New paper on Instanton theory for Fermi's golden rule and superexchange reactions

Previously, we have shown how one can approximate Fermi's golden rule with a semiclassical method called instanton theory. It provides a cost-efficient method of calculating nonadiabatic rates in the golden-rule limit that derives all necessary information from a single classical trajectory. It includes tunnelling and zero-point energy effects and the trajectory sheds light on the reaction mechanism during the tunnelling process.

In this paper, we go beyond the golden rule to deal with bridge-mediated nonadiabatic reactions (see figure). The rate expression for this type of a reaction, sometimes referred to as the superexchange mechanism, involves a sum over numerous bridge states. This makes its evaluation challenging and does not provide any meaningful insights into the reaction pathway. The bridge instanton, much like the golden-rule instanton, is also a single classical trajectory, which makes for an efficient numerical evaluation and an elegant mechanistic interpretation.

Additionally, we have also generalized golden-rule instanton theory to properly treat translational and rotational degrees of freedom, typically present in the study of nonadiabatic molecular reactions.