Derivation of instanton rate theory from first principles

TL;DR

This paper derives the instanton rate theory from fundamental quantum scattering principles, providing a rigorous foundation and extending its applicability to other processes in chemical physics.

Contribution

The first-principles derivation of instanton rate theory from quantum scattering formalism, validating and extending its theoretical basis.

Findings

Justifies instanton approach from first principles

Provides a semiclassical Green's function derivation

Enables derivation of rates for other processes

Abstract

Instanton rate theory is used to study tunneling events in a wide range of systems including low-temperature chemical reactions. Despite many successful applications, the method has never been obtained from first principles, relying instead on the "ImF" premise. In this paper, the same expression for the rate of barrier penetration at finite temperature is rederived from quantum scattering theory [W. H. Miller, S. D. Schwartz, and J. W. Tromp, J. Chem. Phys. 79, 4889 (1983)] using a semiclassical Green's function formalism. This justifies the instanton approach and provides a route to deriving the rate of other processes.