## 4 Results and Discussion
### Vibrational Analysis
-CH\({}_{2}\)-CH-NH\({}_{2}\)CO\({}_{2}\)(H) Moiety Modes (30)  
The 2-aminopropenoic acid (CH\({}_{2}\)-CH-NH\({}_{2}\)CO\({}_{2}\)(H)) moiety can be further sub-divided into five sub-groups: (i) -\({}^{14}\)CH\({}_{2}\) group modes-6, (ii)-\({}^{17}\)CH modes-3, (iii) -NH\({}_{2}\) group modes-6, (iv) CO\({}_{2}\)(H) group modes-6 and (v) side chain skeleton C\({}_{14}\)-C\({}_{17}\)(N\({}_{22}\)) -C\({}_{22}\) modes-9. \({}^{14}\)CH\({}_{2}\) and \({}^{17}\)CH Group Modes (6+3)  
The -CH\({}_{2}\) group has six modes, namely v\({}_{\rm s}\)(-CH\({}_{2}\)), v\({}_{\rm as}\)(-CH\({}_{2}\)), \(\beta_{\rm s}\)(CH\({}_{2}\)), \(\omega\)(CH\({}_{2}\)), \(\rho\)(CH\({}_{2}\)) and t(CH\({}_{2}\)). The mode v\({}_{\rm s}\)(\({}^{14}\)CH\({}_{2}\)) was found to be strongly coupled with the v(\({}^{17}\)C-H) mode. From their PEDs, one mode could not be distinguished from the other mode, since each has 50% contributions to the computed frequencies 2929 and 2938 cm\({}^{-1}\). However, the v\({}_{\rm s}\)(\({}^{14}\)CH\({}_{2}\)) mode is expected to be more intense in the Raman spectrum as compared to the v(\({}^{17}\)C-H) mode. The frequency 2938 cm\({}^{-1}\) is more intense than 2929 cm\({}^{-1}\) in the Raman spectrum, and hence it is correlated to the v\({}_{\rm s}\)(\({}^{14}\)CH\({}_{2}\)) mode and the frequency 2929 cm\({}^{-1}\) to the v(\({}^{17}\)C-H) mode. The v\({}_{\rm as}\)(CH\({}_{2}\)) is a pure mode with the computed frequency 2975 cm\({}^{-1}\), observed at 2964 cm\({}^{-1}\) in both the IR and Raman spectra. The \(\beta_{\rm s}\)(\({}^{14}\)CH\({}_{2}\)) mode seems to be a pure mode and it was computed to be 1449 cm\({}^{-1}\) with medium IR and Raman intensities, and was correlated with a medium-strong band 1439 cm\({}^{-1}\) observed in the IR and Raman spectra. The remaining three modes, \(\omega\)(\({}^{14}\)CH\({}_{2}\)), \(\rho\)(\({}^{14}\)CH\({}_{2}\)) and t(\({}^{14}\)CH\({}_{2}\)), were found to be coupled with the other modes and are computed to be 1339, 1217 and 902 cm\({}^{-1}\), respectively. The computed IR and Raman intensities for these modes were found to be weak. Out of these three modes, only the twisting mode could be observed at 901 cm\({}^{-1}\) in the IR spectrum. The two \({}^{17}\)C-H deformation modes were computed to be 1263 and 1217 cm\({}^{-1}\) and were correlated to the observed frequencies 1249(IR)/1247(R) and 1202 (IR, R) cm\({}^{-1}\). These assignments were found to be in conformity with the assignments of the corresponding modes of the L-dopa molecule reported earlier [12]. -NH\({}_{2}\) Group Modes (6)  
Similar to the -CH\({}_{2}\) group, the -NH\({}_{2}\) group also has the six modes v\({}_{\rm s}\), v\({}_{\rm as}\), \(\beta_{\rm s}\), \(\omega\), \(\rho\) and \(\tau\). The modes v\({}_{\rm s}\) and v\({}_{\rm as}\) for the NH\({}_{2}\) group were observed in the range 3200-3500 cm\({}^{-1}\)[21]. For the two NH\({}_{2}\) stretching modes v\({}_{\rm s}\) and v\({}_{\rm as}\) of the NH\({}_{2}\) group, with two identical N-H bonds, [PERSON] et al. [22] proposed an empirical relation: v\({}_{\rm s}\) = 345.5 + 0.876 v\({}_{\rm as}\). For  
Figure 4: Computed and experimental IR and Raman spectra of L-dopa. a given observed frequency corresponding to one (\(\
u_{\rm s}\)/\(\
u_{\rm as}\)) of the two modes \(\
u_{\rm s}\) and \(\
u_{\rm as}\), the computed frequency for the other (\(\
u_{\rm as}\)/\(\
u_{\rm s}\)) mode would differ from its observed frequency within \(\pm\)5 cm\({}^{-1}\) only. For the L-dopa molecule, the computed frequencies for the \(\
u_{\rm s}\) and \(\
u_{\rm as}\) modes were found to be 3290 and 3378 cm\({}^{-1}\). Considering these two frequencies, 3290 and 3378 cm\({}^{-1}\), as the observed frequencies for the \(\
u_{\rm s}\) and \(\
u_{\rm as}\) modes, the computed frequency using the above empirical relation was found to differ from the observed frequency within \(\pm\)17 cm\({}^{-1}\), indicating that the two N-H bonds are not identical.