Correlation hole of the spin-polarized electron gas, with exact small-wave-vector and high-density scaling

Abstract

For a uniform electron gas of density n=${\mathit{n}}_{\mathrm{\uparrow }}$+${\mathit{n}}_{\mathrm{\downarrow }}$=3/4π${\mathit{r}}_{\mathit{s}}^3$=π${\mathit{k}}_{\mathit{s}}^6$/192 and spin polarization ζ=(${\mathit{n}}_{\mathrm{\uparrow }}$-${\mathit{n}}_{\mathrm{\downarrow }}$)/n, we study the Fourier transform ρ${\mathrm{¯}}_{\mathit{c}}$(k,${\mathit{r}}_{\mathit{s}}$,ζ) of the correlation hole, as well as the correlation energy ${\mathrm{\varepsilon }}_{\mathit{c}}$(${\mathit{r}}_{\mathit{s}}$,ζ)=${\mathcal{F}}_0^{\mathrm{\infty }}$dk ρ${\mathrm{¯}}_{\mathit{c}}$/π. In the high-density (${\mathit{r}}_{\mathit{s}}$→0) limit, we find a simple scaling relation ${\mathit{k}}_{\mathit{s}}$ρ${\mathrm{¯}}_{\mathit{c}}$/π${\mathit{g}}^2$→f(z,ζ), where z=k/${\mathit{gk}}_{\mathit{s}}$, g=[(1+ζ${)}^{2/3}$+(1-ζ${)}^{2/3}$]/2, and f(z,1)=f(z,0). The function f(z,ζ) is only weakly ζ dependent, and its small-z expansion -3z/${\mathrm{\pi }}^2$+4 √3 ${\mathrm{z}}^2$/${\mathrm{\pi }}^2$+... is also the exact small-wave-vector (k→0) expansion for any ${\mathit{r}}_{\mathit{s}}$ or ζ. Motivated by these considerations, and by a discussion of the large-wave-vector and low-density limits, we present two Padé representations for ρ${\mathrm{¯}}_{\mathit{c}}$ at any k, ${\mathit{r}}_{\mathit{s}}$, or ζ, one within and one beyond the random-phase approximation (RPA). We also show that ρ¯ ${}_{\mathit{c}}{}^{\mathrm{RPA}}{}_{}{}^{}$ obeys a generalization of Misawa’s spin-scaling relation for

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This publication has 22 references indexed in Scilit:

• Generalized gradient approximations for exchange and correlation: A look backward and forward
  Physica B: Condensed Matter, 1991
• Quantum-Mechanical Interpretation of the Exchange-Correlation Potential of Kohn-Sham Density-Functional Theory
  Physical Review Letters, 1989
• Static properties of a uniform electron gas: A phenomenological approach
  Physical Review B, 1986
• Electron correlations in the Bogoljubov coupled-cluster formalism
  Physical Review B, 1984
• Ground State of the Electron Gas by a Stochastic Method
  Physical Review Letters, 1980
• Descriptions of exchange and correlation effects in inhomogeneous electron systems
  Physical Review B, 1979
• Exchange and correlation in atoms, molecules, and solids by the spin-density-functional formalism
  Physical Review B, 1976
• The exchange-correlation energy of a metallic surface
  Solid State Communications, 1975
• A local exchange-correlation potential for the spin polarized case. i
  Journal of Physics C: Solid State Physics, 1972
• Correlation Energy of a Free Electron Gas
  Physical Review B, 1958

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