Linear response in theory of electron transfer reactions as an alternativeto the molecular harmonic oscillator model

The effect of solvent fluctuations on the rate of electron transfer reactio ns is considered using linear response theory and a second-order cumulant e xpansion. An expression is obtained for the rate constant in terms of the d ielectric response function of the solvent. It is shown thereby that this e xpression, which is usually derived using a molecular harmonic oscillator ( "spin-boson'') model, is valid not only for approximately harmonic systems such as solids but also for strongly molecularly anharmonic systems such as polar solvents. The derivation is a relatively simple alternative to one b ased on quantum field theoretic techniques. The effect of system inhomogene ity due to the presence of the solute molecule is also now included. An exp ression is given generalizing to frequency space and quantum mechanically t he analogue of an electrostatic result relating the reorganization free ene rgy to the free energy difference of two hypothetical systems [J. Chem. Phy s. 39, 1734 (1963)]. The latter expression has been useful in adapting spec ific electrostatic models in the literature to electron transfer problems, and the present extension can be expected to have a similar utility. (C) 19 99 American Institute of Physics. [S0021-9606(99)01511-1].