Coupled Hartree-Fock method for calculating Sternheimer shielding

Abstract

We have extended our calculations of Sternheimer shielding functions of Ref. 1 by introducing exchange terms via the self-consistent Hartree-Fock perturbation method. This procedure becomes relatively time consuming. It takes for ${\mathrm{Pr}}^{3+}$ 2-1/2 h of CPU time at a TR 440 computer to achieve convergency after 10 iterations. In addition to the accurate method we have also studied an approximate version, which handles the calculation of exchange integrals in a simplified form so as to make the computational procedure very fast. The approximations inherent to this procedure, however, yield unreliable results, unless the wave functions are considerably contracted. Our results from the accurate method are compared with values reported in the literature, which also take consistency, exchange, and correlation effects into account. We conclude from our study that consistency effects in deriving Sternheimer corrections are dominant over correlation effects.