An alternative approach to density functional theory based on self-consistent field theory for ring polymers is applied to neutral atoms hydrogen to neon in their ground-states. The spontaneous emergence of an atomic shell structure and spherical symmetry-breaking of the total electron density are predicted by the model using the ideas of polymer excluded-volume between pairs of electrons to enforce the Pauli-exclusion principle and an exact electron self-interaction correction. The Pauli potential is approximated by neglecting inter-atomic correlations along with other types of correlations, and comparisons to Hartree–Fock theory are made, which also ignores correlations. The model shows excellent agreement with Hartree–Fock theory to within the standards of orbital-free density functional theory for the atomic binding energies and density profiles of the first six elements, providing exact matches for the elements hydrogen and helium. The predicted shell structure starts to deviate significantly past the element neon, and spherical symmetry-breaking is first predicted to occur at carbon instead of boron. The self-consistent field theory energy functional that describes the model is decomposed into thermodynamic components to trace the origin of spherical symmetry-breaking. It is found to arise from the electron density approaching closer to the nucleus in non-spherical distributions, which lowers the energy despite resulting in frustration between the quantum kinetic energy, electron–electron interaction, and the Pauli exclusion interaction. The symmetry-breaking effect is found to have a minimal impact on the binding energies, which suggests that the spherical-averaging approximation used in previous work is physically reasonable when investigating atomic systems. The pair density contour plots display behavior similar to polymer macro-phase separation, where individual electron pairs occupy single lobe structures that together form a dumbbell shape analogous to the 2p orbital shape. It is further shown that the predicted densities satisfy known constraints and produce the same total electronic density profile that is predicted by other formulations of quantum mechanics.
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14 February 2023
Research Article|
February 08 2023
On the origins of spontaneous spherical symmetry-breaking in open-shell atoms through polymer self-consistent field theory
Phil A. LeMaitre
;
Phil A. LeMaitre
a)
(Data curation, Formal analysis, Investigation, Methodology, Software, Validation, Visualization, Writing – original draft, Writing – review & editing)
1
Department of Physics and Astronomy, University of Waterloo
, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada
a)Author to whom correspondence should be addressed: [email protected]
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Russell B. Thompson
Russell B. Thompson
(Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Software, Supervision, Validation, Writing – review & editing)
2
Department of Physics and Astronomy and Waterloo Institute for Nanotechnology, University of Waterloo
, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada
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Phil A. LeMaitre
1,a)
Russell B. Thompson
2
1
Department of Physics and Astronomy, University of Waterloo
, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada
2
Department of Physics and Astronomy and Waterloo Institute for Nanotechnology, University of Waterloo
, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada
a)Author to whom correspondence should be addressed: [email protected]
J. Chem. Phys. 158, 064301 (2023)
Article history
Received:
October 20 2022
Accepted:
January 16 2023
Citation
Phil A. LeMaitre, Russell B. Thompson; On the origins of spontaneous spherical symmetry-breaking in open-shell atoms through polymer self-consistent field theory. J. Chem. Phys. 14 February 2023; 158 (6): 064301. https://doi.org/10.1063/5.0131364
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