Dependence of Photosynthetic Electron-Transfer Kinetics on Temperature and Energy in a Density-Matrix Model

Abstract

We use a multidimensional density-matrix model to explore the temperature dependence of electron transfer from the excited singlet state of the primary electron donor (P*) to the neighboring bacteriochlorophyll (B A ) in photosynthetic bacterial reaction centers. This reaction, which has the unusual property of increasing in rate with decreasing temperature, occurs too rapidly to be treated reliably by approaches that assume thermal equilibration of the vibrational levels of the reactant electronic state. In the density-matrix treatment, the frequencies and displacements of the vibrational modes that are coupled to electron transfer, and the microscopic time constants for transitions between different vibrational states, are obtained from molecular-dynamics simulations by the dispersed-polaron (spin-boson) approach. The electron-transfer dynamics are simulated by integrating the stochastic Liouville equation following excitation of the system with a short pulse of light. In this model, the increase in the rate with decreasing temperature depends strongly on the fact that electron transfer occurs more rapidly than vibrational thermalization. The high rate of electron transfer also affects the dependence of the kinetics on the energy difference between the reactant and product electronic states (ΔE°), making the optimal value of -AE° smaller than the reorganization energy. This interesting effect can be rationalized qualitatively in simple semiclassical and quantum mechanical models.