Electron electron radial and angular holes in the Hartree Fock theory of atoms
Abstract
The two-electron radial D2(r1, r2) and angular A2(Ω1, Ω2) density functions are the probability densities that one electron is located at a radius r1 and another at r2 and that one electron is located along a direction Ω1 = (θ1, phi1) and another along Ω2 = (θ2, phi2), respectively, when any two electrons are considered simultaneously. Within the Hartree-Fock framework, these densities are the sums of contributions Dij2(r1, r2) and Aij2(Ω1, Ω2) from a pair of spin orbitals i and j. Theoretical analyses of the contributions Dij2(r1, r2) and Aij2(Ω1, Ω2) for atoms show that there exist an 'electron-electron radial hole' Dij2(r, r) = 0 and an 'electron-electron angular hole' Aij2(Ω, ± Ω) = 0 for a pair of spin orbitals with particular conditions. The radial and angular holes add new holes to the electron-electron coalescence (or Fermi) hole for two spin orbitals with the same spin and the electron-electron counterbalance hole for two spin orbitals with the same spin and the same spatial inversion symmetry.
- Publication:
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Journal of Physics B Atomic Molecular Physics
- Pub Date:
- November 2007
- DOI:
- 10.1088/0953-4075/40/21/006
- Bibcode:
- 2007JPhB...40.4187K