Constrained density matrix study of simple basis sets for helium

Abstract

The method of Clinton et al. for the direct determination of an idempotent density matrix subject to constraints is used to examine in detail the ability of two basis sets, each consisting of a pair of 1s functions to predict one- and two-electron properties for the helium atom. The two bases differ in that one has variationally optimized exponents. Idempotent density matrices constrained to give each of eleven different expectation values computed from the accurate Pekeris wavefunction are constructed for each basis. These constrained densities are then evaluated in terms of the accuracy of the other expectation values compared to the Pekeris values. As the basis becomes energetically optimized, one-electron properties improve, as expected for an independent-particle model, but all computed two-electron properties become less accurate. Several criteria for over-all quality of the electron densities are examined. Although the density can change significantly in specific regions while the energy changes only slightly, the energy is found to remain a prime indicator of average quality. There is evidence that the accuracy with which a free-variational density already predicts a given property may provide a prior indication of the effectiveness of that property as a constraint in a constrained-variational calculation.