Foundations, Reflections and Applications of Time-dependent Orbital-free Density Functional Theory

Time-dependent orbital-free density functional theory (TD-OF-DFT) is an efficient method for calculating the dynamic properties of large scale quantum systems due to its linear scaling with system size. We present an in principle exact TD-OF-DFT formalism by mapping the real system of interacting fermions into a fictitious system of non-interacting (NI) bosons. Based on this formalism, we derive a time-dependent Schr\"{o}dinger-like equation for real-time propagation and define the Pauli potential that needs to be approximated for the actual calculation. We also present the linear response form of this formalism with the Dyson equation that relates the NI boson and interacting fermion systems. This formalism yields very accurate oscillator strength on Na clusters and qualitatively accurate results on several metallic and III-V semiconductor nanostructures.