GENERALIZATION OF THE MARCUS EQUATION FOR THE ELECTRON-TRANSFER RATE

The Marcus equation for the electron-transfer rate is generalized to the form which is applicable to molecular models of the solvent. The rate constant is expressed in terms of the function phi(DELTAV), which describes the distribution of the electrostatic potential difference DELTAV between donor and acceptor sites, produced by the surrounding fluctuating polar solvent molecules. This expression clearly shows that the functional dependence of the rate constant on the free-energy change of the reaction (the so-called energy gap law) reflects the potential difference distribution phi(DELTAV). The new expression reduces to the well-known Marcus equation, if it is combined with the potential difference distribution calculated on the basis of the dielectric continuum model. A clear physical explanation is given for the reorganization energy which appears as a parameter in the Marcus theory. The applicability of the new expression is not limited to the dielectric continuum model. The new expression can be used to improve the Marcus equation by combining it with the potential difference distribution calculated on the basis of a molecular model of the solvent.