A Hartree-Fock Analysis of the Finite Jellium Model

Abstract

A Hartree--Fock analysis of the ground-state electronic structure of the finite spherical jellium model is carried out for systems containing up to $520$ electrons in a positive background field with densities ranging from $10^{-3}$ to $1$. The study focuses on quantifying the effects of confinement on the local-density models of the exchange and kinetic energies used in orbital-free density-based quantum computation methods. Significant discrepancies are observed between the energies obtained from the Hartree--Fock approximation and those predicted by the local density approximation (LDA) and the Thomas--Fermi model (TF) evaluated at the computed electron densities, both in the inner region and on the surface of the system. To reconcile these differences, refined expressions for the local one-electron energy densities, parametrized by the system's size and background charge density, are proposed. These models are also compared with commonly used gradient-based energy functionals.