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

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

Authors:
;  [1]
  1. Institut für Theoretische Physik und Interdisziplinäres Zentrum für Molekulare Materialien, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Staudtstraße 7/B2, 91058 Erlangen (Germany)
Publication Date:
OSTI Identifier:
22489673
Resource Type:
Journal Article
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 143; Journal Issue: 13; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9606
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; DIAGRAMS; ELECTRON TRANSFER; EVALUATION; FREE ENERGY; INTEGRALS; SEMICLASSICAL APPROXIMATION; TUNNEL EFFECT

Citation Formats

Richardson, Jeremy O., E-mail: jeremy.richardson@fau.de, Bauer, Rainer, and Thoss, Michael. Semiclassical Green’s functions and an instanton formulation of electron-transfer rates in the nonadiabatic limit. United States: N. p., 2015. Web. doi:10.1063/1.4932361.
Richardson, Jeremy O., E-mail: jeremy.richardson@fau.de, Bauer, Rainer, & Thoss, Michael. Semiclassical Green’s functions and an instanton formulation of electron-transfer rates in the nonadiabatic limit. United States. https://doi.org/10.1063/1.4932361
Richardson, Jeremy O., E-mail: jeremy.richardson@fau.de, Bauer, Rainer, and Thoss, Michael. 2015. "Semiclassical Green’s functions and an instanton formulation of electron-transfer rates in the nonadiabatic limit". United States. https://doi.org/10.1063/1.4932361.
@article{osti_22489673,
title = {Semiclassical Green’s functions and an instanton formulation of electron-transfer rates in the nonadiabatic limit},
author = {Richardson, Jeremy O., E-mail: jeremy.richardson@fau.de and Bauer, Rainer and Thoss, Michael},
abstractNote = {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.},
doi = {10.1063/1.4932361},
url = {https://www.osti.gov/biblio/22489673}, journal = {Journal of Chemical Physics},
issn = {0021-9606},
number = 13,
volume = 143,
place = {United States},
year = {Wed Oct 07 00:00:00 EDT 2015},
month = {Wed Oct 07 00:00:00 EDT 2015}
}