Local scaling transformations applied to density-functional calculations of Li and Be atoms

The local scaling transformation is used to generate a wave function ${\mathrm{\Psi }}_{\mathrm{\rho }}$({${\mathbf{r}}_{\mathit{k}}$}) from a reference function ${\mathrm{\Psi }}_0$({${\mathbf{r}}_{\mathit{k}}$}) in such a manner that the generated function ${\mathrm{\Psi }}_{\mathrm{\rho }}$({${\mathbf{r}}_{\mathit{k}}$}) has exactly the same one-electron density as a given density ρ(r). The method enables us to perform a variational determination of the density ρ(r) through the minimization of the energy E[ρ] associated with the wave function ${\mathrm{\Psi }}_{\mathrm{\rho }}$({${\mathbf{r}}_{\mathit{k}}$}). Using the single-ζ wave function as a reference, we apply this procedure to the ground-state Li and Be atoms within the Hartree-Fock approximation. Comparison of the densities themselves as well as the associated position 〈${\mathit{r}}^{\mathit{n}}$〉 and momentum 〈${\mathit{p}}^{\mathit{n}}$〉 moments shows that the present density compares well with the near-Hartree-Fock density.