Uniform electron gases. III. Low-density gases on three-dimensional spheres

Agboola, Davids, Knol, Anneke L., Gill, Peter M. W. and Loos, Pierre-Francois (2015) Uniform electron gases. III. Low-density gases on three-dimensional spheres. Journal of Chemical Physics, 143 8: . doi:10.1063/1.4929353

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Author Agboola, Davids
Knol, Anneke L.
Gill, Peter M. W.
Loos, Pierre-Francois
Title Uniform electron gases. III. Low-density gases on three-dimensional spheres
Journal name Journal of Chemical Physics   Check publisher's open access policy
ISSN 0021-9606
1520-9032
1089-7690
Publication date 2015-08-28
Year available 2015
Sub-type Article (original research)
DOI 10.1063/1.4929353
Open Access Status File (Publisher version)
Volume 143
Issue 8
Total pages 6
Place of publication Melville, NY United States
Publisher AIP Publishing
Collection year 2016
Language eng
Abstract By combining variational Monte Carlo (VMC) and complete-basis-set limit Hartree-Fock (HF) calculations, we have obtained near-exact correlation energies for low-density same-spin electrons on a three-dimensional sphere (3-sphere), i.e., the surface of a four-dimensional ball. In the VMC calculations, we compare the efficacies of two types of one-electron basis functions for these strongly correlated systems and analyze the energy convergence with respect to the quality of the Jastrow factor. The HF calculations employ spherical Gaussian functions (SGFs) which are the curved-space analogs of Cartesian Gaussian functions. At low densities, the electrons become relatively localized into Wigner crystals, and the natural SGF centers are found by solving the Thomson problem (i.e., the minimum-energy arrangement of n point charges) on the 3-sphere for various values of n. We have found 11 special values of n whose Thomson sites are equivalent. Three of these are the vertices of four-dimensional Platonic solids — the hyper-tetrahedron (n = 5), the hyper-octahedron (n = 8), and the 24-cell (n = 24) — and a fourth is a highly symmetric structure (n = 13) which has not previously been reported. By calculating the harmonic frequencies of the electrons around their equilibrium positions, we also find the first-order vibrational corrections to the Thomson energy.
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Non HERDC
 
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Created: Fri, 18 Mar 2016, 11:17:51 EST by Davids Agboola on behalf of School of Medicine