Use of second-moment constraints for the refinement of determinantal wave functions.

Abstract

A constrained least-squares fit procedure wherein the integral F[\ensuremath{\rho}(r)-${\ensuremath{\rho}}_{0}$${(\mathrm{r})]}^{2}$ dr is minimized [${\ensuremath{\rho}}_{0}$(r) is the reference near--Hartree-Fock (NHF) electron density distribution and \ensuremath{\rho}(r) is the refined one obtained from a single Slater determinant] has been developed. The constraints applied are the exact theoretical 〈${p}^{2}$〉 and 〈${r}^{2}$〉 expectation values. These expectation values are expected to tailor the electron density around the nuclear and tail regions, respectively. The procedure has been applied to lithium and beryllium atoms as test cases. Nearly all the 〈${r}^{n}$〉 and 〈${p}^{n}$〉 (for n=-2, -1, 1, 3, 4, and 5) expectation values have been improved with use of this procedure. The sacrifice in the electronic energy, in comparison to the corresponding NHF one, is about 0.02% in both cases.