First order perturbation treatments for relativistic pseudopotentials and corrections to the Hartree-Fock method

Abstract

The lowest order (1/c ²) perturbation theories recently developed [1, 2] to decribe the relativistic corrections to valence orbital energies in both Hartree-Fock and generalized Phillips-Kleinman pseudopotential theories are tested numerically for single valence electron atoms drawn for the entire periodic table. The corrections are analysed into contributions from the direct and indirect relativistic effects, the off-diagonal lagrange multipliers and the pseudopotential corrections.

Theories in which the operators describing the indirect effect, which arises from relativistically induced modifications of the core charge density, are not exactly correct asymptotically and are shown to fail for atoms beyond the first row of the periodic table. Lowest order (1/c ²) perturbation theories in which the core potential is asymptotically exact are shown to give an excellent description of first and second row atoms, a useful description of the first transition series but to be only useful qualitatively for heavier elements.

It is shown that lowest order perturbation theory cannot account for the behaviour of valence s and [pbar] electrons in atoms heavier than the third series of transition elements because it is incapable of describing the large direct relativistic effects occurring in such Hartee-Fock orbitals. The results for the valence pseudo-orbitals confirm the prediction [2] that the contributions, arising for Hartree-Fock orbitals from the direct relativistic effect, are largely transferred to the pseudopotential corrections provided the pseudo-orbital is chosen to be a smooth nodeless function having a low amplitude in the inner spatial regions.