ELECTRON-TRANSFER REACTION DYNAMICS IN NON-DEBYE SOLVENTS

The dynamics of electron transfer in a non-Debye solvent is described by multidimensional Markovian reaction-diffusion equation. To highligh t differences with existing approaches in the simplest possible contex t, the irreversible outer-sphere reaction in a solvent with a biexpone ntial energy-gap autocorrelation function, Delta(t), is studied in det ail. In a Debye solvent, Delta(t)= exp(-t/tau(L)) and the rate can be rigorously expressed as an explicit functional of exp(-t/tau(L)) It ha s been suggested that the exact rate in a non-Debye solvent can be fou nd by replacing exp(-t/tau(L)) With the appropriate (nonexponential) D elta(t). For a ''biexponential'' solvent, our approach is based on an anisotropic diffusion equation for motion on a harmonic surface in the presence of a two-dimensional delta function sink. Three approximatio ns, which reduce the solution of this equation to effective one-dimens ional ones, are considered and compared with exact Brownian dynamics s imulation results. The crudest approximation replaces the non-Debye so lvent with an effective Debye one with tau(eff)(-1)=(-d Delta/dt)(t=0) . The second is obtained by invoking the Wilemski-Fixman-type closure approximation for the equivalent two-dimensional integral equation. Th is approximation turns out to be identical to the above mentioned ''su bstitution'' procedure. When the relaxation times of the two exponenti als are sufficiently different, it is shown how the two-dimensional pr oblem can be reduced to a one-dimensional one with a nonlocal sink fun ction. This anisotropic relaxation time approximation is in excellent agreement with simulations when the relaxation times differ by at leas t a factor of three and the activation energy is greater than k(B)T. F inally, it is indicated how the influence of intramolecular vibrationa l modes (i,e., nonlocal sink functions) can be treated within the fram ework of this formalism. (C) 1998 American Institute of Physics. [S002 1-9606(98)50930-0].