MuAPBEK: An improved analytical kinetic energy density functional for quantum chemistry

Abstract

Orbital-free density functional theory (OFDFT) enables full quantum-mechanical simulations based solely on electron densities but is limited by the lack of accurate kinetic-energy functionals. We improve upon the APBEK functional by tuning its μ parameter for a given system during density initialization and adding two non-empirical corrections based on Kato’s cusp condition and the virial theorem. The resulting functional, MuAPBEK, assessed on atoms and molecules, shows significantly lower energy errors than standard APBEK and Thomas–Fermi–von-Weizsäcker functionals, even when evaluated on converged Kohn–Sham density functional theory (KSDFT) densities. MuAPBEK also produces accurate densities that slightly deviate from those of KSDFT. Its density optimization step is over ten times faster than a single KSDFT SCF cycle and scales as O(N1.96), indicating that accurate, large-scale OFDFT simulations are feasible beyond practical KSDFT limits.