Nonadiabatic ImF instanton rate theory

Semiclassical instanton theory captures nuclear quantum effects, such as tunneling in chemical reactions. It was originally derived from two different starting points, the flux correlation function and the ImF premise. In pursuit of a nonadiabatic rate theory, a number of methods have been proposed-almost all based on the less rigorous ImF premise. Only recently, we introduced a nonadiabatic ring-polymer instanton rate theory in the rigorous flux-correlation function framework that successfully bridges from the Born-Oppenheimer to the golden-rule limit. Here, we examine the previous ImF-based attempts and conclude that they do not capture the two limits correctly. In particular, we will highlight how the last in a series of developments (called mean-field ring-polymer instanton theory) breaks down in the golden-rule limit. We develop a new nonadiabatic ImF rate theory to remedy the failings of previous attempts while taking inspiration from them. We analyze its behavior in the strong- and weak-coupling limits and also consider the crossover from deep tunneling to a high-temperature nonadiabatic rate theory. We test our new nonadiabatic ImF theory on a range of models, including asymmetric and multidimensional systems, and we show reliable results for the deep-tunneling regime but limitations for the related high-temperature rate theory. These findings are also relevant for the development of nonadiabatic ring-polymer molecular dynamics, where similar corrections have been previously proposed.