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].