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

The Journal of Chemical Physics
Davids AgboolaPierre-François Loos

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 t...Continue Reading

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Apr 3, 2012·Physical Review Letters·Pierre-François Loos, Peter M W Gill
May 3, 2013·The Journal of Chemical Physics·Pierre-François Loos, Peter M W Gill
May 17, 2014·The Journal of Chemical Physics·Pierre-François LoosPeter M W Gill
Dec 19, 2014·Physical Chemistry Chemical Physics : PCCP·Pierre-François LoosPeter M W Gill
Jan 3, 2015·The Journal of Chemical Physics·Peter M W GillDavids Agboola
Jun 8, 2015·The Journal of Chemical Physics·Pierre-François Loos, Dario Bressanini

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Citations

Feb 8, 2016·The Journal of Chemical Physics·Vincent Tognetti, Pierre-François Loos
Feb 6, 2017·The Journal of Chemical Physics·Jerzy Cioslowski, Krzysztof Strasburger
Mar 24, 2017·The Journal of Chemical Physics·Pierre-François Loos
Jun 9, 2020·The Journal of Chemical Physics·Pierre-François Loos, Emmanuel Fromager

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