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

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.