Theory of Nonadiabatic Tunneling Splitting

Estimating tunneling splittings is a long-standing quantum mechanical challenge for theoretical methods. Sometimes splittings are so small, i.e., within a fraction of a wavenumber, pushing the limits of experimental detection and computational precision. Currently, most computational methods are able, at best, to obtain only ground-state tunneling splittings, either for symmetric or asymmetric potentials. In this Letter, we introduce a unified theoretical approach, based on a two-state approximation that can be equally applied to symmetric and asymmetric diabatic potential crossing and for excited states, providing reliable estimates even for states near the energy crossing. The method opens the door to analytic approximations for the tunneling splitting of model potential systems. It provides a framework for the introduction of vibrational perturbation theory to the estimation of nonadiabatic tunneling splittings. It also provides new insight into the semiclassical theory, leading to an instanton based steepest descent expression applicable also to excited states. Numerical tests on model systems are promising, providing the groundwork for implementation to future multidimensional applications.