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.

Figure 1

Ground state recovery in neutral GFP chromophore calculated by FSSH-TDKS (crosses) and traditional Ehrenfest-TDKS (circles). The FSSH-TDKS results are well described by a Gaussian plus an exponential. (See text for details.)

Figure 2

(a) Simulation cell for the alizarin-${\mathrm{TiO}}_2$ system. (b)–(c) Electron transfer in alizarin-${\mathrm{TiO}}_2$ calculated by traditional Ehrenfest-TDKS (b) and FSSH-TDDFT (c). Nonadiabatic, adiabatic, and total electron transfer profiles are shown for each method. All fits are single exponential. The nonadiabatic data in (c) were fit with a first-order Taylor expansion of the exponential for the first 30 fs to model the short-time behavior. (See text for details.)