Stochastic and Quasi-Stochastic Hamiltonians for Long-Time Nonadiabatic Molecular Dynamics

In the condensed-matter environments, the vibronic Hamiltonian that describes nonadiabatic dynamics often appears as an erratic entity, and one may assume it can be generated stochastically. This property is utilized to formulate novel stochastic and quasi-stochastic vibronic Hamiltonian methodologies, which open a new route to long-time excited state dynamics in atomistic solid-state systems at negligible computational cost. Using a model mimicking a typical solid-state material in noisy environment, general conclusions regarding the simulation of nonadiabatic dynamics are obtained: (1) including bath is critical to complete excited state relaxation; (2) a totally stochastic modulation of energies and couplings has a net effect of no bath and inhibits relaxation; (3) including a single or several dominant electron phonon modes may be insufficient to complete the excited state relaxation; (4) only the multiple modes, even those that have negligible weights, can represent both the deterministic modulation of system's Hamiltonian and stochastic effects of bath.