## 4 Results and Discussion
### Vibrational Analysis
This is also evident from the two significantly differing bond lengths (N\({}_{22}\)-H\({}_{23}\)) 1.018 and (N\({}_{22}\)-H\({}_{25}\)) 1.014 A. The computed \(\
u_{\rm s}\) and \(\
u_{\rm as}\) modes were found to be much weaker in IR and Raman spectra and seem to be buried under the broad and strong/weak IR/Raman bands originating due to the OH stretching modes. [PERSON] et al. [12] assigned the \(\
u_{\rm s}\) mode at 3209 cm\({}^{-1}\) for L-dopa, while [PERSON] et al. [10] assigned these two modes at 3355 and 3433 cm\({}^{-1}\) for L-dopa and L-tyrosine molecules. The mode \(\beta_{\rm s}\)(NH\({}_{2}\)) appears in the range 1600-1700 cm\({}^{-1}\) with medium to strong IR intensities. The observed frequency 1606 (IR, R) cm\({}^{-1}\) could be assigned to the \(\beta_{\rm s}\)(NH\({}_{2}\)) mode of L-dopa. The computed IR and Raman intensities for this mode were found to be lower than the ring stretching modes 8(a/b) which were also observed around 1600 cm\({}^{-1}\). In the present case, the \(\beta_{\rm s}\)(NH\({}_{2}\)) mode was found to have slightly lower magnitude (20 cm\({}^{-1}\)) as compared to the corresponding mode of aniline. The \(\rho\)(NH\({}_{2}\)), \(\omega\)(NH\({}_{2}\)) and \(\tau\)(NH\({}_{2}\)) modes have higher magnitudes than the corresponding modes of the aniline molecule. The mode \(\rho\)(NH\({}_{2}\)) appears in the range 1000-1200 cm\({}^{-1}\) with weak to medium intensity in aniline and its derivatives [21]. In the present case, this mode was computed to be 1148 cm\({}^{-1}\) and was observed at 1135 cm\({}^{-1}\) with weak IR and Raman intensities. The \(\omega\)(NH\({}_{2}\)) mode of the L-dopa molecule was computed to be 855 cm\({}^{-1}\) and was correlated with the observed frequencies 864(IR)/865(R) cm\({}^{-1}\). The lowest-frequency mode \(\tau\)(NH\({}_{2}\)) of the NH\({}_{2}\) group was computed to be 328 cm\({}^{-1}\) and was observed only in the Raman spectrum at 327 cm\({}^{-1}\). The present assignments for the \(\beta_{\rm s}\)(NH\({}_{2}\)), \(\rho\)(NH\({}_{2}\)), \(\omega\)(NH\({}_{2}\)) and \(\tau\)(NH\({}_{2}\)) modes agree with the assignments of these modes earlier proposed by [PERSON] et al. [12] for the L-dopa molecule. -CO\({}_{2}\)(H) Group Modes (6)  
Out of the six CO\({}_{2}\)(H) group modes, the modes \(\
u\)(C=O) and \(\
u\)(C-O(H)) do not couple with each other. The \(\
u\)(C=O) mode was computed to be 1741 cm\({}^{-1}\) and was correlated to the strong IR band at 1649 cm\({}^{-1}\) in agreement with the assignment of this mode in L-dopa [11; 12]. The computed frequency for the mode \(\
u\)(C-O(H)) was found to be 1177 cm\({}^{-1}\) with weak IR and Raman intensities and could not be observed experimentally. For the remaining four modes, the COO(H) group behaves like a CO\({}_{2}\) group and its four modes were found to arise due to coupling between the C=O and C-O(H) modes. These modes are \(\beta_{\rm s}\)[CO\({}_{2}\)(H)], \(\omega\)[CO\({}_{2}\)(H)], \(\rho\)[CO\({}_{2}\)(H)] and \(\tau\)[CO\({}_{2}\)(H)] with the respective computed frequencies 572, 542, 528 and 88 cm\({}^{-1}\), all with weak Raman intensities. These modes are strongly coupled with the 2-anilinepropene moiety modes. From the GaussView 5.0 animation software, the rocking mode of the COO(H) group seems to arise due to the major deformation of the C=O and minor deformation of the C-O(H) bonds. However, the other three modes were found to arise due to almost equal contributions from the angular deformations of the C=O and C-O(H) bonds. Side Chain Skeleton C\({}_{14}\)-C\({}_{17}\) N\({}_{22}\)-C\({}_{19}\) Modes (9)  
The side chain skeleton C\({}_{14}\)-C\({}_{17}\) N\({}_{22}\)-C\({}_{19}\) has nine normal modes of vibration.