Pair distribution function of the spin-polarized electron gas: A first-principles analytic model for all uniform densities

2002/06/30 by Paola Gori‐Giorgi, Paola Gori-Giorgi, John P. Perdew · 2 citations
Physics and Astronomy · #Advanced Condensed Matter Physics #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #cond-mat

paper · pdf · doi:10.1103/physrevb.66.165118

published as Phys. Rev. B 66, 165118 (2002) · new version, with three new figures, and two new subsections

arxiv created 2002/08/20 · openalex publication_date 2002/10/31 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct analytic formulas that represent the coupling-constant-averaged pair distribution function g_xc(r_s,\ensuremathζ,k_Fu) of a three-dimensional nonrelativistic ground-state electron gas constrained to a uniform density with density parameter r_s=(9\ensuremathπ/4)^1/3/k_F and relative spin polarization \ensuremathζ over the whole range 0<r_s<\ensuremath∞ and \ensuremath-1<\ensuremathζ<1, with energetically unimportant long range (\stackrel\ensuremath→u\ensuremath∞) oscillations averaged out. The pair distribution function g_xc at the physical coupling constant is then given by differentiation with respect to r_s. Our formulas are constructed using only known theoretical constraints plus the correlation energy \ensuremathε_c(r_s,\ensuremathζ), and accurately reproduce the g_xc of the quantum Monte Carlo method and of the fluctuation-dissipation theorem with the Richardson-Ashcroft dynamical local-field factor. Our g_xc is correct even in the high-density (r_s\ensuremath→0) and low-density (r_s\ensuremath→\ensuremath∞) limits. When the spin resolution of \ensuremathε_c into \ensuremath\uparrow\ensuremath\uparrow, \ensuremath\downarrow\ensuremath\downarrow, and \ensuremath\uparrow\ensuremath\downarrow contributions is known, as it is in the high- and low-density limits, our formulas also yield the spin resolution of g_xc. Because of these features, our formulas may be useful for the construction of density functionals for nonuniform systems. We also analyze the kinetic energy of correlation into contributions from density fluctuations of various wave vectors. The exchange and long-range correlation parts of our g_xc(r_s,\ensuremathζ,k_Fu)\ensuremath-1 are analytically Fourier transformable, so that the static structure factor S_xc(r_s,\ensuremathζ,k/k_F) is easily evaluated.

Citations

• Generalized Gradient Approximation Made Simple
• Exchange-correlation kernels for excited states in solids
• Generalized gradient approximation for the exchange-correlation hole of a many-electron system
• Electronic structure of solids

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