Lithium atom spin density from the Hiller-Sucher-Feinberg identity

Abstract

The electronic spin density, which determines the observed Fermi contact hyperfine splitting, is usually represented by a delta function operator at the nucleus. Approximate wavefunctions determined by overall energetic considerations may show large errors for such a highly localized property. Hiller, Sucher, and Feinberg (HSF) have shown that the delta function operator can be replaced by a global operator. The possibility that this may lead to an improved method for calculation of the spin density is examined for the ground and first excited states of the lithium atom. Particular attention is given to simple spin polarization wavefunctions that provide the leading contributions to the spin density. It is found that the delta function and HSF formulations give very nearly the same results when the wavefunctions are determined by essentially exact numerical methods. However, the HSF approach shows clear advantages in calculations carried out with finite Slater or contracted Gaussian type basis sets.