Time-Dependent Orbital-Free Density Functional Theory

We have developed a new dynamic kinetic energy potential (DKEP) for the time-dependent orbital-free density functional theory (TD-OFDFT). Huang-Carter kinetic energy density functional is employed to determine the "static" part of kinetic energy potential, which instantaneously depends on the current density. The "dynamic" part, i.e., DKEP is introduced with a density dependent, nonlocal in both space and time, and dimensionless kernel to ensure a proper frequency-dependent response. We use Lagurerre polynomials with an exponential decay term to expand the DKEP kernel. The advantage of such expansion is that one can calculate the DKEP term explicitly in the time domain by using a recurrence relation. The parameters in the expansion are determined by fitting spectra of TD-OFDFT to the benchmark evaluated by TD-KSDFT. Moreover, the DKEP kernel is designed to satisfy the translational invariance. We also defined the DKEP energy where the conservation of total energy can be maintained during electron dynamics with a constraint potential. The method is demonstrated for applications of sodium nanoclusters, sodium nanorod, and aluminum nanoclusters. The spectra by our TD-OFDFT simulations show a good agreement with that from TD-KSDFT calculations.