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

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