Nonequilibrium oscillatory electron transfer in bacterial photosynthesis

A theory to describe nonequilibrium electronic surface crossing during vibrational relaxation induced by ultrafast photoexcitation is developed and applied to the primary electron transfer (ET) in bacterial photosynthetic reaction centers. As a key concept, we define on a microscopic basis the angle between two reaction coordinates each representing the environmental nuclear displacements coupled to the initial photoexcitation (to the P* state) and to the subsequent ET processes, respectively. The "cross-spectral" density function, whose integral intensity gives the cosine of this angle, is also defined to give a consistent (nonphenomenological) description of the vibrational coherence and its dephasing. In the application to the primary ET in bacterial photosynthesis, we find (1) the time-dependent ET rate exhibits marked oscillation at low temperatures due to the nonequilibrium vibrational coherence in the P* state. However, it does not contribute very much to 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, rather than the dynamical nuclear coherence, are the main origins that reasonably reproduce the ultrafast ET and its anomalous temperature dependence (accelerated as the temperature decreases). From the calculations on alternative parameter regimes, we also examine the conditions in which the nonequilibrium nuclear vibrations may accelerate the photoinduced ET. We further propose that detailed experimental analysis of the transient behavior of the oscillating time-dependent reaction rate may provide useful information on the interplay between the vibrational dephasing and the surface crossing dynamics of ultrafast reactions as well as on the underlying static energetics of the system.