Investigating Algorithms in Non-adiabatic Dynamics: Extension, Benchmark, and Application

Simulating chemical dynamics going beyond the adiabatic approximation can be challenging. Due to the high computational cost of simulating nuclear-electronic coupling, solving the Schrödinger equation becomes prohibitive for high dimensional systems. For decades, scientists have steadily developed affordable semi-classical algorithms to simulate non-adiabatic dynamics. Although these algorithms were designed to handle non-adiabatic dynamics, they necessarily make several underlying approximations, and thus their accuracy inevitably depends on the systems investigated. In this thesis, a few projects involving a host of non-adiabatic algorithms are presented. First, we revisit potential issues in one specific non-adiabatic algorithm, fewest switches surface hopping (FSSH). We extend FSSH to the interesting situation whereby the Hamiltonian is complex and the underlying idea of momentum rescaling is no longer straightforward. We then derive the critical notion of a “Berry force” from the quantum-classical Liouville equation (QCLE), and revisit potential recoherence issues in standard FSSH algorithm. Second, we also benchmark another algorithm, the independent electron surface hopping (IESH) algorithm, and examine its capacity to model electron transfer at a metal surface. Third and finally, we study molecule-metal scattering, evaluating the accuracy of electronic friction (EF), classical master equation (CME), and broadened classical master equation (BCME) for a model simulation of NO scattering off gold