Anharmonic Vibrational Raman Optical Activity of Methyloxirane: Theory and Experiment Pushed to the Limits

Combining Raman scattering and Raman optical activity (ROA) with computer simulations reveals fine structural and physicochemical properties of chiral molecules. Traditionally, the region of interest comprised fundamental transitions within 200–1800 cm–1. Only recently, nonfundamental bands could be observed as well. However, theoretical tools able to match the observed spectral features and thus assist their assignment are rather scarce. In this work, we present an accurate and simple protocol based on a three-quanta anharmonic perturbative approach that is fully fit to interpret the observed signals of methyloxirane within 150–4500 cm–1. An unprecedented agreement even for the low-intensity combination and overtone transitions has been achieved, showing that anharmonic Raman and ROA spectroscopies can be valuable tools to understand vibrations of chiral molecules or to calibrate computational models.


Experimental Methodologies
Samples were purchased from Merck (S-methyloxirane: 540021-5G, R-methyloxirane: 540048-5G) and used without further purification. Raman and ROA spectra were measured by a ROA spectrometer developed at Palacký University Olomouc in collaboration with the ZEBR and Meopta companies. 1 The instrument is based on W. Hug's design using the back-scattering geometry, scattered circular polarization (SCP) modulation scheme, and diode pumped solid state laser with 532 nm excitation wavelength (Opus, LaserQuantum). 2, 3 Samples were measured in a rectangular fused silica cell of 70 μL volume (3 mm width, 4 mm depth, Starna) in the temperature-stabilized compartment at 6.0 ± 0.1°C ensuring lower evaporation of the highly volatile liquid. Raman and ROA spectra were simultaneously collected in the full range from 50 to 4560 cm −1 . The spectral resolution was ~ 6-8 cm -1 . Raman and ROA intensities were calibrated with a black-body type (tungsten-halogen) calibration source, and given as a corrected number of detected electrons per excitation energy per unit wavenumber (i.e. e − ·cm·J −1 ).
The intensities of the combinational transitions are almost two orders of magnitude smaller than the intensities of the fundamental transitions. The recording of the spectra over the entire spectral range is limited by the dynamic range of the detector (pixel-well depth: readout noise ratio), where saturation is limiting for high-intensity bands and readout noise is limiting for low-intensity bands. Therefore, ROA spectra were combined from two measurements differing mainly in the exposure times of the CCD cameras: the first measurements had exposure time of 0.15 s and total accumulation time of 1.0 hour (S-enantiomer) and 2.8 hours (R-enantiomer) at a laser power of 340 mW at sample, and the second measurements had exposure time of 2.9 s and accumulation time of 18.8 h (S-enantiomer) and 32.9 h (R-enantiomer) at a laser power of 540 mW at sample. The first measurement with a short exposure time was used for spectral regions of high Raman intensities (50-160, 355-440, 703-1490, 2860-3094 cm -1 ) and the second one for the rest of the spectrum. Please note that only ROA spectra were combined in this way -shorter accumulation Raman spectra do not have any visible noise and were used for the whole spectral range.
No background correction was applied to the ROA spectra. A fluorescent background is much more difficult to correct in the Raman signal, especially in low-intensity spectral regions.
Fortunately, the S-enantiomer sample has very small fluorescent background (noticeably smaller fluorescent background than the R-enantiomer) and only mild background correction was applied.

Theoretical Methodologies
All quantum-chemical calculations were carried out with a locally modified version of GAUSSIAN 16. 4 We used density functional theory (DFT) with hybrid (B3LYP, B3PW91) and double hybrid (revDSD-PBEP86, B2PLYP) functionals, with the jun-cc-pVTZ basis set, except where specified otherwise. Harmonic frequencies were also calculated at the CCSD(T) level. All employed electronic structure calculation methods are listed in Table S1. A "verytight" criterion was used for geometry optimizations, with maximum forces of 2×10 -6 Hartrees/Bohr, and maximum displacements of 6×10 -6 Å. Then, analytical harmonic force fields and vibrational frequencies were computed. Anharmonic force constants (third and fourth derivatives of the potential energy) were calculated by numerical differentiation of the second energy derivatives. In the same way, higher property derivatives were obtained numerically from analytical first derivatives. The differentiation step along the massweighted normal coordinates was 0.01 amu 1/2 Å. 5 The computation of the anharmonic constants is more expensive, since it requires in theory running 2N+1 times the calculations necessary to obtain the vibrational energies and intensities at the harmonic level, with N is the number of normal modes. As the displacements are independent of one another, this process can be sped up by running each job on separate machines and carry out the numerical differentiation afterwards. The gain in time will thus depend on the number of available computing nodes. Another way to cut the computational time is to combine different levels of theory for the harmonic and anharmonic data, using a cheaper level for the latter. The principle is that the harmonic level is responsible for the largest contribution to the energies (and intensities), and the anharmonic correction is significantly smaller, so that small inaccuracies in the latter will have a marginal impact. Nevertheless, such hybrid scheme can only be applied if the two levels of theory are consistent, which means that the equilibrium geometry and the normal coordinates in the two levels (Q H , Q A ) must be very close to each other. This can be checked automatically by computing a transformation like the one proposed by Duschinsky 6 , where the squared elements of the transformation matrix J must be above 0.9, while the elements of the shift vector K must have a magnitude of a few dozen atomic units at most. Further technical details can be found in references. 7,8 In this case, both J matrix and K vector present the hybrid are shown in Figure S10. Since ROA properties are not available for double-hybrid functionals, only hybrid functionals were used to compute the intensities.
In the generalized VPT2 (GVPT2) scheme, terms identified as resonant are removed from the Based on these results, the following criteria were used. For Fermi resonances, For 1-1 Darling-Dennison resonances, for 2-2 Darling-Dennison resonances (between 1 st overtones or 2-quanta binary combinations), And for 1-3 Darling-Dennison resonances, where i, j, k, l refer to the normal modes, ωi are the harmonic wavenumbers, / &'( is the third derivative of the potential energy with respect to the dimensionless normal coordinates, qi, qj and qk. 7 8 is the contact-transformed Hamiltonian 11 and δ is the Kronecker symbol. Here, the Dirac notation was used to represent the harmonic states as a vector of number of quanta. For the sake of readability, only the non-null quanta are listed. In the rest of this document, as well as in the main manuscript, a slightly different, more intuitive form is used, where the number of quanta is indicated between parentheses, following the mode (ex: In the final spectra, idealized experimental spectra averaged over the two enantiomers [ΔIROA=(ΔIR-ΔIS)/2 for ROA, and IRaman=(IR+IS)/2 for Raman] are presented. The calculated intensities are broadened using Gaussian bands with half-widths at half-maximum (HWHM) of 7 cm -1 below 2900 cm -1 and 10 cm -1 above 2900 cm -1 .
The simulated spectra in the range of 2900~4500 cm -1 are shifted by -18 cm -1 .

Figure S3
Solvent effects. Spectra were simulated with 2-hexaneone (ε=11.66), dichloromethane (ε=8.93), pentanal (ε=10.00), and tetrahydrofuran (ε=7.46). Figure S4. Spectra simulated including property-related (blue) and mechanical (green) anharmonicities. The upper panel includes the whole range, the lower panel is a zoom of a part without fundamental transition ("zone II"). Figure S5. Influence of the Coriolis couplings on the total anharmonic contributions. The upper panel include the whole spectra, the lower panel is a zoom of a part without fundamental transition ("zone II"). Figure S6. Simulated and experimental spectra of R-methyloxirane in the 150-4300 cm -1 region. For better visualization, the harmonic and anharmonic spectra of III and IV have been shifted along the yaxis. The theoretical intensities were normalized based on the Raman experiment, with the ROA/Raman ratio conserved.  Figure S11. Influence of the threshold used to identify 1-1 DDRs on the band-shape.