Underdamped vibrations control the primary electron transfer in photosynthesis at low temperatures.

Measurements performed with the help of ultrafast laser spectroscopy have clearly shown that the primary electron transfer in photosynthesis lasts no longer than a few picoseconds. Equally fast are processes of vibrational relaxation which have to be taken into account in the correct description of the phenomenon. Here, we consider a simple theory combining the electron transfer process with diffusion in the energy space of a chosen underdamped vibrational mode of protein environment. Analytical formulas for effective transition rate constants are derived, and a transient kinetics is considered. The quality of analytical approximations is verified by numerical simulations for various physical conditions. Efficient parallel computations have been applied. The model can explain a peculiar temperature dependence of pump-probe spectra observed.