Damien Dargent

Bruno Madebène

Pascale Soulard

Benoît Tremblay

Emilie-Laure L Zins

Mohammad Esmaïl Alikhani

Pierre Asselin
email: pierre.asselin@upmc.fr

The Conformational Landscape of the 1/1 Diacetyl/water Complex Investigated by Infrared Spectroscopy and Ab Initio Calculations

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

I -Introduction

It is now well established that non-covalent interactions such as hydrogen bonds involved in small hydrated clusters play an essential role in atmospheric chemistry, astrophysics and also in many biochemical and catalytic processes. 1 Since the pioneering spectroscopic works about the enthalpy and the hydrogen bridges in crystallographic structures such as ice and liquid water, 2,3 many advanced experimental methods were developed in the last thirty years to interpret the bulk water structure and dynamics. In this context, the spectroscopic study of small water clusters produced at very low temperature in nearly isolated conditions proved to be determinant for improving the building of reliable intermolecular potential energy surfaces based on a back and forth procedure between experiment and theory. As a first step toward this objective, we can cite the challenging studies based on jet-cooled far-and near-IR laser and microwave spectroscopy which yielded new insights into the tunneling motions of the water dimer [START_REF] Busarow | Measurement of the Perpendicular Rotation-Tunneling Spectrum of the Water Dimer by Tunable Far Infrared Laser Spectroscopy in a Planar Supersonic Jet[END_REF][START_REF] Liu | Water Clusters[END_REF][6] and allowed to determine a polarisable water pair potential. [START_REF] Fellers | Spectroscopy Determination of the Water Dimer Intermolecular Potential Energy Surface[END_REF] The huge capacity of water to establish hydrogen bonds with the close environment owing to its twice role of hydrogen-bond donor and acceptor would suggest to use a molecular approach based on a step by step increase of the size of hydrates for most studies related to the hydration process of organic species. It has been shown in many previous solid 8 and gas phase studies [START_REF] Zwier | Laser Probes of Conformational Isomerization in Flexible Molecules and Complexes[END_REF][START_REF] Çarcabal | Binding Energies of Micro-Hydrated Carbohydrates: Measurements and Interpretation[END_REF][START_REF] Mons | Intra-and Intermolecular π-Type Hydrogen Bonding in Aryl Alcohols: UV and IR-UV Ion Dip Spectroscopy[END_REF] that very different structural architectures of hydrated organic M/H 2 O clusters could be obtained, depending on the nature of the organic molecule M involved.

The objective of the present work is to characterize by a combined experimental and theoretical approach the first step of hydration of an organic molecule M. In a recent paper [START_REF] Dargent | Topological Insights into the 1/1 Diacetyl/Water Complex Gained using a New Methodological Approach[END_REF] , a six-step methodological approach aiming at characterizing the conformational landscape of mono-hydrated 1/1 M/H 2 O isomers emphasized the value of topological methods to evidence the most stable isomers.

We selected the small centro-symmetric diacetyl molecule (C 4 H 6 O 2 , DAC) as partner of the hydration process. This atmospheric pollutant [START_REF] Klöpffer | Atmospheric Degration of Organic Substances: Persistence, Transport Potential, Spatial, Range[END_REF]14 can be considered as the simplest analogue of a small biologic molecule with two methyl and two carbonyl groups, the latter ones being possibly involved in π-hole-like interactions. Two previous experimental studies were reported about the 1/1 DAC/H 2 O complex: a Fourier Transform InfraRed (FTIR) study by Mucha and Mielke [START_REF] Mucha | Complexes of Atmospheric Alpha-Dicarbonyls with Water: FTIR Matrix Isolation and Theoretical Study[END_REF] in argon matrix evidenced two 1/1 isomeric structures from annealing effects realized about intramolecular perturbed DAC and H 2 O vibrations. With the support of ab initio calculations at the MP2/6-311++G(2d,2p) level, they assigned them to two nearly isoenergetic forms (noted S 1 and S 2 , respectively) for which the water molecule may be zusammen or entgegen with respect to the methyl group attached to the same carbonyl group to which water is linked. More recently, a rotational study of Favero and Caminati [START_REF] Favero | Hydrated Complexes of Atmospheric Interest: Rotational Spectrum of Diacetyl-Water[END_REF] by FT microwave spectroscopy nicely confirms that the most stable form is the zusammen (S 1 ) one, complemented by the determination of very weak barriers (around 4 kJ/mol) to the internal rotation of methyl groups.

In the following we reported a series of experiments mainly achieved in solid neon and at a least degree in the supersonic expansion of the Jet-AILES facility on the infrared beamline of the SOLEIL synchrotron. Previous studies realized in our group about the characterization of small hydrated complexes highlighted all the interest to combine gas and solid neon phases spectroscopic methods over the whole infrared range to gain information from intermolecular modes, overtones and combinations, while anharmonic ab initio calculations are necessary to guide the assignment of vibrational signatures related to the conformation of a complex of a given size and in counterpart to validate the choice of the selected theoretical method. [START_REF] Cirtog | The (CH 2 ) 2 O-H 2 O Hydrogen Bonded Complex. Ab Initio Calculations and Fourier Transform Infrared Spectroscopy from Neon Matrix and a New Supersonic Jet Experiment Coupled to the Infrared AILES Beamline of Synchrotron SOLEIL[END_REF]18 The present paper is structured as follows: section II provides experimental details about neon matrix and Jet-AILES set-ups coupled to FTIR spectroscopy and computational details. Section III reports on ab initio, jet-cooled and neon matrix results, mainly on the 1/1 complex and few ones on the 1/2 complex. In section IV, vibrational analyses of low temperature FT spectra are finally discussed with the support of anharmonic vibrational calculations related to the most stable isomers.

II Experimental and computational details II-1 Helium cryostat device.

Diacetyl + H 2 O samples were prepared in a closed-cycle helium cryostat (Cryomech PT-405) by slow deposition (10 mmol/h) of about 30 up to 120 mn in double injection (diacetyl/neon and water/neon) on one side of a highly polished, Rh-plated copper mirror maintained at 3 K. The temperature was measured using silicon diodes, and thermal annealing was regulated by a Neocera LTC-II temperature controller.

Molar ratios (X/Ne, X= DAC, H 2 O) between 5.10 -3 to 5 % were prepared in a vacuum line but variable desorption of water from the stainless steel vacuum line precluded accurate concentration measurements for H 2 O/Ne. Ne gas was obtained from Air Liquide with a purity of 99.995 % and DAC was obtained from Sigma Aldrich with a purity of 97 % while natural water was degassed in situ.

Absorption spectra in the mid-IR and far-IR ranges were collected on samples through ICS and polyethylene windows respectively mounted on a rotatable flange separating the interferometer vacuum (10 -3 mbar) from the cryostatic cell vacuum (10 -7 mbar). Bare mirror backgrounds, recorded from 50 to 8000 cm -1 prior to sample deposition were used as references in processing the sample spectra. Infrared absorption spectra of the resulting samples were recorded at 3 K with a Bruker IFS 120 HR spectrometer equipped with suitable combinations of infrared sources (globar, W filament), beamsplitters (composite, KBr/Ge, Si/CaF 2 ), and detectors (InSb, HgCdTe, Si-B bolometer). Matrix spectra of 50-200 coadded interferograms were recorded at a resolution of 0.5 cm -1 .

II-2 Jet-AILES apparatus

Jet-cooled spectra have been recorded using the Jet-AILES apparatus already described in detail in previous studies [START_REF] Pirali | The far infrared spectrum of naphtalene characterized by high resolution synchrotron FTIR and anharmonic ab initio calculations[END_REF] and coupled to the high resolution Bruker IFS 125 FT spectrometer associated with AILES beamline at the synchrotron facility SOLEIL. Briefly, a slit nozzle of 60 mm length and 80 µm width was used to expand the sample into a expansion chamber connected to a set of roots pumps delivering a pumping capacity of about 1800 m 3 h -1 . The flow of H 2 O vapor was regulated using a Controlled Evaporation Mixer (Bronkhorst CEM model W303A-22-K) supplied by a first flow of argon as buffer gas (Bronkhorst 2-100 l min -1 model F-202AV) and liquid water (Bronkhorst mini CORI-FLOW 1000 g h -1 model M13). In the absence of a second CEM, DAC vapor was carried from an oven and swept by argon through a second gas line independent from the first one and finally the H 2 O/DAC/Ar gas mixture flows through a mildly heated gas line (310 K) upstream of the stagnation reservoir of the slit nozzle.

In our supersonic expansion conditions, backing and residual pressures were typically comprised in the 250-400 Torr and 0.3-0.5 Torr ranges, respectively. Relative concentrations of DAC in the ternary mixture were estimated from relative variations of backing pressures measured with and without DAC. FT spectra were recorded in the OH stretching range of H 2 O using the configuration W filament/CaF 2 /InSb. A band pass filter centered on the 3300-3800 cm -1 spectral range was used to maximize the number of photons in the investigated spectral window.

II-3 Computational details

Dunning and coworkers augmented correlation consistent basis set aug-cc-pVDZ (AVDZ) and aug-cc-pVTZ (AVTZ) have been used. [START_REF] Dunning | Gaussian Basis Sets for Use in Correlated Molecular Calculations. I. The Atoms Boron through Neon and Hydrogen[END_REF][START_REF] Kendall | Electron Affinities of the First-Row Atoms Revisited. Systematic Basis Sets and Wave Functions[END_REF] Second order Møller-Plesset (MP2) calculations have been performed using the Gaussian09 package. [START_REF] Frisch | Gaussian 09, Revision D.01[END_REF] All geometry optimizations were performed with « tight » convergence. Anharmonic frequencies have been calculated at MP2/AVTZ level of theory using vibrational perturbation theory (VPT2) approach as implemented in Gaussian09 for 1/1 DAC/H 2 O isomers. Due to computational limitations for 1/2 DAC/H 2 O isomers, only MP2/AVDZ harmonic frequencies have been computed.

III Results

III-1 Theoretical results

In a recent theoretical paper about 1/1 DAC/H 2 O complex [START_REF] Dargent | Topological Insights into the 1/1 Diacetyl/Water Complex Gained using a New Methodological Approach[END_REF] we have shown that the analysis of monomers realized with the combination of topological tools, mainly MESP, ELF and QTAIM allowed identifying favorable interaction sites to predict 1/1 structures. Three isomers have been characterized, namely S 1 , S 2 and S 3 , and their structures optimized at the MP2/AVTZ level of theory are reported in Figure 1. This topological approach allowed to identify the S 3 isomer which had not previously been reported in the literature. The striking results about the structural, energetic and topological analyses of the three isomers of complex 1/1 DAC/H 2 O can be summarized as follows:

• Each 1/1 DAC/H 2 O isomer has a cyclic structure involving two complementary interactions. • In the case of S 1 and S 2 , the complex is stabilized by traditional non covalent hydrogen bonds. The water molecule lies within the symmetry plane of DAC and the primary hydrogen bond is formed between one hydrogen atom of water and the oxygen atom of one of the carbonyl groups of DAC. The oxygen from water molecule interacts with the hydrogen of the closest methyl leading to one (S 1 ) or two (S 2 ) secondary hydrogen bonds. • In the case of S 3 , the water molecule is perpendicular to symmetry plane of DAC. The oxygen atom of the water molecule is involved in two non covalent bonds: one hydrogen bond with hydrogen atom of a methyl group and one non covalent bond with the oxygen atom of the carbonyl. • The three isomers are nearly isoenergetic with ZPE-corrected binding energies D 0 at 17.5, 17.5 and 16.2 kJ/mol (MP2/AVTZ level) for S 1 , S 2 and S 3 , respectively. Caminati et al. observed the S 1 isomer as proved by the excellent agreement (within 0.2%) between their experimental [START_REF] Favero | Hydrated Complexes of Atmospheric Interest: Rotational Spectrum of Diacetyl-Water[END_REF] and our calculated ground state rotational constants. Equilibrium and ground state rotational constants and binding energies of the three isomers are reported in Table 1.

In the present work we complete the energetic and topological studies of the complex 1/1 DAC/H 2 O by the vibrational properties of the three isomers. First, our computational approach has been validated on H 2 O and DAC monomers [START_REF] Dargent | Topological Insights into the 1/1 Diacetyl/Water Complex Gained using a New Methodological Approach[END_REF] . Harmonic and anharmonic frequencies have been computed at MP2/AVTZ level of theory for both molecules and are reported in the electronic supplementary material (SM1) with experimental frequencies: from Ref 23 for water (gas phase), from Ref 24 for diacetyl IR active modes (gas phase) and from Ref 25 for IR inactive modes (liquid phase). The computed anharmonic frequencies for both water and DAC molecules are in satisfactory agreement with observed frequencies. The root mean square deviation from experimental values (RMSD) is only 20 cm -1 with a maximum deviation of 40 cm -1 for the methyl torsions in DAC, which are not supposed to be properly described by VPT2 approach.

All harmonic and anharmonic frequencies of the three 1/1 DAC/H 2 O isomers have been computed at the same level of theory and are reported in supplementary material SM2.

Only the calculated frequencies of main bands observed for 1/1 isomers and corresponding monomers are gathered in Table 2. Frequency shifts with respect to the frequency of monomers are also reported for the three isomers.

The following informations can be deduced from the analysis of Table 2: • Either in the middle or the far infrared, each isomer has several modes with enough intense frequencies to be observed. • As expected water vibrational modes are the most affected ones. Bonded (ν OHb ) and free (ν OHf ) O-H stretching are substantially red shifted (with respect to the H 2 O monomer) for the three isomers. Experimental and theoretical frequency shifts between 1/1 and monomer bands (hereafter noted ∆ exp and ∆ th ) will be used to guide our assignments. • Few DAC vibrational modes in the complexes are slightly affected by the formation of the isomers. • Overall, S 1 and S 2 have a quite similar vibrational spectrum, while that of S 3 reveals two major differences: the intensity of the ν OHb band is weaker and intermolecular frequencies are smaller than for the other isomers. These data are consistent with the different bonding nature of S 3 compared to the more traditional hydrogen bond within the S 1 and S 2 complexes.

III-2 Jet-cooled data

The bands observed at 3601, 3532, 3397 and 3354 cm -1 in the pure H 2 O/Ar jet-FT spectrum (Figure 2a) are unambiguously assigned to bonded OH stretching bands of (H 2 O) n=2-5 while the broad peak at about 3719 cm -1 corresponds to the stacking of free OH stretching bands of (H 2 O) n=2-5 . [START_REF] Moudens | Direct Absorption Spectroscopy of Water Clusters Formed in a Continuous Slit Nozzle Expansion[END_REF] When adding DAC to the H 2 O/Ar gas mixture, additional bands are expected to be observed. Only two jet-FT spectra with largely different DAC/H 2 O molar flow ratios could be recorded. In order to enhance the formation of the 1/1 dimer, DAC and H 2 O gas flows were firstly injected in nearly equimolar proportion (Figure 2b). The DAC/Ar spectrum (not shown in Figure 2) only displayed a weak peak at 3463 cm -1 assignable to the first overtone of the antisymmetric CO stretching (ν C=O as ) mode of DAC monomer. Two new bands are observed at 3575 and 3599 cm -1 with respect to the pure H 2 O/Ar spectrum. Additional broad and unstructured absorptions are observed when still increasing the water concentration (Figure 2c): two peaks at 3497 and 3560 cm -1 (30 cm -1 fullwidth-at-half-maximum) will be further discussed because they could correspond to larger 1/n hydrated heteroclusters.

Unlike in oxirane-H 2 O jet-FT spectra previously recorded in the OH stretch range with Jet-AILES 18 no partially resolved rovibrational band contour was observed in the jet spectra of DAC-H 2 O. The presence of low barriers to internal rotation for the two methyl groups (determined to be about 4 kJ/mol from rotational spectroscopy) could explain the broadening of bands observed even when recording jet-FT spectra at 0.1 cm -1 resolution. In these conditions, the sensitivity limits of the Jet-AILES set-up in its actual configuration only

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The Journal of Physical Chemistry allows to provide vibrational gas phase data on small DAC/H 2 O clusters in the region of intense OH stretching bands.

III-3 Neon matrix data

The high detectivity of the neon matrix isolation technique over all the infrared range is likely to reveal most of the vibrational transitions of the 1/1 dimer, such as intra-and intermolecular fundamentals. Due to the small neon matrix induced perturbations, the observed vibrational frequencies are expected to be only slightly shifted with respect to gas phase ones. When DAC and H 2 O are codeposited in a neon matrix, new bands are observed near H 2 O and DAC fundamentals, in the region of intermolecular modes and higher in energy due to combinations and overtones.

III-3-1 The 1/1 complex H 2 O stretching region: 3550-3850 cm -1 Figure 3 displays three neon matrix spectra recorded in the OH stretching mode region, firstly with only DAC (a) and H 2 O (b) diluted in Ne, and lastly with a DAC/H 2 O/Ne ternary mixture (c) suitable to the formation of dimeric species, as proved by the only absorptions of water monomer and dimer observed in the pure water neon matrix spectrum (Figure 3b). Four additional absorptions at 3568.2, 3594.2, 3726.8 and 3732.7 cm -1 are observed in the spectrum (c) with respect to the pure water and DAC spectra. The concentration dependence of these bands varies linearly with respect to either H 2 O or DAC, which gives confidence for assigning these four absorptions to a 1/1 dimer. Adsorbed residual water on gas line walls contributes to weak 1/1 absorptions (as shown in Figure 3a) while pure DAC background recordings are wanted.

H 2 O bending and DAC CO stretch region: 1580-1750 cm -1

Other absorptions were evidenced in the 1580-1750 cm -1 region : one band in the bending mode region of H 2 O at 1603.2 cm -1 and two strong ones at 1721.6 and 1726.1 cm -1 and one weaker at 1734 cm -1 near the CO stretch band of DAC monomer at 1731 cm -1 . They are all correlated with the four bands observed in the OH stretching region, and consequently belong to species with the same 1/1 stoichiometry.

Intermolecular mode region: 100-600 cm -1 Figure 4 illustrates the complexity to extract intermolecular neon solid data of weakly bound binary hydrated complexes owing to the competition with strong absorptions of small pure water clusters. Three DAC monomer bands (Figure 4a) and eleven bands (some of them in overlap) assigned to water dimer [START_REF] Bouteiller | The Vibrational Spectrum of the Water Dimer: Comparison between Anharmonic Ab Initio Calculations and Neon Matrix Infrared Data between 14000 and 90 cm -1[END_REF] , trimer [START_REF] Tremblay | The Vibrational Spectrum of the Water Trimer: Comparison between Anharmonic Ab Initio Calculations and Neon Matrix Infrared Data between 11000 and 90 cm -1[END_REF] and tetramer [START_REF] Ceponkus | Intermolecular Vibrations of the Water Trimer, a Matrix Isolation Study[END_REF] (Figure 4b) are observed in the 100-600 cm -1 range, likely to mask weak absorptions of DAC-H 2 O heteroclusters. On the grounds of concentration effects of the DAC/H 2 O/Ne mixture, three intermolecular bands at 115.9, 282.1 and 322.8 cm -1 could be assigned to the 1:1 dimer as well as a broad band at 547 cm -1 (with a shoulder at 545.5 cm -1 ) blue-shifted by 7 (5.5) cm -1 with respect to a strong DAC monomer band. The vibrational analysis of the intermolecular mode region will be detailed in section IV with the support of combination band analysis and ab initio calculations.

Combinations and overtones region: 1900-7500 cm -1 In the near-IR region, the same hindrances as in the far-IR one exist, due to the presence of strong water clusters bands few shifted in frequency with respect to binary water complexes. Nevertheless, 11 bands are unambiguously correlated with the 1/1 complex (Table 3). Figure 5 displays neon matrix spectra in the 3900-4200 cm -1 range, dense in combination bands involving one ν intra intramolecular mode (OH proton donor stretching band ν OHb or ν OHf ) and one ν inter intermolecular mode. Besides the four bands ascribed to a 1/1 complex, one band at 4098 cm -1 is found to correlate with a larger complex.

III-3-2 The 1/2 complex

When H 2 O concentration is growing, seven new bands between 3500 and 7300 cm -1 (3503.7, 3555.8, 4098.9, 5110, 6881, 7111 and 7232.3 cm -1 ) and possibly one at 375 cm -1 are correlated to the relative intensity variations of the water dimer. Figure 6 displays a series of neon matrix spectra from (a) to (c) recorded in the OH stretching region for different relative molar ratios DAC/H 2 O with respect to Ne. Two new bands at 3503.7 et 3555.8 cm -1 grow in the same time and on both sides of bonded OH stretchings (at 3517.5 and 3529.5 cm -1 ) of H 2 O trimer and at lower frequencies as the 1/1 bands (Figure 6c). The behavior of all these bands argues in favor of a 1/2 complex and will be discussed hereafter. [START_REF] Mucha | Complexes of Atmospheric Alpha-Dicarbonyls with Water: FTIR Matrix Isolation and Theoretical Study[END_REF] As a first step, neon matrix experiments realized throughout the infrared region enabled to identify almost thirty bands to the 1/1 hetero dimer and seven ones probably assignable to the 1/2 hetero trimer. For going further in the assignments, ab initio calculations should be used.

IV Discussion

We exploit now the vibrational analyses carried out for the three calculated nearly isoenergetic S 1 , S 2 and S 3 isomers of 1/1 DAC-H 2 O. The objective is to fully assign each band observed to the vibrational mode of a specific isomer of the 1/1 complex. In the case of larger complexes, tentative assignments will be proposed with the support of ab initio harmonic calculations realized about the three most stable isomers of the 1/2 complex. [START_REF] Dargent | Energy, Structure and Topological Characterization of the Isomers of The 1/2 Diacetyl/Water Complex[END_REF]

H 2 O fundamentals

In the OH stretching region of H 2 O, jet-cooled bands at 3575 and 3599 cm -1 correspond to the same bands as neon matrix ones at 3568.2 and 3594.2 cm -1 taking into account the small redshift (about 6 (1) cm -1 ) due to the solid neon cage with respect to the gas phase. These bands are clearly assigned to bonded OH (ν OHb ) stretching modes of S 1 and S 2 with ∆ exp equal to -97 and -71 cm -1 , respectively, and ∆ th equal to -106 and -72 cm -1 . The frequency shift between ν OHb bands of S 1 and S 2 is 24 cm -1 (gas), 26 cm -1 (solid neon) and 34 cm -1 (MP2/AVTZ anharmonic) which fully validates the mode assignments. With the same arguments, the bands at 3726.8 and 3732.7 cm -1 with ∆ exp equal to -41 and -35 cm -1 are assigned to free OH ones (ν OHf ) of both S 1 and S 2 . The corresponding ∆ th are equal to -35 and -31 cm -1 . About the S 3 isomer, the frequency calculated 5 to 9 cm -1 higher than for S 1 and S 2 (Table 2) suggests that this OH band could be overlapped by the proton donor ν 3 band of water dimer (Figure 3c).

In the δ bending mode region, one weak band of the 1/1 complex was observed at 1603.2 cm -1 surrounded by intense absorptions of H 2 O monomer, dimer and trimer. Compared to the largely positive value of ∆ exp (+7 cm -1 ), the ∆ th shifts for S 1 , S 2 and S 3 , respectively equal to 16, 15 and -1 cm -1 , do not allow to clearly assign this band to a specific isomer. On the other hand, the presence of two bands very close in frequency at 3181.1 and 3184.8 cm -1 well correlate with our observations in the δ fundamental mode region and to very close ∆ th shift values for S 1 and S 2 . Consequently, these 2 bands are assigned to the (2δ) overtone of S 1 and S 2 with x δδ = -12.7 and -10.8 cm -1 , respectively.

DAC fundamentals

Besides the intense antisymmetric ν C=O as CO stretch at 1731 cm -1 , several slightly shifted bands were observed on both sides of three weaker intense infrared active DAC modes: the symmetric γ CH3 s and antisymmetric γ CH3 as at 950 and 1120.4 cm -1 and the δCH3 s symmetric bend CH 3 at 1360.5 cm -1 . [START_REF] Profeta | Quantitative Infrared Intensity Studies of Vapor-Phase Glyoxal, Methylglyoxal, and 2,3-Butanedione (Diacetyl) with Vibrational Assignments[END_REF][START_REF] Durig | Vibrational Spectra and Structure of Biacetyl[END_REF] Comparison between values of ∆ exp and ∆ th (Table 2) generally provides no clear tendency. Theoretical shifts derived from MP2/AVTZ frequency calculations give too large uncertainties which make doubtful any assignment when ∆ exp is smaller than 10 cm -1 .

In this context, we take advantage of argon matrix spectra recorded by Mucha and Mielke [START_REF] Mucha | Complexes of Atmospheric Alpha-Dicarbonyls with Water: FTIR Matrix Isolation and Theoretical Study[END_REF] for which two sets of bands were evidenced using annealing effects. The global agreement observed between ∆ exp values both measured in neon and argon matrices leads us to assign nine bonded DAC bands observed in neon matrix (cf Table 4).

Consequently, assigning experimental bands to a specific 1/1 isomer on the grounds of comparison with anharmonic ab initio calculations is not relevant to few perturbed DAC fundamentals, even in the favorable case of bonded ν C=O as bands, both intense (> 100 km/mol) and most shifted ones (3-10 cm -1 ) with respect to DAC monomer. The intermolecular mode region remains to investigate to evidence other fingerprints of the 1/1 isomers.

Intermolecular modes

The bands observed at 115.9, 282.1, 322.8, 545.5 and 547 cm -1 and correlated to a 1/1 dimer are compared with anharmonic calculated frequencies. Accounting for the detectivity of the neon matrix set-up, only modes with intensities larger than 35 km/mol are likely to be observed, which represents 14 possible intermolecular signatures including two low frequency modes of DAC (δC=O as and δC-C-C as) and three of the six intermolecular modes of 1/1 DAC/H 2 O isomers (γ H2O f , γ H2O b and δH2O). Some of them fall in far-IR windows where absorptions of DAC and of water complexes up to the tetramer are predominant (Figure 4). Among the five bands observed, three intermolecular ones and the bonded δC=O as DAC one are calculated close to neon matrix frequencies : γ H2O f (S 2 or S 3 ) for the 115.9 cm -1 band, γ H2O b (S 1 ) and γ H2O b (S 2 ) for the bands at 322.8 and 282.1 cm -1 , and δC=O as (S 1 or S 2 ) for the 545.5-547 cm -1 one. We have the opportunity to validate independently these intermolecular signatures in the near-IR range by the assignment of combinations of the type (ν intra + ν inter ).

Combination modes

In the 3900-4200 cm -1 range, four bands respectively at 3914.4, 4013.0, 4054.7 and 4139.6 cm -1 are correlated with a 1/1 dimer. Taking into account the calculated x ij anharmonic coupling constants for the three isomers at the MP2/AVTZ level, the numbering of all possible combinations of fundamental frequencies close to these bands provides the following (ν intra + ν inter ) sums: ν OHb (S 1 ) + 322.8 or ν OHb (S 2 ) + 322.8 for the 3914 cm -1 band, ν OHf (S 1 ) + 282.1 or ν OHf (S 2 ) + 282.1 for the 4013 cm -1 band, ν OHf (S 1 ) + 322.8 or ν OHb (S 1 ) + δH2O for the 4054.7 cm -1 band and ν OHb (S 2 ) + 545.5(547) for the 4139.6 cm -1 band.

The 3914.4 cm -1 band

On the grounds of the strong coupling calculated between ν OHb and γ H2Ob (x ij (calc) = 32 cm -1 for S 1 ), this band is assigned to the combination mode ν OHb (S 1 ) + γ H2O b (S 1 ) with x ij (exp) equal to 23.4 cm -1 rather than its analogue with S 2 which would give x ij equal to -2.6 cm -1 , very different from the calculated one (25 cm -1 for S 2 ). Consequently the 322.8 cm -1 band is unambiguously attributed to γ H2O b (S 1 ).

The 4013.0 cm -1 band

Using the same arguments, this band is associated to the combination mode ν OHf (S 2 ) + γ H2O b (S 2 ). Indeed x ij (exp) = -1.8 cm -1 is closer to x ij (calc) = 0 for S 2 while for its analogue with S 1 , a larger difference is observed between x ij (exp) = +4.2 cm -1 and x ij (calc) = -2 cm -1 , which enables to assign the 282.1 cm -1 band to γ H2O b (S 2 ).

The 4054.7 cm -1 band

The only possible assignment for this band is the analogue of the 4013 cm -1 band for S 1 , namely the combination ν OHf (S 1 ) + γ H2O b (S 1 ) which would give x ij (exp) = +5.1 cm -1 , reasonably close from the x ij (calc) value equal to -2 cm -1 .

The 4139.6 cm -1 band

The most probable attribution is the combination band ν OHb (S 2 ) + δC=O as but error margins in x ij (calc) values for S 1 and S 2 do not allow for unique assignment of the 545.5 and 547 cm -1 bands to the S 1 or S 2 isomer. The x ij (calc) value equal to +1 cm -1 for S 2 , slightly closer to x ij (exp) = -0.1 cm -1 with the 545.5 cm -1 band than x ij (exp) = -1.6 cm -1 with the 547 cm -1 one is not a decisive argument for an isomer assignment.

The assignments of other overtones and combination bands involving H 2 O fundamentals is rather straightforward, excepted for the band at 1927.7 cm -1 which could not be assigned to the combination δ + γ H2O b of the S 1 isomer because it would imply a very difference between x ij (exp) and x ij (calc) (+1.7 against -14 cm -1 ).

In summary, the analysis of neon matrix combination bands gives confidence for assigning the 282.1 and 322.8 cm -1 bands to the γ H2Ob mode of S 2 and S 1 isomers and the 545.5 and 547 cm -1 bands to the δC=O as mode of S 1 or S 2 . MP2/AVTZ anharmonic calculations well agree with neon matrix intermolecular frequencies (less than 5 % obs. -calc. difference). About the lowest frequency band at 115.9 cm -1 , anharmonic frequencies for the free OH rocking mode (γ H2O f ) of S 2 and S 3 are very close with similar intensities but the predominance of S 1 and S 2 isomers in the whole infrared range highly supports the assignment of the 115.9 cm -1 band to γ H2O f (S 2 ) . A balance sheet of our assignments clearly shows that intermolecular modes with intensities smaller than 80 km/mol could not be detected with our neon matrix set-up, excepted for the broad band observed around 547 cm -1 (main component) . likely composed of two δC=O as bands very close in frequency of S 1 and S 2 (calculated at 545 and 542 cm -1 with intensities around 40 km/mol). However, there exists a large discrepancy between calculated and experimental intensities for this band, the most intense one observed for the 1/1 complex. Other intermolecular modes could not be detected due to the probable overlap of the γ H2O f (S 1 ) mode by rotational bands of water monomer, and of the γ H2O f (S 2 ) mode by the acceptor wag mode of the water dimer at 122.6 cm -1 . [START_REF] Bouteiller | The Vibrational Spectrum of the Water Dimer: Comparison between Anharmonic Ab Initio Calculations and Neon Matrix Infrared Data between 14000 and 90 cm -1[END_REF] Table 4 gathers the intramolecular (fundamentals, combinations and two-quanta transitions) and intermolecular modes of mainly two isomers of the 1/1 dimer derived from the assignments of neon (or argon [START_REF] Mucha | Complexes of Atmospheric Alpha-Dicarbonyls with Water: FTIR Matrix Isolation and Theoretical Study[END_REF] ) matrix spectra and compared to anharmonic MP2/AVTZ ab initio calculations. Table 5 reports the anharmonic coupling constants derived from neon matrix experiments compared to corresponding MP2/AVTZ calculated ones.

The vibrational analysis of neon matrix spectra enabled to evidence several vibrational signatures of the S 1 and S 2 isomers of the 1/1 dimer. No evidence of the S 3 isomer could be proved in the whole infrared region. Overlapping with water clusters bands is always possible but we should expect that the less stable S 3 isomer bands are more difficult to observe experimentally than those of S 1 or S 2 isomers. Previous experimental studies have focused either on one (S 1 for the microwave study [START_REF] Favero | Hydrated Complexes of Atmospheric Interest: Rotational Spectrum of Diacetyl-Water[END_REF] ) or two isomeric forms (S 1 and S 2 for the argon matrix study [START_REF] Mucha | Complexes of Atmospheric Alpha-Dicarbonyls with Water: FTIR Matrix Isolation and Theoretical Study[END_REF] ) while three nearly isoenergetic forms were calculated. [START_REF] Dargent | Energy, Structure and Topological Characterization of the Isomers of The 1/2 Diacetyl/Water Complex[END_REF] Nevertheless, our neon matrix set-up enables to probe the whole infrared region, particularly the far-infrared region where significant frequency differences are often observed between the intermolecular modes of isomeric forms. On the other hand, bonded intramolecular frequencies are either too weakly shifted with respect to the free ones, or overlapped by water clusters. Due to the comparable binding energy D 0 of water dimer [START_REF] Feyereisen | Hydrogen Bond Energy of The Water Dimer[END_REF] and trimer [START_REF] Nielsen | Accurate Structures and Binding Energies for Small Water Clusters: The Water Trimer[END_REF] (13 and 44 kJ/mol, respectively) with respect to those of most stable isomers of 1/1 and 1/2 (17 and 53 kJ/mol, respectively), a delicate balance should be found to maximize the absorption signals of hetero water clusters containing DAC with respect to those of pure water ones.

About the microwave study reported by Favero and Caminati [START_REF] Favero | Hydrated Complexes of Atmospheric Interest: Rotational Spectrum of Diacetyl-Water[END_REF] it would be interesting to bring a definite answer about the presence of other isomers than S 1 in the jet-cooled He seeded pulsed expansion of very diluted DAC/H 2 O mixtures. It is difficult to anticipate a priori the stabilization of slightly less stable isomers, by considering the quick relaxation in axisymmetric supersonic expansions toward very low rotational temperatures (around 1 K). The rather weakly relaxing effect of helium with respect to argon is rather favorable to stabilize also less stable isomers with small differences of binding energies with respect to the most stable one, unless that these conformers are separated by low interconversion barriers. [START_REF] Ruoff | Relaxation of Conformers and Isomers in Seeded Supersonic Jets of Inert Gases[END_REF] The 1/2 complex Among the neon matrix bands assigned to the 1/2 complex, we are focusing on the bands at 3503.7 and 3555.8 cm -1 assigned to bonded OH stretching modes more red shifted than the 1/1 dimer, in agreement with the increase of the vibrational red shift depending on the size of pure water clusters. [START_REF] Cirtog | The (CH 2 ) 2 O-H 2 O Hydrogen Bonded Complex. Ab Initio Calculations and Fourier Transform Infrared Spectroscopy from Neon Matrix and a New Supersonic Jet Experiment Coupled to the Infrared AILES Beamline of Synchrotron SOLEIL[END_REF]18 The frequency positions of neon matrix bands are rather close of jet-cooled 1/n bands estimated at about 3497 and 3560 cm -1 in the spectrum rich in water (Figure 2c), and should correspond to OH stretching bands of the 1/2 complex. The three most stable isomers noted π_like_(H 2 O) 2 _side_P2, π_like_(H 2 O) 2 _side_P1 and P1_(H 2 O) 2 in a recent paper [START_REF] Dargent | Energy, Structure and Topological Characterization of the Isomers of The 1/2 Diacetyl/Water Complex[END_REF] will be designated hereafter by T1, T2 and T3. The bonded OH stretching ν OHb1 mode of the water molecule in interaction with the carbonyl group should be distinguished from the ν OHb2 mode in interaction with the oxygen atom of the second water molecule. We are searching now to attribute these bands to a specific isomer with the support of ab initio calculations. Experimental and harmonic MP2/AVDZ 30 calculated frequencies relative to the OH stretching modes of the most stable isomers of the 1/2 complex and water dimer are gathered in Table 6. Structure optimizations revealed that most stable 1/2 isomers are predominantly water dimers interacting with the diacetyl molecule. [START_REF] Dargent | Energy, Structure and Topological Characterization of the Isomers of The 1/2 Diacetyl/Water Complex[END_REF] Consequently, we compared experimental (∆ exp ) and theoretical (∆ th1 , ∆ th2 and ∆ th3 ) frequency differences between the three 1/2 isomers and the water dimer, The ∆ exp values for ν OHb2 and ν OHb1 , respectively equal to -86 and -34 cm -1 , are largely closer to ∆ th1 than ∆ th3 , and at a least degree than ∆ th2 On these grounds, we tentatively assign these two experimental bands to the T1 isomer. However, we cannot fully exclude the T2 isomer because MP2 calculations tend to overestimate vibrational shifts (by about 10 % for the 1/1 isomers). The other 1/2 bands observed at 4098.9, 5110, 6881 and 7232.3 cm -1 are attributed to (ν OHf + 375), (ν OHb2 + δ), (2ν OHb2 ) and (ν OHb2 + ν OHf ) combination bands, respectively.

Conclusion

In the present work, Fourier transform spectra of diacetyl-water complexes have been recorded in neon matrix spectra over the whole infrared range, and in a supersonic jet in the OH stretching region of H 2 O, to find vibrational signatures aiming to characterize the conformational landscape of binary and ternary hydrated complexes.

About the 1/1 dimer, vibrational analyses of FTIR neon matrix spectra have been realized with the support of high level anharmonic MP2/AVTZ calculations to guide our attributions:

-Several vibrational signatures of the two most stable isomers S 1 and S 2 have been unambiguously identified from the fundamentals, combinations and overtones (9 for S 1 , 9 for S 2 ). -No vibrational signature could be proved for the less stable S 3 isomer even in the intermolecular mode region. Two possible reasons could be explain this result : (i) the expected lower population of the less stable S 3 isomer makes more probable the overlapping of S 3 bands by small water clusters and DAC monomer bands, (ii) the neon matrix technique reached its limits in the case of DAC-H 2 O system to properly discriminate vibrational bands of 1/1 heterodimers likely to be masked by intense bands of water and DAC monomers in the mid-IR range, or of pure water dimer and trimer in the far-IR range.

The present solid neon study coupled to FT spectroscopy also reveals the difficulty to characterize hetero hydrated clusters beyond dimer because of recurrent overlapping bands and competition with water clusters. However, in the H 2 O stretching region where large red shifts enable to discriminate between water trimer and the 1/2 complex, two bonded OH bands could be tentatively assigned to the most stable isomer noted T1 on the grounds of relative vibrational shifts between water dimer and the three most stable 1/2 complexes, both characterized by the presence of a water dimer interacting with the diacetyl molecule and large cooperative effects in terms of interaction energies. [START_REF] Dargent | Energy, Structure and Topological Characterization of the Isomers of The 1/2 Diacetyl/Water Complex[END_REF] As a perspective, high resolution gas phase rovibrational spectroscopy coupled to supersonic expansions recently proved its capacity to untangle the conformational landscape of weakly bound complexes or to discriminate between small sized clusters. [START_REF] Rezaei | Infrared Spectra Reveal Box-Like Structures for a Pentamer and Hexamer of Mixed Carbon Dioxide-Acetylene Clusters[END_REF]35 In a near future, the present neon matrix study could be exploited to target a spectral region favorable to the searching of hetero hydrated clusters using the tunable IR laser spectrometer coupled to a pulsed supersonic jet recently developed in our group. a Assignments from annealing effects in argon matrix spectra 15 b The assignment of the band at 115.9 cm -1 to the S 3 isomer is not fully discarded (cf text)

Figure 1 :

 1 Figure 1: The three isomers for the 1/1 complex optimized at MP2/AVTZ level of theory.

Figure 2 :

 2 Figure 2: Jet-AILES FTIR spectrum in the OH bonded and free stretching region of water containing complexes recorded at 0.5 cm -1 resolution for different dilutions of the ternary mixture DAC/H 2 O/Ar: (a) 0/8/1000, (b) 8/8/1000, (c) 8/16/1000. The notation D stands for water dimer, T for water trimer, Q for water tetramer and P for water pentamer.

Figure 3 :

 3 Figure 3: Neon matrix spectra after deposition at 3.5 K recorded in the OH stretching region of H 2 O monomer, H 2 O and 1/1 dimers for different dilutions of the ternary mixture DAC/H 2 O/Ne: (a) 2/0/1000, (b) 0/1/16000, (c) 1/0.025/1000. The notation W stands for H 2 O monomer and D for water dimer.

Figure 4 : 29 Page

 429 Figure 4: Neon matrix spectra after deposition at 3.5 K recorded in the intermolecular mode region of H 2 O dimer and trimer and 1/1 dimers for different dilutions of the ternary mixture DAC/H 2 O/Ne: (a) 6/0/1000, (b) 0/1/1000, (c) 6/1/1000. The notation D stands for H 2 O dimer, T for H 2 O trimer, Q for H 2 O tetramer. Neon matrix assignments for water dimer and trimer in the intermolecular mode region come from Perchard et al.,[START_REF] Bouteiller | The Vibrational Spectrum of the Water Dimer: Comparison between Anharmonic Ab Initio Calculations and Neon Matrix Infrared Data between 14000 and 90 cm -1[END_REF][START_REF] Tremblay | The Vibrational Spectrum of the Water Trimer: Comparison between Anharmonic Ab Initio Calculations and Neon Matrix Infrared Data between 11000 and 90 cm -1[END_REF] and those for water tetramer from Ceponkus et al.[START_REF] Ceponkus | Intermolecular Vibrations of the Water Trimer, a Matrix Isolation Study[END_REF]

Figure 5 :

 5 Figure 5: Neon matrix spectra after deposition at 3.5 K recorded in the 3900-4200 cm -1 region of ν(OH) + ν inter combinations of small H 2 O and DAC-H 2 O clusters for different dilutions of the ternary mixture DAC/H 2 O/Ne: (a) 6/0/1000, (b) 0/2/1000, (c) 3/3/1000.

Figure 6 :

 6 Figure 6: Neon matrix spectra after deposition at 3.5 K recorded in the OH stretching region of small H 2 O cluster, 1/1 and 1/2 complexes for different dilutions of the ternary mixture DAC/H 2 O/Ne: (a) 0.17/0.3/1000, (b) 0.5/0.3/1000, (c) 0.5/1/1000. The presence of the band at 3580 cm -1 , assigned to the N 2 -(H 2 O) 2 trimer, is due to small leaks of N 2 (tens of ppm) in the gas line.

Table 3

 3 gathers all the vibrational bands of H 2 O and DAC monomers, 1/1 and 1/2 complexes observed in the present work from neon matrix experiments and compared to argon matrix data of Mucha and Mielke.

Page 17 of 27 ACS Paragon Plus Environment The Journal of Physical Chemistry

	S 1	S 2	S 3
	A e 0.16093	0.11351	0.08234
	A 0 0.15938 (0.159688) 0.11219	0.08152
	B e 0.04154	0.05226	0.07044
	B 0 0.04046 (0.040464) 0.05067	0.07051
	C e 0.03342	0.03625	0.05473
	C 0 0.03272 (0.032735) 0.03562	0.05526
	D e 24.7	24.8	21.8
	D 0 17.5	17.5	16.2

Table 1 :

 1 Equilibrium (X e ) and ground state (X 0 ) rotational parameters (cm -1 ) and binding energies (kJ.mol -1 ) for 1/1 isomers. MP2/AVTZ (Experimental).[START_REF] Favero | Hydrated Complexes of Atmospheric Interest: Rotational Spectrum of Diacetyl-Water[END_REF]

					ν		∆ν
			Monomers S 1	S 2	S 3	S 1 S 2 S 3
	H 2 O	ν OHf ν OHb	3768 3654	3733 (135) 3737 (152) 3742 (90) 3548 (334) 3582 (298) 3624 (10)	-35 -31 -26 -106 -72 -30
		δ	1578	1594 (90)	1593 (62)	1577 (133)	16 15 -1
		ν C=O as 1703	1703 (98)	1702 (161) 1706 (151)	0 -1	3
		ν C=O s 1696	1692 (67)	1697 (40)	1699 (6)	-4 1	3
	Diacetyl	δCH3 s 1353 γ CH3 as 1116 γ CH3 s 943	1358 (58) 1126 (70) 945 (5)	1361 (60) 1125 (60) 946 (4)	1350 (63) 1121 (63) 947 (8)	5 10 9 8 2 3	-3 5 4
		δC=O as 535	545 (37)	542 (39)	537 (42)	10 7	2
		δC-C-C as 253	247 (50)	236 (15)	231 (35)	-6 -17 -22
	Inter.	δH2O γ H2O b γ H2O f		479 (60) 315 (129) 14 (118)	407 (60) 297 (143) 208 (72) 231 (46) 140 (110) 138 (113)

Table 2 :

 2 Calculated frequencies (cm -1 ) of the main bands observed for the isomers of 1/1 complex and the corresponding frequencies of monomers. The shifts from monomer frequencies (∆ν) and anharmonic MP2/AVTZ frequencies (harmonic intensities in parenthesis in km.mol -1 ) are also reported.

	Neon matrix	Argon matrix a

Table 3 :

 3 Observed frequencies of H 2 O and DAC monomers, 1/1 and 1/2 complexes in the present neon matrix experiments compared to those obtained in the previous argon matrix study of Mucha and Mielke.[START_REF] Mucha | Complexes of Atmospheric Alpha-Dicarbonyls with Water: FTIR Matrix Isolation and Theoretical Study[END_REF] Experimental intensities of most 1/1 bands, referenced with respect to the intensity of the 3568.2 cm -1 band set to 100, are reported between parentheses.

		Neon matrix			Ab initio
		S 1	S 2	S 1		S 2		S 3
	Fundamentals
	γ H2O f		115.9 b	<102 * (118) 140	(110) 138	(113)
	γ H2O b	322.8	282.1	315	(129) 297	(143) 208	(72)
	δC=O as	545.5 / 547	545	(37)	542	(39)	537	(42)
	γ CH3 s	952 a	946.4 a	945	(5)	946	(4)	947	(8)
	γ CH3 as	1126.7 a 1123.8 a	1126	(70)	1125 (60)	1121	(63)
	δCH3 s	1363.3 a 1361.5 a	1358	(58)	1361 (60)	1350	(63)
	δ	1603.2 1603.2	1594	(90)	1593 (62)	1577	(133)
	ν C=O as	1721.6 a 1726.1 a	1703	(98)	1702 (161) 1706	(151)
	ν OHb	3568.2 3594.2	3548	(334) 3582 (298) 3624	(10)
	ν OHf	3726.8 3732.7	3733	(135) 3737 (152) 3742	(90)
	Combination modes
	ν OHb + γ H2O b	3914.4
	ν OHf + γ H2O b	4054.7 4013.0
	ν OHb + δC=O as	4139.6
	δ + ν OHb	5163.9 5189.3
	Two quanta modes
	2δ	3181.1 3184.8
	2ν OHb	6956.8 7020.4

Table 4 :

 4 Attribution of vibrational bands (fundamentals, combination modes and two-quanta transitions) of the S 1 and S 2 isomers of the 1/1 dimer observed in neon matrix experiments in the far-mid-and near-infrared regions, compared to the anharmonic MP2/AVTZ frequencies. All wavenumbers are expressed in cm -1 . Harmonic infrared intensities are reported in parentheses in km/mol. The notation * corresponds to the harmonic frequency of the γ H2Of mode for the S 1 isomer.

			δ		ν OHb	ν OHf
			S 1	S 2	S 1	S 2	S 2
		S 1			23.4 [32]
	γ H2O b	S 2				-1.8 [0]
	δC=O as	S 2				-1.6/-0.1 [1]
		S 1	-12.7 [-18.3]		-7.3 [-12.0]
	δ	S 2		-10.8 [-17.6]		-8.2 [-13.9]
	ν OHb	S 1 S 2			-89.6 [-81.5]	-84.1 [-72.2]

Table 5 :

 5 Anharmonic coupling constants (cm -1 ) for the S 1 and S 2 isomers of the 1/1 dimer derived from neon matrix experiments. Calculated constants from VPT2 calculation at MP2/AVTZ level of theory are reported in square brackets.

			MP2/AVDZ			Neon matrix
	(H 2 O) 2	T1	T2	T3	(H 2 O) 2 1/2
	ω(I_IR)	ω(I_IR)	∆ th1 ω(I_IR)	∆ th2 ω(I_IR)	∆ th3 ν	ν	∆ exp
	ν OHb2 3704 (280) 3616 (184) -88 3606 (207) -98 3599 (439) -105 3590 3504 -86
	ν OHb1 -	3675 (328) -29 3666 (345) -38 3647 (509) -57 -	3556 -34
	D 0	53.4	52.9	42.6

Table 6 :

 6 Calculated harmonic MP2/AVDZ and neon matrix vibrational frequencies (cm -1 ) of the OH stretching modes for the three most stable isomers of the 1/2 complex. Harmonic infrared intensities are reported in parentheses in km/mol. The notation ∆ corresponds to the experimental or calculated vibrational shift (cm -1 ) of the two intramolecular modes of the three isomers perturbed with respect to the pure water dimer. MP2/AVDZ binding energies D 0 are also reported (kJ.mol -1 )

	Page

22 of 27 ACS Paragon Plus Environment The Journal of Physical Chemistry SM1

  : Calculated and experimental vibrational properties of water and diacetyl monomer. Harmonic frequencies, [anharmonic frequencies], (harmonic IR intensities), experimental frequencies. Wavenumbers in cm -1 , intensities in km.mol -1 : stretching δ : bending γ : rocking τ : torsion s: symmetric as: antisymmetric Experimental data from Refs 23 and 24 (a), this work (b) and Ref 25 (c)

				Ab initio		Experiment
		Vibrational		MP2/AVTZ	IR	Raman
		mode (symmetry)				Gaz a	Ne Matrix a	Liquid a
		ν OH as (b2)	3948 [3768] (75)	3756 3759
		ν OH s (a1)	3822 [3654] (6)	3657 3665
	H 2 O	δ (a1)	1628 [1578] (72)	1595 1596
		νCH 3 as (b u )	3209 [3065] (7)	3024 3037
		νCH 3 as (a g )	3209 [3065] (0)	3016
		νCH 3 as (b g )	3164 [3019] (0)	2978
		νCH 3 as (a u )	3163 [3019] (2)	2979 2995
		νCH 3 s (b u )	3083 [2969] (1)	2945 2947
		νCH 3 s (a g )	3083 [2969] (0)	2928
		νC=O as (b u )	1736 [1703] (166)	1729 1731
		νC=O s (a g )	1734 [1696] (0)	1720
		δCH 3 as (b g )	1485 [1431] (0)	1431
		δCH 3 as (a u )	1480 [1428] (20)	1426 1433
		δCH 3 as (b u )	1473 [1429] (31)	1424 1426
		δCH 3 as (a g )	1473 [1427] (0)	1424
		δCH 3 s (a g )	1408 [1365] (0)	1364
	Diacetyl	δCH 3 s (b u ) νC-C (ag) γCH 3 (b u )	1395 [1353] (58) 1309 [1277] (0) 1147 [1120] (67)	1360 1358 1116 1121	1275
		γCH 3 (b g )	1073 [1046] (0)	1050
		γCH 3 (a g )	1018 [998] (0)	1005
		γCH 3 (a u )	968 [943] (4)	950	950
		νC-CH 3 as (b u )	927 [908] (20)	912	907
		νC-CH 3 s (a g )	704 [686] (0)	685
		γC =O s (b g )	619 [609] (0)	608
		δC=O as (b u )	539 [535] (39)	540	540
		δC=O s (a g )	526 [521] (0)	537
		δC-C-C s (a g )	363 [363] (0)	369
		γC =O as (a u )	345 [348] (6)	340	348
		δC-C-C as (b u )	239 [253] (16)	249	251
		τCH 3 s (b g )	128 [121] (0)
		τCH 3 as (a u )	127 [121] (0)	112
		τC-C (a u )	55	[47]	(11)	48

ν

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