## 3 Discussion
### Introducing Intensity-Carrying Modes in VCD  
Among the observations pointed out in [79], we highlight that _\"the intensities, both in absorption and in VCD, are generally larger for FEN than for MEFEN and for CAM than for MECAM\"_. Indeed, the inspection of Figures 6a and 7a confirms that the polarizabilities of the carbonyl-containing molecules FEN and CAM display larger values than MEFEN and MECAM. To directly point out the role of the carbonyl group in causing the intensity increase in both VCD and IR calculations, we compute the Intensity Carrying Modes (ICM) of the four molecules. This useful concept was introduced by [PERSON] et al. in the framework of IR and Raman spectroscopy [32; 33], connected to vibrational polarizabilities (and hyperpolarizabilities) [33], and later extended to Raman Optical Activity (ROA) by [PERSON] et al. [86]. However, to the best the authors' knowledge, the use of ICM in the context of VCD is unprecedented. Therefore, it is worth recalling the notation used for IR spectroscopy, and extend it to VCD. ICMs are introduced as collective nuclear displacements along which the IR intensity (or Raman or ROA intensity) is maximized. This leads to an eigenvalue problem [33; 86] for the \(\mathbf{\mathcal{M}}\) matrix, which, \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**(a)** & **(b)** & **(c)** & **(d)** & **(e)** & **(f)** & **(g)** \\ \hline \(\bar{\
u}_{k}\) & \(\mathbf{10^{4}\cdot D_{0k}}\) & \(\mathbf{10^{7}\cdot R_{0k}}\) & \(\mathbf{10^{4}\cdot g_{0k}}\) & \(\mathbf{10^{40}\cdot D_{0k}}\) & \(\mathbf{10^{44}\cdot R_{0k}}\) & \(\mathbf{10^{4}\cdot g_{0k}}\) \\ \(\mathbf{(cm^{-1})}\) & **(at. un.)** & **(at. un.)** & **(dimensionless)** & **(\(\mathbf{\mathrm{e}su^{2}\) cm^{2}}\)** & **(\(\mathbf{\mathrm{e}su^{2}\) cm^{2}}\)** & **(dimensionless)** \\ \hline
211 & 1.07 & 7.15 & 1.94 & 7.30 & 3.46 & 1.89 \\
368 & 6.49 & \(-\)26.54 & \(-\)1.19 & 41.96 & \(-\)12.44 & \(-\)1.19 \\
411 & 6.62 & \(-\)10.04 & \(-\)0.44 & 42.62 & \(-\)4.81 & \(-\)0.45 \\
771 & 6.01 & 27.05 & 1.31 & 38.79 & 12.75 & 1.31 \\
842 & 32.85 & 8.60 & 0.08 & 212.20 & 4.06 & 0.08 \\
909 & 1.79 & 53.14 & 8.68 & 11.55 & 25.05 & 8.68 \\
973 & 9.67 & \(-\)73.10 & \(-\)2.21 & 62.50 & \(-\)34.46 & \(-\)2.21 \\
1044 & 5.10 & 13.38 & 0.77 & 32.94 & 6.31 & 0.77 \\
1131 & 3.63 & \(-\)15.52 & \(-\)1.25 & 23.42 & \(-\)7.31 & \(-\)1.25 \\
1159 & 1.32 & 10.50 & 2.33 & 8.50 & 4.94 & 2.33 \\
1169 & 1.62 & \(-\)26.62 & \(-\)4.78 & 10.50 & \(-\)12.55 & \(-\)4.78 \\
1191 & 0.49 & 1.34 & 0.80 & 3.15 & 0.63 & 0.80 \\
1295 & 3.21 & \(-\)20.81 & \(-\)1.89 & 20.73 & \(-\)9.81 & \(-\)1.89 \\
1409 & 1.28 & 4.71 & 1.07 & 8.30 & 2.21 & 1.07 \\
1440 & 9.06 & 30.39 & 0.98 & 58.53 & 14.33 & 0.98 \\
1485 & 2.26 & 3.73 & 0.48 & 14.58 & 1.76 & 0.48 \\
1499 & 2.53 & \(-\)2.97 & \(-\)0.34 & 16.32 & \(-\)1.40 & \(-\)0.34 \\
1530 & 2.35 & 11.85 & 1.47 & 15.19 & 5.59 & 1.47 \\
3028 & 3.63 & 2.77 & 0.22 & 23.48 & 1.31 & 0.22 \\
3080 & 5.46 & 0.96 & 0.05 & 35.24 & 0.45 & 0.05 \\
3085 & 3.78 & \(-\)3.99 & \(-\)0.31 & 24.41 & \(-\)1.88 & \(-\)0.31 \\
3088 & 1.77 & \(-\)15.01 & \(-\)2.47 & 11.45 & \(-\)7.08 & \(-\)2.47 \\
3110 & 7.31 & 14.04 & 0.56 & 47.20 & 6.62 & 0.56 \\
3164 & 5.28 & \(-\)11.24 & \(-\)0.62 & 34.10 & \(-\)5.30 & \(-\)0.62 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of the results from a VCD calculation carried out with Gaussian09 on (\(R\))-methyloxirane at the B3 LYP/aug-cc-pVQZ level, and the results obtained by a corresponding polar calculation based on the numerical data contained in the *.fchk file associated with the Gaussian calculation. Column (a) is the wavenumbers computed by Gaussian09 and polar are not distinguishable at the shown precision.