Fig. 6

Umbrella inversion motion of \(\hbox {NH}_2\) belonging to a generic amino acid backbone. The torsional angle \(\phi\) = C1-\(\hbox {C}_\alpha\)-N-H1 differs in structures a and b but the structure is the same. The improper torsion \(\varphi _{12}\) of structure b changed sign during the optimization in such a way that \(\varphi _{12}^{\mathrm{opt,(a)}}=-\varphi _{12}^{\mathrm{opt,(b)}}\). Therefore structure b can be transformed into structure a by exchanging H1 and H2