Uniform electron gases. III. Lowdensity gases on threedimensional spheres
By combining variational Monte Carlo (VMC) and completebasisset limit HartreeFock (HF) calculations, we have obtained nearexact correlation energies for lowdensity samespin electrons on a threedimensional sphere (3sphere), i.e., the surface of a fourdimensional ball. In the VMC calculations, we compare the efficacies of two types of oneelectron 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 curvedspace 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 minimumenergy arrangement of n point charges) on the 3sphere 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 fourdimensional Platonic solids — the hypertetrahedron (n = 5), the hyperoctahedron (n = 8), and the 24cell (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 firstorder vibrationalmore »
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 Research School of Chemistry, Australian National University, Canberra ACT 2601 (Australia)
 Publication Date:
 OSTI Identifier:
 22493565
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Chemical Physics; Journal Volume: 143; Journal Issue: 8; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMPARATIVE EVALUATIONS; CRYSTALS; DIAGRAMS; ELECTRON CORRELATION; ELECTRONS; FOURDIMENSIONAL CALCULATIONS; GAUSS FUNCTION; HARTREEFOCK METHOD; MONTE CARLO METHOD; POINT CHARGE; SOLIDS; SPIN; SURFACES; THREEDIMENSIONAL LATTICES; VARIATIONAL METHODS