Inequivalent electron densities derived from an approximate correlated ground-state wavefunction using the Hiller-Sucher-Feinberg identity: comparisons with quantum Monte Carlo densities for He and Ne atoms

The Hiller-Sucher-Feinberg (HSF) identity is combined with the three-parameter correlated wave function of Chandrasekhar in order to generate an alternative electron density rho(r) for the He atom. This and the conventional "local" operator form of rho(r) are then compared with a diffusion quantum Monte Carlo density An exact limiting relation is also presented, via HSF identity, between the one-particle density matrix and the pair density in a many-electron atom, which transcends its Hartree-Fock counterpart and has no N-representability difficulties. For the Ne atom, the accuracy of the semiempirical correlated electron density recently obtained by Cordero et al. (Phys. Rev. A 2007, 75, 052502) using fine-tuning of Hartree-Fock theory was assessed by appealing to the ground-state density from diffusion quantum Monte Carlo. The high accuracy of the Cordero et al. density was thereby confirmed. A HSF calculation on neon, with a correlated many-body wave function as starting point, is a worthwhile future aim.