Gaussian basis functions for an orbital‐free‐related density functional theory of atoms

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 energ...

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Bibliographic Details
Published in:International journal of quantum chemistry 2023-06, Vol.123 (12), p.n/a
Main Authors: LeMaitre, Phil A., Thompson, Russell B.
Format: Article
Language:English
Subjects:
Basis functions
Chemistry
Density functional theory
Electron density
Field theory
Functionals
Hydrogen
Kinetic energy
Krypton
Neon
Neutral atoms
orbital‐free
Physical chemistry
polymer physics
Polymers
Quantum physics
self‐consistent field theory
Shells (structural forms)
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Summary: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 examined without some approximations which permit cancellation of errors and spontaneous shell structure is observed. Correlations are neglected 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. Polymer self‐consistent field theory can be used to solve quantum many‐body systems through the Feynman quantum‐classical isomorphism. Gaussian basis functions are shown to be particularly effective for expressing and solving the polymeric equations, giving very good radial electron densities and binding energies for the first 36 elements of the periodic table.
ISSN:0020-7608
1097-461X
DOI:10.1002/qua.27111