Dynamical Theory of the Photoisomerization of Rhodopsin Chromophore. I. Calculations of the Transition Probability

Abstract

Assuming that the stretching-vibrational energy of rhodopsin chromophore dissipates to the protein moiety during the photoisomerization, we consider the deformed excited state Ψ 2 and the virtual ground state Ψ 1 of the π-electron system. We also consider the normal vibrational states { U r j } of the stretching and torsional vibrations in these transient π-electronic states {Ψ r }. The non-stationary state of the chromophore is then expressed as a linear combination of {Ψ r U r j }, 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 Ψ 2 to Ψ 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 {Ψ r }.