Density-functional approach to electron dynamics: Stable simulation under a self-consistent field

We propose efficient and stable numerical methods for simulating the electr on dynamics within the time-dependent density-functional theory and the non local pseudopotential. In this scheme, time evolution of the wave function is followed by self-consistently solving the time-dependent Kohn-Sham equat ion using the higher-order Suzuki-Trotter type split-operator method. To el iminate the numerical instability problem and increase the time step for th e integration, we introduce the railway curve scheme to interpolate the sel f-consistent potential and the cutoff schemes to smooth the kinetic energy operator and the charge density. Applying these techniques to the electron dynamics of an Al cluster and the electron-ion dynamics of an excited K clu ster, we found that they significantly improve the stability and efficiency . This opens the possibility of performing subpicosecond-long simulations o f the transient dynamics of electrons and ions for a number of materials. [ S0163-1829(99)14403-5].