Theoretical Spectroscopic Study of Two Ketones of Atmospheric Interest: Methyl Glyoxal (CH3COCHO) and Methyl Vinyl Ketone (CH3COCH=CH2)

Two ketones of atmospheric interest, methyl glyoxal and methyl vinyl ketone, are studied using explicitly correlated coupled cluster theory and core–valence correlation-consistent basis sets. The work focuses on the far-infrared region. At the employed level of theory, the rotational constants can be determined to within a few megahertz of the experimental data. Both molecules present two conformers, trans/cis and antiperiplanar (Ap)/synperiplanar (Sp), respectively. trans-Methyl glyoxal and Ap-methyl vinyl ketone are the preferred structures. cis-Methyl glyoxal is a secondary minimum of very low stability, which justifies the unavailability of experimental data in this form. In methyl vinyl ketone, the two conformers are almost isoenergetic, but the interconversion implies a relatively high torsional barrier of 1798 cm–1. A very low methyl torsional barrier was estimated for trans-methyl glyoxal (V3 = 273.6 cm–1). Barriers of 429.6 and 380.7 cm–1 were computed for Ap- and Sp-methyl vinyl ketone. Vibrational second-order perturbation theory was applied to determine the rovibrational parameters. The far-infrared region was explored using a variational procedure of reduced dimensionality. For trans-methyl glyoxal, the ground vibrational state was estimated to split by 0.067 cm–1, and the two low excited energy levels (1 0) and (0 1) were found to lie at 89.588 cm–1/88.683 cm–1 (A2/E) and 124.636 cm–1/123.785 cm–1 (A2/E). For Ap- and Sp-methyl vinyl ketone, the ground vibrational state splittings were estimated to be 0.008 and 0.017 cm–1, respectively.


■ INTRODUCTION
Atmospheric processes involving volatile organic compounds (VOCs), such as the oxidation of isoprene (C 5 H 8 ) by hydroxyl radicals and ozone, lead to the formation of methyl vinyl ketone (MVK, CH 3 COCHCH 2 , butenone), further oxidation of which produces methyl glyoxal (CH 3 COCHO) and other products. 1,2 Methyl glyoxal has been recognized as an important precursor of secondary organic aerosols (SOAs) through an atmospheric heterogeneous process. 3 It has a short lifetime (∼2 h in daytime) and can also be taken up by aqueous aerosols and cloud droplets on account of their high water solubility. 3 Thus, methyl glyoxal, which is a reduced derivative of pyruvic acid, 1 represents an atmospherically important dicarbonyl compound produced in the atmosphere from the oxidation of a number of biogenic and anthropogenic VOCs. 3 When nitrogen oxide abundances are low, acetone is an efficient secondary precursor. 3 UV photolysis and the reaction with hydroxyl radical are the main gas-phase loss processes for methyl glyoxal 1 and yield carbon monoxide, acetaldehyde, and formaldehyde.
On the other hand, MVK can originate from the primary emissions produced by fuel evaporation and combustion in urban areas and by biomass burning. 4,5 For short unsaturated ketones, atmospheric destruction is mostly controlled by the reaction with OH radicals. 6 Atmospheric oxidation of unsaturated ketones produces a variety of products following the addition of the oxidant to the double bond. Both photolysis and reaction with OH radicals are very effective loss processes for unsaturated dicarbonyls, leading to lifetimes of a few hours. The reaction of MVK with OH has been investigated in atmospheric simulation chambers. 7 Atmospheric research on pollutants requires previous laboratory studies contemplating structural and spectroscopic properties and chemical processes. Different theoretical and experimental techniques can be employed. 6 Ab initio calculations can help the interpretation of the observations, providing viewpoints that are especially relevant for features that are difficult to address experimentally. Unfortunately, few previous works have been devoted to methyl glyoxal and MVK. The first electronic transitions of α,β-dicarbonyls, such as glyoxal and its methyl derivatives, have been extensively studied. 8−12 Franck− Condon analysis of methyl glyoxal shows unambiguously that excitation from the ground state to the lowest triplet state is accompanied by a rotation of the methyl group. A similar change occurs in the first excited singlet state. 8 Assignments of the electronic transitions or studies of the photodissociation processes must take into account the torsional structure of the methyl derivatives. 12 Detailed assignments of the vibronic bands in the dispersed fluorescence spectra due to the S 1 (n, π*) ← S 0 transition were made. The complicated vibrational structures of the fluorescence and phosphorescence excitation spectra of methyl glyoxal and diacetyl were analyzed in terms of the internal rotational modes of the methyl group and the skeletal modes of the glyoxal framework.
The rotational and vibrational spectra of both methyl glyoxal and MVK have been previously measured and assigned. 13−23 Both molecules show two stable conformers of C s symmetry that interconvert through large-amplitude motions, although spectroscopic data are unavailable for cis-methyl glyoxal. The rotational spectrum of trans-methyl glyoxal was first measured and assigned by Dyllick-Brenzinger and Bauder, 13 who provided the rotational constants, the components of the electric dipole moment (μ a = 0.1597 (11), μ b = 0.9620 (7)), and the internal rotation barrier (V 3 = 269.1(3) cm −1 ). The methyl torsional fundamental was predicted at 101.6 cm −1 from the results of the internal rotation splittings, although a considerably higher value of 122.7 cm −1 was determined from the relative intensity measurements. The authors found the interaction between the methyl and skeletal torsions to be the origin of this discrepancy. Recently, Bteich et al. 14 measured the rotational spectrum in its ground vibrational state in the 4−500 GHz region. The torsion of the central bond was studied by Fateley et al. 15 Profeta et al. 16 provided the pressure-broadened quantitative infrared spectrum covering the 520−6500 cm −1 range with a resolution of 0.112 cm −1 . To complete the vibrational assignments, the far-infrared (FIR) spectrum in the 25−600 cm −1 region was reported in the same paper. 16 Previous experimental 17−23 and theoretical 24−26 studies of methyl vinyl ketone are available. The IR and Raman spectra have been described. 18−20 Two stable geometries, the antiperiplanar (A p ) and synperiplanar (S p ) conformers, have been identified, although old studies attended to the most stable conformer A p . The rotational spectrum of the A p form was first analyzed in 1965 by Foster et al. 17 The methyl group internal rotation barrier was estimated to be V 3 = 437.19 cm −1 (1250 ± 20 cal/mol) and the electric dipole moment to be 3.16 ± 0.05 D. 17 The torsional splittings and the interaction between the methyl and skeletal torsions were considered in the work of Fantoni et al. 21 for the antiperiplanar form. The presence of a very stable secondary minimum was reported for the first time in 2011 in the microwave study of Wilcox et al. 22 Recently, a rotational study of both conformers was performed by Zakharenko et al. 23 The present study is based on highly correlated ab initio calculations. The goal is to provide structural and spectroscopic theoretical data with an emphasis on the FIR region following the same procedure employed for the interconnecting carbonyl species pyruvic acid and acetone. 27−29 We study both molecules  The Journal of Physical Chemistry A pubs.acs.org/JPCA Article in the same paper because they share properties. Both species can be considered as acetone derivatives in which one acetone methyl group has been substituted by another functional group, −CHO or −CH�CH 2 . Both species present two interacting torsional modes. The work represents a step of a general project dealing with atmospheric ketones. We seek to underline aspects that are not fully understood or are the object of discussion. In methyl glyoxal, the cis structure is almost unidentified, and discrepancies due to the strong coupling between the two torsional modes are present in the previous assignments of the spectra of the trans structure. For both conformers, special attention is given to the FIR region. In MVK, the coupling between large-amplitude motions hinders the assignments. Both species show very low methyl torsional barriers (V 3 < 400 cm −1 ), whose effects make interpretation difficult.
The FIR spectra of the two species are simulated using a variational procedure of reduced dimensionality implemented in an original code that uses data from ab initio calculations as input. This procedure allows us to provide information concerning the large-amplitude motions and the interactions, barriers, and torsional parameters and to map the low-lying vibrational states and their splittings. This information can be useful for the interpretation of measurements in the FIR region and also can help in the assignments of rotational and rovibrational spectra.

■ THEORETICAL METHODS
The geometries of the minimum-energy structures and the ab initio potential energy surfaces of reduced dimensionality were computed using explicitly correlated coupled cluster theory with single and double substitutions augmented by a perturbative treatment of triple excitations (CCSD(T)-F12b) 30,31 as implemented in Molpro 32 using default options. All of the core and valence electrons were correlated in the post-SCF process. The core−valence correlation-consistent basis set cc-pCVTZ-F12 developed for the explicitly correlated methods was employed as the basis set in connection to the additional basis sets optimized for use in the resolution of the identity. 33 In all of the work, different levels of theory were selected by taking into consideration the required precision and the available computational tools. Second-order Møller-Plesset perturbation theory (MP2) 34 as implemented in Gaussian 16, revision C.01 35 was employed in connection with the aug-cc-pVTZ (AVTZ) basis set 36 to obtain anharmonic spectroscopic properties and the vibrational corrections for the rotational parameters and potential energy surfaces. The full-dimensional anharmonic force field was determined at all of the minima.
Vibrational second-order perturbation theory (VPT2) as implemented in Gaussian 16, revision C.01 37 was employed to obtain spectroscopic properties for the low-and mediumamplitude vibrational motions. The two torsional modes were studied variationally using the code ENEDIM 38−40 following a procedure that allows mapping of the low-lying vibrational energy levels and the splittings.   Throughout the work, to save computational time, different levels of ab initio calculation were employed and combined. First-order parameters (structures, equilibrium rotational constants) were computed using CCSD(T)-F12 theory, whereas the vibrational corrections were determined at a lower level of theory such as MP2. Then the relevant contributions to the observable parameters were obtained and found to be very accurate. Further corrections are less dependent on the correlation energy.

■ RESULTS AND DISCUSSION
Structures of the Conformers. Both methyl glyoxal and MVK show two conformers, trans/cis and A p /S p , respectively. trans-Methyl glyoxal and A p -MVK are the preferred structures. In trans-methyl glyoxal, "trans" refers to the relative positions of the two oxygen atoms with respect to the C1−C2 bond. In A p -MVK, "antiperiplanar" refers to the relative positions of the two double bonds. In Table 1, the corresponding structural parameters computed at the CCSD(T)-F12/CVTZ-F12 level of theory are collected. For the computation, all of the core and valence electrons were correlated in the post-SCF process. For an easy understanding of Table 1, Figure 1 shows the atom distributions in the most stable geometries. Table 1 shows the CCSD(T)-F12/CVTZ-F12 equilibrium rotational constants and the MP2/AVTZ components of the electric dipole moment referred to the principal axes system, the relative energies of the conformers, and the two torsional barriers, V 3 (methyl group torsion) and V α (central bond torsion). The vibrationally corrected relative energies of the conformers are shown in Figure 2. The energy profiles accompanying the conformer conversions are represented in Figures 3 and 4.
For methyl glyoxal, the relative energy between the conformers was computed to be ΔE = 1835 cm −1 , and the relative     Figures 3, 4, and 5 are one-dimensional cuts of the potential energy surfaces described in the next sections. The barrier for the trans → cis process was estimated to be 1980 cm −1 , assuring the prominent feasibility of the trans form. The inverse cis → trans process, which is restricted by a very low barrier of ∼150 cm −1 , can occur at very low temperatures. This draws a secondary cis minimum of very low stability and justifies the unavailability of experimental data for the cis form.
On the other hand, in MVK the A p → S p process shown in Figure 4 is restricted by a barrier of 1798 cm −1 . The A p and S p conformers are almost isoenergetic, but their interconversion is hampered by the relatively high torsional barrier.
The methyl torsional barriers of trans-and cis-methyl glyoxal were computed to be 273.6 and 361.9 cm −1 at the CCSD(T)-F12/CVTZ-F12 level of theory. For the trans form, the barrier is in very good agreement with the experimental value of 271.718(24) cm −1 . 14 In A p -and S p -MVK, these parameters were estimated to be 429.6 and 380.7 cm −1 , respectively, which can be compared with the experimental values of 443.236(78) and 385.28(30) cm −1 , respectively. 23 Contrary to what is usual, there is better agreement between the calculated and experimental values for the secondary minimum than for the preferred one. It must be considered that the two structures are almost isoenergetic. 41 Figure 5 shows the energy variation with the internal rotation of the methyl groups computed for different α values. Differences between the profiles denote the potential interactions between the two torsional modes of each molecule.
In a previous work devoted to acetone, 28 the computed methyl torsional barrier of acetone (V 3 = 246 cm −1 ) 28 was compared with those of methyl formate (V 3 = 368 cm −1 ) 42 and dimethyl ether (V 3 = 951 cm −1 ). 43 The theoretical work, 28 which was performed using highly correlated ab initio methods, highlighted the effects derived from the very low barrier of acetone, which made the computation of the low vibrational energy levels and the force field using numerical derivatives challenging. Effects that made the experimental spectrum assignments difficult were also observed (see ref 28 and references therein). Computations of the rovibrational parameters were less problematic for methyl formate 42 and dimethyl ether, 43 for which the barriers are higher than in acetone. Thus, trans-methyl glyoxal can be expected to behave like acetone. In MVK, the barriers are like that of methyl formate.
Rovibrational Parameters. The ground vibrational state rotational constants B 0 shown in Table 2 were computed using the following equation and the CCSD(T)-F12/CVTZ-F12 equilibrium rotational constants: where ΔB vib is the vibrational contribution derived from the VPT2 α r i vibration−rotation interaction parameters determined from the MP2/AVTZ cubic force field. In Table 2, the computed results are compared with experimental results. All of these experimental parameters are referred to the principal axis system, although different authors employed different definitions of the reference axis and effective Hamiltonians (principal axis method (PAM), rho axis method (RAM), or internal axis method (IAM)).
It is worth noting the very good agreement between the computed and experimental data for the three rotational constants. In previous studies, we determined the parameters discriminating valence and core electrons. Correlation effects due to the valence electrons were evaluated at the CCSD(T)-F12 level of theory, while CCSD(T) theory was used to describe the core correlation effects. [27][28][29]45,46 Generally, the approximation led to an error in one of the constants larger than for the other two parameters. In the present case, both correlation effects were treated together using CCSD(T)-F12 and a suitable basis set. In the absence of high-resolution IR data, the microwave parameters are the only experimental values to be compared with calculations. This at least qualitatively gives an estimation of the accuracy one should expect for the FIR predictions described in the next sections.
The computed parameters are closer to the available experimental ones derived with the PAM and IAM methods (| B calcd − B exptl | < 2 MHz) than those obtained using RAM. This last fitting procedure is more suitable for species showing low internal rotation barriers. The differences are similar for methyl glyoxal, showing a lower barrier than for MVK. They can be related to the number of fitting parameters, to the MP2/AVTZ force field accuracy, or to the theoretical procedure applied for the computation of the α r i vibration−rotation interaction parameters developed for semirigid systems. In addition to a different model Hamiltonian, the data from refs 14 and 23 include many more and much higher energy levels obtained from microwave spectra. The constants are then expected to be more accurate but are also effective due to the RAM Hamiltonian. Table 3 collects the quartic centrifugal distortion constants. For trans-methyl glyoxal, the computed values are compared with those of ref 13 obtained using the Watson asymmetrically reduced Hamiltonian. 47 Some discrepancies with the experimental data are relevant for Δ J and Δ K , we omit the sextic constants. The quartic centrifugal distortion constants are provided to complete the theoretical information on this research.
Vibrational Fundamentals. The vibrational energies for all of the vibrational modes were computed using the following equation: where the ω i are the harmonic fundamentals, v i and v j are vibrational quanta, and x ij are the anharmonic constants. The "harmonic contribution" was obtained using CCSD(T)-F12/ AVTZ-F12, whereas the anharmonic constants were derived using VPT2 and the MP2/AVTZ force field. The anharmonic fundamentals are shown in Table 4.
The calculated values are compared with available experimental data from refs 11, 15, and 16 in the case of methyl glyoxal and from ref 19 in the case of methyl vinyl ketone. In general, there is an expectable agreement between computations and observations for the medium and high frequencies. An exception ensues for the modes ν 18  Fermi displacements were predicted using VPT2 as implemented in Gaussian 16 35 and the cubic force field. Those displacements were considered to obtain the values Figure 6. Two-dimensional potential energy surfaces of the methyl-glyoxal and methyl vinyl ketone. The Journal of Physical Chemistry A pubs.acs.org/JPCA Article shown in Table 4. The bands that are strongly affected by the interactions are emphasized in boldface type. Previous studies of trans-methyl glyoxal evidence disagreements for the assignments of the ν 20 and ν 21 torsional modes because for both normal modes the methyl and C−C CH 3 torsions present strong interactions. 13 Therefore, separability of the two torsions is not feasible. This was highlighted in ref 14, attending to the displacement L matrices. Then the lowestfrequency mode, assigned in ref 11 to the methyl torsional mode, is attributed in ref 14 to the C−C torsion. The present results and the analysis of the internal coordinate contributions to the normal modes, as well as the wave functions derived from the variational procedure, confirm the calculations of Bteich et al., 14 which are in good agreement with the assignments of Profeta et al. 16 To obtain a better understanding, we determined the band positions for three different isotopic varieties using the variational procedure described below. In Table 5, the resulting frequencies are compared with harmonic frequencies computed using the MP2/AVTZ force field. Those results allow us to assign ν 20 and ν 21 to the methyl and C−C torsional modes, respectively.
Far-Infrared Region. The low-lying vibrational energy levels corresponding to the two torsional modes, the methyl torsion θ and the C−C torsion α, were obtained by solving the following Hamiltonian variationally: 38−40 This Hamiltonian was defined by assuming the separability of the two torsional modes from the remaining vibrational modes on the basis of vibrational energies and the predicted resonances derived from VPT2. In eq 3, B qd i qd j and V eff are the kinetic energy parameters and the effective potential, which is defined as the sum of three contributions: eff ZPVE (4) where V(θ, α) is the ab initio two-dimensional potential energy surface, V′(θ, α) is the Podolsky pseudopotential, and V ZPVE (θ, α) is the zero-point vibrational energy correction.  (6) where X cdm is the center of mass of the vinyl group CH�CH 2 . The two ab initio potential energy surfaces were computed using the CCSD(T)-F12/CVTZ-F12 total electronic energies of 26 geometries defined for different values of θ (0°, 90°, 180°, −90°) and α (0°, 30°, 60°, 90°, 120°, 150°, 180°). In all of these geometries, 3N a − 8 internal coordinates (where N a is the number of atoms) were allowed to relax at the MP2/AVTZ level of theory. The energies were fitted to the following double Fourier series: This function transforms as the totally symmetric representation of the G 6 molecular symmetry group. 29,48 Formally identical expressions were employed for V′, V ZPVE , V eff , and the kinetic terms. Details concerning the computation of the Hamiltonian parameters from ab initio energies and geometries can be found in refs 39 and 40. V ZPVE was computed using the MP2/AVTZ harmonic fundamentals calculated at all 26 geometries. Figure 6 presents the two effective surfaces. Thus, for methyl glyoxal, the following expression for V eff was obtained: Equations formally identical to eq 8 were employed for the three kinetic parameters. For methyl glyoxal, the coefficients A 00 cc were computed to be B θ = 5.5841 cm −1 , B α = 2.2379 cm −1 , and B θα = −0.1861 cm −1 .
For methyl vinyl ketone, the following expression for V eff was obtained: For methyl vinyl ketone, the coefficients A 00 cc were computed to be B θ = 5.5885 cm −1 , B α = 1.7971 cm −1 , and B θα = −0.1898 cm −1 .
The energy levels shown in Tables 6 and 7 were determined by diagonalizing the Hamiltonian matrices, which factorize into blocks due to the symmetry conditions. The levels are classified using the symmetry representations of the G 6 molecular symmetry group, and the two quanta represent excitations of the C−C and methyl torsional modes. They are compared with available experimental data and with the results obtained using VPT2.
For trans-methyl glyoxal, the splitting of the ground vibrational state was estimated to be 0.067 cm −1 . The two lowest excited energy levels, (1 0) and (0 1), were computed to be 89.588 cm −1 (A 2 ) and 88.683 cm −1 (E) and 124.636 cm −1 (A 2 ) and 123.785 cm −1 (E). The low-lying energies of cismethyl glyoxal are also provided in Table 6, but as has been already highlighted, the viability of this conformer is very low.
However, in MVK the two conformers show very similar stabilities. As they are separated by a relatively high barrier, the energies can be allocated as if they were two different molecules. In MVK, both modes υ 27 and υ 26 can be assigned as the torsional modes without any confusion. For A p -MVK, the splitting of the ground vibrational state was estimated to be 0.008 cm −1 . The two low excited energy levels (1 0) and (0 1) were computed to be 105.344 cm −1 (A 2 ) and 105.354 cm −1 (E) and 137.217 cm −1 (A 2 ) and 136.869 cm −1 (E). For S p -MVK, the splitting of the ground vibrational state was estimated to be 0.017 cm −1 , and the two lowest excited energy levels (1 0) and (0 1) were computed to be 81.940 cm −1 (A 2 ) and 81.954 cm −1 (E) and 127.732 cm −1 (A 2 ) and 127.130 cm −1 (E).
The two conformers A p -MVK and S p -MVK show very similar V 3 barriers, which were computed to be 429.6 and 380.7 cm −1 , respectively. On the basis of the barriers, similar splittings of the ground vibrational state will be expected. However, the ZPVEs are very different (128.389 cm −1 for A p and 271.375 cm −1 for S p ), and when they are considered, it is easy to understand that the S p splitting is double the A p splitting.

■ CONCLUSIONS
In this study, the far-infrared spectra of methyl glyoxal and methyl vinyl ketone have been simulated using a variational procedure of reduced dimensionality starting from geometries The Journal of Physical Chemistry A pubs.acs.org/JPCA Article and potential energy surfaces computed using highly correlated ab initio calculations. The procedure allows us to derive theoretical information concerning the large-amplitude motions and their interactions. Torsional barriers and parameters are provided. The low-lying vibrational states and their splittings have been mapped. We believe that this information can be useful for the interpretation of further measurements in the farinfrared region and also can help with assignments of rotational and rovibrational spectra. The energy difference between the trans-and cis-methyl glyoxal conformers has been estimated to be 1747 cm −1 . The profile of the trans → cis process draws a secondary cis minimum of very low stability and justifies the unavailability of experimental data for the cis form. The A p and S p conformers of methyl vinyl ketone are almost isoenergetic, but their interconversion is hampered by a relatively high torsional barrier of 1798 cm −1 . The methyl torsional barriers of trans-methyl glyoxal, A p -MVK, and S p -MVK have been computed to be 273.6, 429, and 380.7 cm −1 , respectively.
Previous studies of methyl glyoxal showed disagreements for the assignments of the ν 20 and ν 21 normal modes because they cannot be understood in terms of two different local modes, one describing the CH 3 internal rotation and the other describing the C−C central bond torsion. The two internal rotations interact strongly and contribute to the two normal modes. The comparison of the computed far-infrared spectra of three different isotopic varieties helped to correlate ν 20 to the methyl torsion and ν 21 to the C−C torsion.
The low-lying torsional energy levels of methyl glyoxal and methyl vinyl ketone were computed variationally up to 450 cm −1 . The energies were assigned to the two conformers of methyl glyoxal and to the two conformers of MVK. The first excited levels of cis-methyl glyoxal have been computed, although the lifetime of this structure is very short. For transmethyl glyoxal, the splitting of the ground vibrational state has been estimated to be 0.067 cm −1 . The two lowest excited energy levels (1 0) and (0 1) were computed to be 89.588/88.683 cm −1 (A 2 /E) and 124.636/123.785 cm −1 (A 2 /E). For MVK the splittings of the ground vibrational state have been estimated to be 0.008 cm −1 (A p ) and 0.017 cm −1 (S p ). The two lowest excited energy levels (1 0) and (0 1)