Abstract

In two recent papers the photoinduced electron transfer process within a porphyrin quinon cyclophane complex has been studied experimentally /1/ and theoretically /2/ as a model system for the photosynthetic reaction center. The observed rate of the charge separation process depends strongly on the solvent polarity. This dependence could be described analytically using macroscopic models for the dielectric behavior of the solvent. In general, however, such systems may show nonexponential behavior /3/ and the solvent dynamics has to be considered explicitly in a microscopic model. This is the aim of the present paper. We present a microscopic model for the solvent induced transition from the optically excited state (P^*) to the charge separated state (CT). Due to its large permanent dipole moment the CT state energy fluctuates strongly in a polar environment. These fluctuations are modeled by a dichotomic process. The energy difference Δ=E(CT)-E(P^*) is described as a random telegraph signal which switches between two values Δ₊>0 and Δ₋<0 . This process is characterized by its correlation time and the probability of finding Δ<0. As long as Δ<0 the transition P^* −> CT takes place whereas in the opposite case Δ>0 the CT state may either decay into the ground state or the transfer may be reversed (see fig.1). The combination of solvent fluctuations plus intramolecular transitions is described by a master equation which can be solved analytically. The general solution shows multi exponential behavior. It contains the two limiting cases of slow and fast dielectric relaxation (as compared to the intramolecular transition rates) as special cases and is also able to describe the intermediate region where the timescales of solvent dynamics and intramolecular transitions are comparable.

© 1992 The Author(s)