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 highlight differences with existing approaches in the simplest possible context, the irreversible outer-sphere reaction in a solvent with a biexponential energy-gap autocorrelation function, Δ(t), is studied in detail. In a Debye solvent, Δ(t)=exp(−t/τL) and the rate can be rigorously expressed as an explicit functional of exp(−t/τL). It has been suggested that the exact rate in a non-Debye solvent can be found by replacing exp(−t/τL) with the appropriate (nonexponential) Δ(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 approximations, which reduce the solution of this equation to effective one-dimensional ones, are considered and compared with exact Brownian dynamics simulation results. The crudest approximation replaces the non-Deby...

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