Nonequilibrium oscillatory electron transfer in bacterial photosynthesis

A theory to describe nonequilibrium electronic surface crossing during vibr ational relaxation induced by ultrafast photoexcitation is developed and ap plied to the primary electron transfer (ET) in bacterial photosynthetic rea ction centers. As a key concept, we define on a microscopic basis the angle between two reaction coordinates each representing the environmental nucle ar displacements coupled to the initial photoexcitation (to the P* state) a nd to the subsequent ET processes, respectively. The "cross-spectral" densi ty function, whose integral intensity gives the cosine of this angle, is al so defined to give a consistent (nonphenomenological) description of the vi brational coherence and its dephasing. In the application to the primary ET in bacterial photosynthesis, we find (1) the time-dependent ET rate exhibi ts marked oscillation at low temperatures due to the nonequilibrium vibrati onal coherence in the P* state. However, it does not contribute very much t o accelerate the primary ET rate with respect to the total population decay of the P* state. (2) The static energetics (that give a small barrier for the ET) and the nuclear quantum tunneling effect at low temperatures, rathe r than the dynamical nuclear coherence, are the main origins that reasonabl y reproduce the ultrafast ET and its anomalous temperature dependence (acce lerated as the temperature decreases). From the calculations on alternative parameter regimes, we also examine the conditions in which the nonequilibr ium nuclear vibrations may accelerate the photoinduced ET. We further propo se that detailed experimental analysis of the transient behavior of the osc illating time-dependent reaction rate may provide useful information on the interplay between the vibrational dephasing and the surface crossing dynam ics of ultrafast reactions as well as on the underlying static energetics o f the system.