Electron transfer model for the electric field effect on quantum yield of charge separation in bacterial photosynthetic reaction centers

The effect of an electric field on a photoinduced charge separation process is treated theoretically. The system considered is a reaction center (RC) of photosynthetic bacteria, involving an electron transfer (ET) from the electronically excited singlet state of the bacteriochlorophyll dimer (P) to the bacteriopheophytin (II) and quinone (Q). In contrast to formulations which focus only on the forward steps and do not explain the major effect on the quantum yield of P(+)Q(-) or, in Q-depleted samples, of P+H-, the present study includes the effect on the back reactions, an effect which we find to be large. The low-frequency medium and high-frequency intramolecular vibrational modes are included in the calculation of the various ET rates. Recent experimental results on the ET energetics, including the estimated effect of static heterogeneity in RCs, are incorporated. The rate equations for the population densities of distinct states are solved for both oriented and randomly oriented (isotropic) RC samples, and the results are compared with experimental data for the field-induced reduction of the quantum yield of formation of charge-separated state P(+)Q(-). A simple (quasiequilibrium) model calculation illustrates the essential features of this analysis of the electric field effect and compares reasonably well with these numerical results of the more detailed model. The question of the electric field effect on the fluorescence quantum yield is also addressed, and a suggestion is made for consistency with the data on the formation of P(+)Q(-).