Computationally enabling surface-hopping dynamics on the Anderson-Holstein Hamiltonian

The electron-electron repulsion in molecular orbitals interacting with metals is often treated using a mean-field approach or is ignored altogether while examining the dynamics of molecules at metal surfaces. This simplification is common because the complex interactions among electrons can become computationally intractable due to the presence of a metal continuum. In this paper, we propose an algorithm to selectively incorporate discretized metallic states during the construction of the Hamiltonian. The constrained Hamiltonian thus formed allows us to perform surface hopping dynamics. Hence, we refer to our algorithm as the active space surface hopping algorithm. We benchmark the results of our method against results from Marcus theory for the Anderson-Holstein Hamiltonian, demonstrating its utility in simulating the dynamics of systems with significant electron correlation effects. Furthermore, we show that the surface hopping method effectively captures coherent quantum effects that a rate theory-based method cannot.