Trajectory Surface Hopping in the Time-Dependent Kohn-Sham Approach for Electron-Nuclear Dynamics

The mean-field treatment of electron-nuclear interaction results in many qualitative breakdowns in the time-dependent Kohn-Sham (TDKS) density functional theory. Examples include current-induced heating in nanoelectronics, charge dynamics in quantum dots and carbon nanotubes, and relaxation of biological chromophores. The problem is resolved by the trajectory surface-hopping TDKS approach, which is illustrated by the photoinduced electron injection from a molecular chromophore into ${\mathrm{TiO}}_2$, and the excited-state relaxation of the green fluorescent protein chromophore.