Electron electron radial and angular holes in the Hartree Fock theory of atoms
Abstract
The twoelectron radial D_{2}(r_{1}, r_{2}) and angular A_{2}(Ω_{1}, Ω_{2}) density functions are the probability densities that one electron is located at a radius r_{1} and another at r_{2} and that one electron is located along a direction Ω_{1} = (θ_{1}, phi_{1}) and another along Ω_{2} = (θ_{2}, phi_{2}), respectively, when any two electrons are considered simultaneously. Within the HartreeFock framework, these densities are the sums of contributions D^{ij}_{2}(r_{1}, r_{2}) and A^{ij}_{2}(Ω_{1}, Ω_{2}) from a pair of spin orbitals i and j. Theoretical analyses of the contributions D^{ij}_{2}(r_{1}, r_{2}) and A^{ij}_{2}(Ω_{1}, Ω_{2}) for atoms show that there exist an 'electronelectron radial hole' D^{ij}_{2}(r, r) = 0 and an 'electronelectron angular hole' A^{ij}_{2}(Ω, ± Ω) = 0 for a pair of spin orbitals with particular conditions. The radial and angular holes add new holes to the electronelectron coalescence (or Fermi) hole for two spin orbitals with the same spin and the electronelectron counterbalance hole for two spin orbitals with the same spin and the same spatial inversion symmetry.
 Publication:

Journal of Physics B Atomic Molecular Physics
 Pub Date:
 November 2007
 DOI:
 10.1088/09534075/40/21/006
 Bibcode:
 2007JPhB...40.4187K