Relativistic theory of an inhomogeneous electron liquid in relation to atomic binding energies

Abstract

Experimentally determined ionization potentials in the literature are used to plot the binding energies for neutral atoms as a function of atomic number Z for Z = 2–30, 32, 36, 42. From this pretty smooth plot we have subtracted non-relativistic Hartree–Fock binding energies, using both available numerical values and the almost analytical result, based on the non-relativistic Thomas–Fermi statistical theory valid for large Z. The difference is still relatively smooth. For Mo, with Z = 42, the difference is about 70 atomic units. This difference is then analyzed using first relativistic theory of an inhomogeneous electron liquid and then the Local Density Approximation (LDA), and for Mo their results yield approximately 88 and 67 atomic units respectively. We infer that a highly accurate relativistic many-electron theory will therefore be needed before reliable electron correlation energies can be extracted from the experimental binding energies for atoms heavier than Argon. This fact has prompted us to use available LDA calculations to confront three theoretical predictions of the Z dependence of non-relativistic electron correlation energies at large Z.