Open AccessInstanton theory for Fermi’s golden rule and beyond
Author(s) -
Imaad M. Ansari,
Eric R. Heller,
George Trenins,
Jeremy O. Richardson
Publication year - 2022
Publication title -
philosophical transactions - royal society. mathematical, physical and engineering sciences/philosophical transactions - royal society. mathematical, physical and engineering sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.074
H-Index - 169
eISSN - 1471-2962
pISSN - 1364-503X
DOI - 10.1098/rsta.2020.0378
Subject(s) - instanton , superexchange , semiclassical physics , quantum tunnelling , physics , quantum mechanics , fermi's golden rule , electron transfer , statistical physics , born–oppenheimer approximation , quantum , born–huang approximation , theoretical physics , fermi gamma ray space telescope , chemistry , mathematics , molecule , ion , organic chemistry , approximation error
Instanton theory provides a semiclassical approximation for computing quantum tunnelling effects in complex molecular systems. It is typically applied to proton-transfer reactions for which the Born–Oppenheimer approximation is valid. However, many processes in physics, chemistry and biology, such as electron transfers, are non-adiabatic and are correctly described instead using Fermi’s golden rule. In this work, we discuss how instanton theory can be generalized to treat these reactions in the golden-rule limit. We then extend the theory to treat fourth-order processes such as bridge-mediated electron transfer and apply the method to simulate an electron moving through a model system of three coupled quantum dots. By comparison with benchmark quantum calculations, we demonstrate that the instanton results are much more reliable than alternative approximations based on superexchange-mediated effective coupling or a classical sequential mechanism. This article is part of the theme issue ‘Chemistry without the Born–Oppenheimer approximation’.