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

Journal Article · Wed Oct 07 04:00:00 EDT 2015 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.4932361· OSTI ID:22489673

Bauer, Rainer; Thoss, Michael ^[1]

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1. Institut für Theoretische Physik und Interdisziplinäres Zentrum für Molekulare Materialien, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Staudtstraße 7/B2, 91058 Erlangen (Germany)

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 Paper II [J. O. Richardson, J. Chem. Phys. 143, 134116 (2015)], we discuss numerical evaluation of the formulae.

• OSTI ID: 22489673
• Journal Information: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 13 Vol. 143; ISSN JCPSA6; ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
DIAGRAMS
ELECTRON TRANSFER
EVALUATION
FREE ENERGY
INTEGRALS
SEMICLASSICAL APPROXIMATION
TUNNEL EFFECT