Basis-Discretized Surface Hopping for Auger Processes

We develop a basis-discretized nonadiabatic molecular dynamics approach that enables large-scale simulations involving millions of states. The approach introduces a density-of-states (DOS) weighted discretization scheme that maps electronic state quasi-continua onto a manageable discrete set, while preserving the original DOS profile, with enhanced resolution near band edges. Benchmarks using both time-dependent Schrödinger equation and fewest-switches surface hopping confirm that the dynamics remain consistent before and after the discretization. The method is applied to study Auger-type processes in a silicon quantum dot by reducing an otherwise intractable basis set to a manageable discretized model. The simulations show that biexciton and triexciton states significantly broaden energy dissipation pathways and accelerate electron-vibrational energy relaxation via Coulomb-mediated Auger processes, as compared to the single exciton dynamics. The work offers an efficient and robust framework for accurate simulations of excited-state dynamics in low-dimensional and nanoscale materials at the atomistic level.