Electric Field Modulation of Electron Transfer Reaction Rates in Isotropic Systems: Long-Distance Charge Recombination in Photosynthetic Reaction Centers

A general method is demonstrated for experimentally obtaining the rate constant of electron transfer as a function of the free energy of the reaction in nonoriented systems. An external electric field is used to modulate the energy levels of dipolar states and thereby affect the electron-transfer rate. The method is valid for any electron-transfer system which has a fixed distance between the donor and acceptor. The method is employed to obtain the experimental rate vs applied electric field curve of the charge recombination reaction between the oxidized special pair electron donor and the reduced ubiquinone acceptor in bacterial reaction centers of Rb. sphaeroides at 80 K . The experimental rate vs electric field curve is shown to be equivalent to the rate vs free energy curve when it is linearly scaled by the dipole moment of the charge-transfer state and the local field correction. The reaction is biexponential at zero field, and possible mechanisms that could give rise to two populations are discussed in the context of the electric field effect. The rate vs free energy curve for each of the two processes is compared to several theoretical models for the rate constant. The apparent absence of structure due to quantum mechanical resonances in the experimentally determined energy gap law is addressed, and calculations based only on the free energy dependence of the Franck-Condon factors are contrasted with a model including superexchange in the electronic coupling.