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arXiv · 1508.04919

Semiclassical Green's functions and an instanton formulation of electron-transfer rates in the nonadiabatic limit

Jeremy O. Richardson·Rainer Bauer·Michael Thoss
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Abstract

We present semiclassical approximations to Green's functions of multidimensional systems, extending Gutzwiller's work to the classically forbidden region. Based on steepest-descent integrals over these functions, we derive an instanton method for computing the rate of nonadiabatic reactions, such as electron transfer, in the weak-coupling limit, where Fermi's golden-rule can be employed. This generalizes Marcus theory to systems for which the environment free-energy curves are not harmonic and where nuclear tunnelling plays a role. The derivation avoids using the Im F method or short-time approximations to real-time correlation functions. A clear physical interpretation of the nuclear tunnelling processes involved in an electron-transfer reaction is thus provided. In the following paper, we discuss numerical evaluation of the formulae.

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Jeremy O. Richardson, Rainer Bauer, Michael Thoss. 2015-08-20. Semiclassical Green's functions and an instanton formulation of electron-transfer rates in the nonadiabatic limit. https://doi.org/10.1063/1.4932361

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