Time-Dependent Orbital-Free Density Functional Theory: A New Development of the Dynamic Kinetic Energy Potential

Time-dependent orbital-free density functional theory (TD-OFDFT) is a promising method for investigating electronic dynamics in large metallic systems. One key component in TD-OFDFT is the dynamic kinetic energy potential (DKEP), which contains the memory effect missed in the adiabatic OFDFT. In this work, we developed a new DKEP based on a density-dependent kernel that is nonlocal in both space and time. The kernel is expanded in terms of the Laguerre polynomials multiplied by exponential decay functions. The parameters in the expansion are determined by fitting the TD-OFDFT dipole oscillations to those from time-dependent Kohn-Sham DFT (TD-KSDFT) simulations. This work also resolves a long-standing problem in TD-OFDFT: the lack of a well-defined total energy. The total energy of a system should be conserved when the external stimulating potential is switched off. Without a properly defined total energy, there is no guarantee that a long-time TD-OFDFT simulation will be stable. This problem is tackled by introducing an energy term for DKEP. The performance of this new TD-OFDFT formalism was examined by simulating several sodium clusters and a sodium nanorod. In most cases, the results are in good agreement with the TD-KSDFT calculations.