Accuracy of the Hartree-Fock and Local Density Approximations for Electron Densities: A study for Light Atoms

We compare the electron densities and Hartree potentials in the local density and the Hartree-Fock approximations to the corresponding quantities obtained from more accurate correlated wavefunctions. The comparison is made for a number of two-electron atoms, Li, and for Be. The Hartree-Fock approximation is more accurate than the local density approximation within the 1 s shell and for the spin polarization in Li, while the local density approximation is slightly better than the Hartree-Fock approximation for charge densities in the 2 s shell. The inaccuracy of the Hartree-Fock and local density approximations to the Hartree potential is substantially smaller than the inaccuracy of the local density approximation to the ground-state exchange-correlation potential.