The Influence of Dissipation on Vibrational Dynamics in a System of Two Interacting Electronic States

Abstract

The vibrational dynamics of a nonadiabatic transition between two interacting electronic states in a molecular system in a thermal environment was considered. Two models were used. In one of these, both states, and in the other, only one state interacted with the environment. The electronic states were described by one-dimensional harmonic oscillators on the assumption that the interaction amplitude with the environment (bath) linearly depended on the coordinates of the bath and system. Model parameters typical of electron transfer in photosynthesis reaction centers were selected. The numerical solutions to the Redfield equations for the reduced density matrix were used to calculate the time characteristics of the system, including the mean vibrational energy, product population, and the degree of vibrational motion coherence. The influence of temperature and intensity of interactions with the bath on the time dependence of these values was studied. The character of vibrational dynamics had features common to both models, namely, (1) the vibrational energy monotonically decreased with the time, and this dependence was close to one-exponential in the majority of cases and (2) the time dependence of reaction yield, i.e., product population, was a step function, and the probability of the electron transition decreased as the temperature increased. It was found that there was a fundamental difference between the models under consideration: if only the reaction product interacted with the bath, vibrational coherence was retained for a long time (up to 2000 fs).