Excited State Chemical Dynamics: Beyond the Born-Oppenheimer Approximation

Abstract

Herein, numerical approaches for describing the time evolution of molecular systems in nonequilibrium, and excited electronic states using the tools of non-adiabatic molecular dynamics will be built up from the full molecular Hamiltonian and associated quantum mechanical equation of motion. This common formalism, from which all of the approximate methods emerge, is rst presented in detail. The working equations for these methods, which are found to naturally arise from successive approximations to the quantum mechanical treatment of all molecular degrees of freedom, and presented along with details of their implementations in electronic structure programs utilizing atom-centered basis sets. Specic scientic studies and methodological developments relying on the resulting methods are then presented to highlight the utility of the developments. A central theme throughout this document will be to exploit the disparate timescales on which the heavy and light particles comprising molecular systems evolve through the combination of explicitly time dependent methods (in a mixed quantum-classical framework), and the tools of time-dependent perturbation theory to extract the temporal evolution of molecular systems in far-from-equilibrium conditions.