Gaussian Basis Functions for a Polymer Self-Consistent Field Theory of Atoms

TL;DR

This paper develops a polymer self-consistent field theory framework using Gaussian basis functions to accurately compute atomic properties, incorporating electron interactions and Pauli exclusion, and compares results with Hartree-Fock theory.

Contribution

It introduces a novel Gaussian basis set approach for polymer self-consistent field theory applied to atoms, including exact electron self-interaction correction and Pauli-exclusion modeling.

Findings

Accurate binding energies for atoms hydrogen to krypton.

Radial electron densities closely match quantum calculations.

Analysis of Pauli-exclusion potential effects.

Abstract

A representation of polymer self-consistent field theory equivalent to quantum density functional theory is given in terms of non-orthogonal basis sets. Molecular integrals and self-consistent equations for spherically symmetric systems using Gaussian basis functions are given, and the binding energies and radial electron densities of neutral atoms hydrogen through krypton are calculated. An exact electron self-interaction correction is adopted and the Pauli-exclusion principle is enforced through ideas of polymer excluded-volume. The atoms hydrogen through neon are additionally examined without some approximations which permit cancellation of errors. Correlations are neglected for both cases in the interest of simplicity and comparisons are made with Hartree-Fock theory. The implications of the Pauli-exclusion potential and its approximate form are discussed, and the Pauli model is analyzed using scaling theory for the uniform electron density case where the correct form of the Thomas-Fermi quantum kinetic energy and the Dirac exchange correction are recovered.