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

Abstract

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.

9 pages, 6 figures (14 .eps files); revised version, to appear in Phys. Rev. A

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• System-adapted correlation energy density functionals from effective pair interactions
• Degeneracy and size consistency in electronic density functional theory
• Spin and temperature dependent study of exchange and correlation in thick two-dimensional electron layers
• Intracule densities in the strong-interaction limit of density functional theory
• Ground-state densities and pair correlation functions in parabolic quantum dots
• Range separation combined with the Overhauser model: Application to the H${}_2$ molecule along the dissociation curve
• Variations of the Hartree-Fock fractional-spin error for one electron
• Conditional probability density functional theory
• Kohn-Sham calculations combined with an average pair-density functional theory
• Ground-state energy and Wigner crystallization in thick 2D-electron systems
• The scaling properties of exchange and correlation holes of the valence shell of second row atoms
• The Classical-Map Hyper-Netted-Chain (CHNC) technique for inhomogeneous electron systems. Application to quantum dots
• Physical condition and spin-resolved exchange correlation kernels in an inhomogeneous many electron system