Derivation of instanton rate theory from first principles

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 “Im F” 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.