Imaginary-time path-integral or 'ring-polymer'methods have been used to simulate quantum
(Boltzmann) statistical properties since the 1980s. This article reviews the more recent …

Instanton theory provides a simple description of a quantum tunnelling process in terms of
an optimal tunnelling pathway. The theory is rigorously based on quantum mechanics …

Since the earliest explorations of quantum mechanics, it has been a topic of great interest
that quantum tunneling allows particles to penetrate classically insurmountable barriers …

We extend ring-polymer molecular dynamics (RPMD) to allow for the direct simulation of
general, electronically non-adiabatic chemical processes. The kinetically constrained (KC) …

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 …

Fermi's golden rule defines the transition rate between weakly coupled states and can thus
be used to describe a multitude of molecular processes including electron-transfer reactions …

We present semiclassical approximations to Green's functions of multidimensional systems,
extending Gutzwiller's work to the classically forbidden region. Based on steepest-descent …

A partial linearized path integral approach is used to calculate the condensed phase
electron transfer (ET) rate by directly evaluating the flux-flux/flux-side quantum time …

Fermi's golden rule (GR) describes the leading-order behavior of the reaction rate as a
function of the diabatic coupling. Its asymptotic (ℏ→ 0) limit is the semiclassical golden-rule …

Marcus–Levich–Jortner (MLJ) theory is one of the most commonly used methods for
including nuclear quantum effects in the calculation of electron-transfer rates and for …