A Hartree-Fock Analysis of the Finite Jellium Model

TL;DR

This paper performs a Hartree-Fock analysis of finite spherical jellium models to evaluate and improve local-density approximations for exchange and kinetic energies in quantum computations.

Contribution

It provides a detailed comparison between Hartree-Fock results and local-density models, proposing refined energy density expressions based on system size and charge density.

Findings

Significant discrepancies between Hartree-Fock and local-density energies.

Refined energy density models improve agreement with Hartree-Fock results.

Comparison with gradient-based functionals highlights areas for model improvement.

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.