energies. The relative energies ∆E in kcal • mol -1 are E IN x -E 2MF + E NO 3 for the addition pathways and E P x + E HNO 3 -E 2MF + E NO 3 for the H-abstraction pathways.

  Experimental value obtained from BELGI-C s . b Experimental value taken from[31]. c Experimental value taken from[32]. d Experimental value taken from[33]. e Experimental value taken from[34].

	2-MF 2-MT 2-MP	376.12 (22) [420.3157 (35)] a 198.08 (33) [194.1] b 263.62 (67) [279.7183 (26)] c	-1.49 (22) [-9.010 (11)] a 1.71 (33) 1.96 (67)	-0.40 [-2.143] 0.86 0.74
	3-MF 3-MT 3-MP	348.92 (50) [357.77 (22)] a 254.47 (20) [259] d 223.55 (34) [245.14101 (89)] e	-10.81 (50) [-2.481 (13)] a -8.27 (20) -7.71 (34)	-3.10 [-0.693] -3.25 -3.45

a

  2 O highlight the exceptional selectivity of the technique, which should be able to detect anomalous isotopic fractionation. Moreover the rotational absorbance allows an absolute quantification of the absorbing compound without a standard calibration. The demonstration was performed on stable N 2 O and reactive O 3 greenhouse gases. According to the measured S/N ratio, the LOD are limited to 75 ppmv for N 2 O and 15 ppmv for O 3 due to the baseline oscillations involving numerous standing waves occurring in MULTICHARME. Work is in progress to characterize how these standing waves affect the detected THz signal in the modified Chernin-cell and to study the possibility to correctly model the THz baseline oscillations. This step is required to improve the sensitivity of the method in order to reach subppmv LOD for most small polar atmospheric molecules showing intense rotational transitions at THz frequencies. We have also to think about the possibility in the future to couple a THz cavity ring-down spectrometer to CHARME[START_REF] Hindle | Terahertz gas phase spectroscopy using a high-finesse Fabry-Pérot cavity[END_REF], in this way we hope to be competitive with IR and UV-visible techniques in terms of LOD. Finally, THz monitoring has been used to quantify the decay of ozone at low pressure in CHARME. The ozone lifetime of 3.4 ± 0.1 h deduced at low pressure in the chamber by THz spectroscopy is shorter than those obtained in previous measurements at atmospheric pressure using a UV photometry analyzer. At low pressure the ozone losses by diffusion on the ASC are accentuated.

Table 2 -

 2 Molecular constants of Chapter 7 in the RAM system of 2-methylfuran obtained by a global fit using program BELGI-C s .

	204

  • C. Finally, for the first time, the mm-wave spectrometer was coupled into an ASC and the potential of carrying out online and in-situ submillimeter monitoring of atmospherical reactions is demonstrated in this thesis.Keywords: oxygenated aromatic compounds; precursors of secondary organic aerosols; terahertz gas phase spectroscopy; quantum chemistry methods; intramolecular hydrogen bonds Laboratoire de Physico-Chimie de l'Atmosphère Dunkerque Maison de la Recherche en Environnement Industriel 2 (MREI2) -189A, Avenue Maurice Schumann -59140 Dunkerque -France Chimie quantique et spectroscopie THz des composés organiques volatils biogéniques précurseurs d'aérosols organiques secondaires dans l'atmosphère Résumé L'objectif principal de cette thèse était d'étudier les composés organiques volatils COV oxygénés identifiés comme étant impliqués dans la chimie de l'atmosphère, en particulier dans la formation d'aérosols organiques secondaires AOS. La spectroscopie rovibrationnelle en phase gazeuse a permis d'étudier les liaisons hydrogène intramoléculaires (LHIs) stabilisant certains composés organiques aromatiques oxygénés quasi-planaires. La principale molécule étudiée par spectroscopie THz à température ambiante et par calculs de chimie quantique (CQ) est le catéchol. Dans cette molécule, deux groupes hydroxyles voisins forment une LHI et par une rotation concertée de 180 • ils peuvent inverser leurs rôles de donneur et d'accepteur. Les paramètres spectroscopiques ont été ajustés pour l'état fondamental et les quatre états vibrationnels excités de plus basse énergie. Il a été possible de relier directement la dynamique de la LHI à ces paramètres spectroscopiques. Plusieurs autres molécules apparentées ont été étudiées théoriquement avec différentes méthodes de CQ mettant en évidence le potentiel, les limites et les difficultés de ces approches traitant des LHI particulièrement faibles. Un autre objectif principal de cette thèse était l'étude des composés furanes méthylés. Ces COV hétérocycliques ont également été identifiés comme précurseurs gazeux d'AOS. Pour estimer la contribution du 2-méthylfurane (MF) en particulier, des calculs de CQ ont été effectués montrant le potentiel du 2-MF à réagir avec le NO 3 qui est le principal réactif dans l'atmosphère pendant la nuit. La spectroscopie à ondes millimétriques à température ambiante du 3-MF et l'analyse des spectres obtenus ont été réalisées. En raison de la division des raies de rotation causée par la rotation interne du groupe méthyle, cette analyse a nécessité un traitement spécifique pour ce mouvement de grande amplitude. Comme l'approche locale couramment utilisée du code XIAM n'était pas suffisante pour ajuster correctement les paramètres du premier état excité, l'approche globale du code BELGI a été utilisée non seulement pour 3-MF mais également appliquée au 2-MF mesuré précédemment dans la littérature. Pour aller plus loin dans l'utilisation de la spectroscopie THz dans les sciences de l'atmosphère, nous avons développé un système de chauffage sur la cellule à gaz et, par ailleurs, nous avons démontré qu'il était possible de coupler le spectromètre à ondes submillimétriques dans une chambre de simulation atmosphérique (CSA). Avec le système de chauffage, la pression de vapeur de la molécule étudiée peut être augmentée, élargissant le champ des molécules potentielles aux COV semi-volatils. Les premiers spectres ont été obtenus pour le méthylcatéchol avec une température optimisée à 70 • C. Enfin, pour la première fois, par le couplage du spectromètre à ondes millimétriques à une CSA nous avons montré qu'il était possible de réaliser un suivi submillimétrique in situ des réactions atmosphériques dans une CSA.

	Mots clés : composés aromatiques oxygénés ; précurseurs d'aérosols organiques secon-
	daires ; spectroscopie térahertz en phase gazeuse ; méthodes de chimie quantique ;
	liaisons hydrogène intramoléculaires

Molecules 2021, 26, 3645. https://doi.org/10.3390/molecules26123645 https://www.mdpi.com/journal/molecules

Supplementary Materials:The following are available at, a directory "supp-mat" of 17 files, which contains a pdf file "note" with a table that sums up the meaning and content of the other 16 files to be used with SPFIT/SPCAT in a single compressed directory.

global (BELGI) approaches.

Molecules 2022, 27, 3591. https://doi.org/10.3390/molecules27113591 https://www.mdpi.com/journal/molecules

Atmos. Meas. Tech., 15, 1201-1215, 2022 https://doi.org/10.5194/amt-15-1201-2022

https://doi.org/10.5194/amt-15-1201-2022 Atmos. Meas. Tech., 15, 1201-1215, 2022

Acknowledgments xi

Acknowledgments

First of all, I would to thank the Jury members Professor Michael Schmitt, Professor Anne Zehnacker-Rentien, Professor Martin Schwell and Dr. Halima Mouhib for accepting and examine my thesis.

Acknowledgments xv xvi

Acknowledgments: The AILES beamline team, especially the beamline manager P. Roy, and the JET-AILES team, especially P. Asselin, are thanked for the synchrotron-based FT-far-IR experiments. We are grateful to O. Pirali for his sound advice for the hot bands assignment. Quantum chemistry calculations presented in this paper were carried out using the CALCULCO computing platform, supported by SCoSI/ULCO (Service COmmun du Système d'Information de l'Université du Littoral Côte d'Opale).

Acknowledgments: Quantum chemistry calculations presented in this paper were carried out using the CALCULCO computing platform, supported by SCoSI/ULCO (Service COmmun du Système d'Information de l'Université du Littoral Côte d'Opale). The collaboration between Isabelle Kleiner and Arnaud Cuisset is part of the ATMOS project n o 872081 funded by the H2020-MSCA-RISE-2019 program.

Acknowledgements. The LPCA towards CHARME is an associated partner of the ATMO-ACCESS European facility.

We are grateful to the logistics department of the Dunkirk University Management Center for their help in installing the MULTI-CHARME flanges. Marc Fourmentin is also thanked for his help in the graphical abstract conception.

This work was supported by the CaPPA project (Chemical and Physical Properties of the Atmosphere) funded by the French National Research Agency (ANR-11-LABX-0005-01) and the CLIMIBIO program supported by the Hauts-de-France Regional Council, the French Ministry of Higher Education and Research and the European Regional Development Fund. Jean Decker and Jonas Bruckhuisen were funded by CLIMIBIO and the Pôle Métropolitain de la Côte d'Opale, respectively. MULTICHARME was founded by the Research Quality Bonus of the University of Littoral Côte d'Opale, the Optics, Photonics, Applications Lasers (OPAL) network and the IRenE program.

Financial support. This research has been supported by the Agence Nationale de la Recherche (grant no. ANR-11-LABX-0005-01) and the Région Hauts-de-France (grant no. CPER CLIMIBIO).

Review statement. This paper was edited by Mingjin Tang and reviewed by two anonymous referees.

Funding: This work was supported by the CaPPA project (Chemical and Physical Properties of the Atmosphere) funded by the French National Research Agency (ANR-11-LABX-0005-01) and the CLIMIBIO program supported by the Hauts-de-France Regional Council, the French Ministry of Higher Education and Research and the European Regional Development Fund.

Data Availability Statement:

The data presented in this study is available in the supplementary materials.

Data Availability Statement:

The data presented in this study is available in the Supplementary Materials.

Conflicts of Interest:

The authors declare no conflict of interest.

Sample Availability: Not available.

Abbreviations

The following abbreviations are used in this manuscript:

α / degrees fitting the experimental line positions. We observe that the V 3 parameter determined from quantum computations underestimates the XIAM or BELGI-Cs values by 10% for 2-MF (3% for 3-MF) while the V 6 parameter (in absolute value) underestimates the fitted values by a factor 5 or more for 2-MF (overestimates by a factor 4 for 3-MF). Such a disagreement is not surprising, because the V 3 and V 6 parameters obtained from the XIAM and BELGI-C s codes consider the averaging over the harmonic motion of the nuclei belonging to the furan frame and of the zero-point energy in the torsional potential.

Because the previous measurements on 2-MF and 3-MF were focused on the ground state [11] or treat the v t = 0 and v t = 1 states independently in a local approach [12], those prior experimental studies dedicated to large amplitude internal rotation were only able to fit the V 3 barrier height without the higher-order V 6 correction. That was also the case for other heterocyclic analogs of methylfuran (MF) as methylthiophene (MT) and methylpyrrole (MP). In Table 3, we notice that the V 3 parameters were experimentally determined for the 2-and 3-isomers of each heterocyclic compounds but the higher-order V 6 correction could not be determined before our study of 2-MF and 3-MF mm-wave spectra since it requires the access to the v t = 1 excited torsional state and a global fit including both v t = 0 and v t = 1 allowed by the BELGI-C s code. Therefore no V 6 experimental values exist for the other heterocyclic compounds and the comparison should be performed with V 3 and V 6 values fitted on the theoretical data (hereafter B3LYP/aug-cc-pVTZ calculations).

Supplementary Materials:

The following supporting information can be downloaded at https: //www.mdpi.com/article/10.3390/molecules27113591/, a directory "supp-mat" of 4 Tables: S1 and S2 contain the full set of RAM parameters fitted BELGI-C s , respectively for 2-MF and 3-MF. S3 and S4 are the produced rotational-torsional mm-wave line lists, respectively for 2-MF and 3-MF.

Author Contributions:

Conflicts of Interest:

The authors declare no conflict of interest.

The Following Abbreviations are Used in This Manuscript

B3LYP

Becke, 3-parameter, Lee-Yang-Parr CAM Combined Axis Method DFT Density Functional Theory ERHAM Effective Rotational-torsional HAMiltonian FFT Fast Fourier Transform GC-MS Gas Chromatography-Mass Spectrometry Chapter 9

THz monitoring in an atmospheric simulation chamber

The here presented publication: "MULTICHARME: a modified Chernin-type multi-pass cell designed for IR and THz long-path absorption measurements in the CHARME atmospheric simulation chamber", [30] was a colaborative work with Jean Decker, Éric Fertein, Nicolas Houzel, Pierre Kulinski, Bo Fang, Weixiong Zhao,Francis Hindle, Guillaume Dhont, Robin Bocquet, Gaël Mouret, Cécile Coeur and Arnaud Cuisset.

While the technical development, installation and IR experiments were mainly managed by the engineers Jean Decker and Éric Fertein I was in charge for the THz experiments. I started contributing to the project after the development, installation, visible (He-Ne) and IR alignments of the Chernin-type multi-pass cell. I began with the installation and alignment of the THz setup, consisting of a similar AMC, the same ZBDs, frequency generator and lock-in amplifier but instead of off-axis parabolic mirrors lenses were used to collimate the beam at the entrance of the ASC and refocus the output beam onto the zero-biased detector. This part of my work is described in the section 2.2.3 of the following article. Afterwards, the section 3.2 present different THz spectroscopic experiments of stable N 2 O and reactive O 3 were carried out highlighting the spectrum of application possibilities.

Supporting information

Appendix A Résumé de la thèse La combustion globale de la biomasse conduit à l'émission d'énormes quantités de particules carbonées primaires et de gaz traces dans l'atmosphère. Les émissions de combustion de la biomasse sont la deuxième source atmosphérique mondiale de composés organiques non méthaniques en phase gazeuse. Ces émissions ont une influence significative sur la qualité de l'air local, le climat et même la santé humaine. Malheureusement les compositions et contributions des émissions gazeuses de composés de masse moléculaire plus élevée restent mal connues. Souvent quelques minutes après l'émission, ces composés organiques volatils (COVs) subissent des réactions photochimiques complexes. Cela provoque une modification des concentrations des principaux réactifs atmosphériques comme l'ozone O 3 , le radical hydroxyle OH ou les oxydes d'azote NOx et peut conduire à la formation d'aérosols organiques secondaires (AOS).

L'influence globale sur le climat est difficile à estimer en raison des différentes forces radiatives de tous ces processus potentiels complexes avec des impacts parfois contraires. Par conséquent, une meilleure compréhension des réactions atmosphériques et une quantification précise de ces composés dans l'atmosphère est d'un grand intérêt.

L'objectif principal de cette thèse intitulée "Chimie quantique et spectroscopie THz des composés organiques volatils oxygénés (COVO) biogéniques précurseurs d'aérosols organiques secondaires dans l'atmosphère" réalisée au Laboratoire de Physico-Chimie de l'Atmosphère de l'Université du Littoral Côte d'Opale était d'étudier les composés organiques volatils oxygénés identifiés comme étant impliqués dans la chimie de l'atmosphère, notamment dans la formation d'AOS.

Deux familles de COVO ont été ciblées pour cette thèse : en premier lieu, les dérivés phénoliques comme le catéchol, dérivés aromatiques du benzène avec des groupes fonctionnels oxygénés. Cette famille de COVO est principalement émise lors de la combustion de la lignine [94], constituant fondamental du bois. L'autre famille, étudiée dans cette thèse, est le groupe des furanes. Ces composés hétérocycliques oxygénés, contenant des cycles à cinq chaînons sont produits par la combustion de l'hémicellulose, substance contenue dans la membrane des cellules végétales [83].

Le premier projet de cette thèse était consacré au catéchol (benzène-