We propose efficient and stable numerical methods for simulating the electron dynamics within the time-dependent density-functional theory and the nonlocal pseudopotential. In this scheme, time evolution of the wave function is followed by self-consistently solving the time-dependent Kohn-Sham equation using the higher-order Suzuki-Trotter type split-operator method. To eliminate the numerical instability problem and increase the time step for the integration, we introduce the railway curve scheme to interpolate the self-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 cluster, we found that they significantly improve the stability and efficiency. This opens the possibility of performing subpicosecond-long simulations of the transient dynamics of electrons and ions for a number of materials.

• Received 30 July 1998

DOI:https://doi.org/10.1103/PhysRevB.59.2579