## 4 Results and Discussion
#### 4.1.2 Barrier Heights for Different Tops  
Barrier heights are determined from the plots of the total energy vs. dihedral angle curves for different tops. Every local minimum of each curve corresponds to a stable configuration of the molecule and a maximum between two adjacent minima corresponds to the transition state configuration of the molecule. The energy difference between a minimum and one of the adjacent maxima is the barrier height. The barrier heights of the seven top axes are listed in Table 2. The rotation of the O\({}_{12}\)H\({}_{13}\) group when the H\({}_{11}\) atom of the O\({}_{10}\)H11 group faces towards the O\({}_{12}\) atom gives rise to a one-fold barrier with the height of 9.35 kcal/mol (Figure 2a) and does not yield any new stable structure. The points A and C in Figure 2a represent the same stable configuration in which both the H atoms of the two OH groups are directed towards the atom H\({}_{7}\). The rotation of the O\({}_{12}\)H\({}_{13}\) group, when the H\({}_{11}\) atom of the O\({}_{10}\)H\({}_{11}\) group is directed away from the atom O\({}_{10}\), yields a two-fold barrier (Figure 2b). The transition A/E \(\rightarrow\) C via the barrier maxima B/D requires 2.588/2.854 kcal/mol energies, and for the reverse transition the required energies are 6.314/6.517 kcal/mol. The total energy vs. dihedral angle curve for the rotation of the O\({}_{10}\)H\({}_{11}\) group yields a two-fold barrier as shown in Figure 2c. In this case, the point C corresponds to the configuration in which the H atoms of the O\({}_{12}\)H\({}_{13}\) and O\({}_{10}\)H\({}_{11}\) groups are directed away from each other. The barrier heights for the forward and reverse transitions C \(\rightarrow\) A/E via B/D are 2.232 and 9.223 kcal/mol. The barrier heights for the OH groups attached to the phenyl ring of the L-dopa molecule are found to be in agreement with the OH group in dopamine [16] and one order higher than the OH group in phenol (3.8 kcal/mol) [17]. However, the barrier height for the OH group of the carboxylic group is found to be 3-5 times higher than the OH group of phenol due to strong intra-molecular H-bonding (O\({}_{20}\)-H\({}_{22}\)\(\ldots\) NH\({}_{2}\)) in the L-dopa molecule. As mentioned earlier, the total energy vs. dihedral angle scan curves for all five tops of the 2-aminopropenoic acid moiety are shown in Figure S1. The rotations about the \begin{table}
\begin{tabular}{c c c c c} \hline
**Conf.** & \begin{tabular}{c} **Total Energy** \\ **Hartree** \\ \end{tabular} & \
\begin{tabular}{c} **Hartree** \\ \end{tabular} &
\begin{tabular}{c} **\(\Delta\)E Relative to C-I** \\ **kcal/mol** \\ \end{tabular} \\ \hline C-I & \(-\)705.460596 & 0 & 0 & 0.0 \\ \hline C-II & \(-\)705.459368 & 0.001228 & 0.771 & 388 \\ C-III & \(-\)705.458329 & 0.002267 & 1.423 & 716 \\ C-IV & \(-\)705.458148 & 0.002449 & 1.537 & 773 \\ C-V & \(-\)705.457772 & 0.002824 & 1.772 & 892 \\ C-VI & \(-\)705.457510 & 0.003086 & 1.936 & 975 \\ \hline \end{tabular}
\end{table} 
Table 1: Total energies and their differences for the first 6 lowest-energy monomeric conformers. \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Top** & **Foldness** & \(\Delta\)**E\({}_{\textbf{AB}}\)** & \(\Delta\)**E\({}_{\textbf{BC}}\)** & \(\Delta\)**E\({}_{\textbf{CD}}\)** & \(\Delta\)**E\({}_{\textbf{DE}}\)** & \(\Delta\)**E\({}_{\textbf{EF}}\)** & \(\Delta\)**E\({}_{\textbf{FG}}\)** \\ \hline C\({}_{19}\)-OH & 2 & 20.565 & 11.340 & 11.340 & 20.565 & - & - \\ \hline C\({}_{1}\)-OH & 1 & 9.775 & - & - & - & - & - \\ \hline C\({}_{6}\)-OH & 2 & 9.223 & 2.232 & 2.232 & 9.223 & - & - \\ \hline C\({}_{14}\)-C\({}_{17}\) & 3 & 5.992 & 2.936 & 3.140 & 0.126 & 5.580 & 10.890 \\ \hline C\({}_{3}\)-C\({}_{14}\) & 2 & 2.301 & 1.544 & 1.945 & 2.710 & - & - \\ \hline C-CO\({}_{2}\)H & 2 & 6.013 & 6.395 & 2.988 & 2.606 & - & - \\ \hline C\({}_{1}\)-OH \({}^{\lx@sectionsign}\) & 2 & 2.588 & 6.314 & 6.517 & 2.854 & - & - \\ \hline \end{tabular}
\end{table} 
Table 2: Barrier heights * for all the tops of L-dopa.