Simple model for the spherically- and system-averaged pair density: Results for two-electron atoms

Physical Review A (Impact Factor: 2.81). 11/2004; 71(3). DOI: 10.1103/PhysRevA.71.032513
Source: arXiv


As shown by Overhauser and others, accurate pair densities for the uniform electron gas may be found by solving a two-electron scattering problem with an effective screened electron-electron repulsion. In this work we explore the extension of this approach to nonuniform systems, and we discuss its potential for density functional theory. For the spherically- and system-averaged pair density of two-electron atoms we obtain very accurate short-range properties, including, for nuclear charge $Z\ge 2$, ``on-top'' values (zero electron-electron distance) essentially indistinguishable from those coming from precise variational wavefunctions. By means of a nonlinear adiabatic connection that separates long- and short-range effects, we also obtain Kohn-Sham correlation energies whose error is less than 4 mHartree, again for $Z\ge 2$, and short-range-only correlation energies whose accuracy is one order of magnitude better. Comment: 9 pages, 6 figures (14 .eps files); revised version, to appear in Phys. Rev. A

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Available from: Paola Gori-Giorgi, Aug 26, 2013
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    ABSTRACT: Attempts to generalize the density functional theory are summarized. A possible pair density functional theory is linked to the Overhauser parametrization of the electron- gas pair density. The importance of the cumulant partitioning is stressed and a modied Overhauser approach for the cumulant 2-body reduced density matrix, the contraction of which determines the 1-body reduced density matrix, is discussed.
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    ABSTRACT: We present an extensive comparative study of ground-state densities and pair distribution functions for electrons confined in two-dimensional parabolic quantum dots over a broad range of coupling strength and electron number. We first use spin-density-functional theory to determine spin densities that are compared with Diffusion Monte Carlo (DMC) data. This accurate knowledge of one-body properties is then used to construct and test a local approximation for the electron-pair correlations. We find very satisfactory agreement between this local scheme and the available DMC data, and provide a detailed picture of two-body correlations in a coupling-strength regime preceding the formation of Wigner-like electron ordering.
    Full-text · Article · Feb 2005 · Physical review. B, Condensed matter
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    ABSTRACT: The exchange and correlation $E_{xc}$ of strongly correlated electrons in 2D layers of finite width are studied as a function of the density parameter $r_s$, spin-polarization $\zeta$ and the temperature $T$. We explicitly treat strong-correlation effects via pair-distribution functions, and introduce an equivalent constant-density approximation (CDA) applicable to all the inhomogeneous densities encountered here. The width $w$ defined via the CDA provides a length scale defining the $z$-extension of the quasi-2D layer resident in the $x$-$y$ plane. The correlation energy $E_c$ of the quasi-2D system is presented as an interpolation between a 1D gas of electron-rods (for $w/r_s>1$) coupled via a log(r) interaction, and a 3D Coulomb fluid closely approximated from the known {\it three-dimensional} correlation energy when $w/r_s$ is small. Results for the $E_{xc}(r_s,\zeta,T)$, the transition to a spin-polarized phase, the effective mass $m^*$, the Land\'e $g$-factor etc., are reported here. Comment: Revtex manuscript, 9 postscript figures
    Preview · Article · Jun 2005 · Physical review. B, Condensed matter
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