Nonadiabatic Molecular Dynamics in Momentum Space Beyond Harmonic Approximation: Hot Electron Relaxation in Photoexcited Black Phosphorus.

We simulated hot-electron relaxation in black phosphorus using the nonadiabatic molecular dynamics (NA-MD) approach with a non-Condon effect in momentum space beyond the harmonic approximation. By comparing simulations at the Γ point in a large supercell with those using a few k -points in a smaller supercell─while maintaining the same number of electronic states within the same energy range, we demonstrate that both setups yield remarkably consistent energy relaxation times, regardless of the initial state energy. This consistency arises from the complementary effects of supercell size in real space and the number of k -points in the reciprocal space. This finding confirms that simulations at a single k -point in large size supercells are an effective approximation for NA-MD with a non-Condon effect. This approach offers significant advantages for complex photophysics, such as intervalley scattering and indirect bandgap charge recombination, and is particularly suitable for large systems without the need for a harmonic approximation.