Semiempiricał Calculations of Force Constants for Torsional and Stretching Vibrations in Excited States of Retinal and Its Related Compounds

We consider the ground state (GS), the excited state on absorption (ESA), the virtual ground (VGS) and the deformed excited state (DES) of π-electron system in hexaene, retinal, retinal Schiff-base (RSB), protonated retinal Schiff-base (PRSB) or our model for rhodopsin chromophore, and we semiempirically calculate the following two kinds of force constants for the pairs of bonded atoms in each of the four π-electronic states: (1) the force constants of torsional vibrations; (2) those of the interactions between torsional and stretching vibrations. The calculations are carried out by our LCAO-ASMO-SCF-CI method for π-electrons, selecting such a part of the total energy of π-electron system that gives a significant contribution to the force constants.