DYNAMIC THEORY OF THE PHOTOISOMERIZATION OF RHODOPSIN CHROMOPHORE .2. CALCULATIONS OF THE TRANSITION-PROBABILITY

Assuming that the stretching-vibrational energy of rhodopsin chromophore dissipates to the protein moiety during the photoisomerization, we consider the deformed excited state PSI-2 and the virtual ground state PSI-1 of the pi-electron system. We also consider the normal vibrational states {U(rj)} of the stretching and torsional vibrations in these transient pi-electronic states {PSI(r)}. The non-stationary state of the chromophore is then expressed as a linear combination of {PSI(r)U(rj)}, and the equation for its coefficients is derived by explicitly taking account of the kinetic energy of atomic cores. On this basis, the probability of the non-adiabatic transition from PSI-2 to PSI-1 is calculated as a function of the angle of cis-trans isomerization, as well as the energy dissipation from the chromophore to confirm the reasonability of our proposition of {PSI(r)}.