Direct ab Initio (Meta-)Surface-Hopping Dynamics

Tractable methods for studying the molecular dynamics of chemical processes driven by electronic nonadiabaticity are highly sought after to provide insight into, for example, photochemical reaction mechanisms, molecular collisions, and thermalized electronic band structures. Starting from the time-dependent Schrödinger equation for a many-body system, a direct ab initio trajectory surface-hopping (TSH) method relying on an analytical treatment of nonadiabatic couplings between electronic states is developed in this work. An approach that combines time-dependent perturbation theory and explicit time evolution via TSH to expedite calculation of nonadiabatic transition rates, namely, meta-surface-hopping dynamics, is presented, and an extrapolatory approach using time-dependent perturbation theory for recovering unbiased transition rates is assessed. The meta-surface-hopping method is applied to the problem of estimating nonradiative relaxation rates of a photoexcited iminium ion, CH₂NH₂⁺, and evidence for internal consistency of the combined dynamics/perturbation theory approach is presented.