Density-Matrix Study of Atomic Ground and Excited States. III. Geminal Energy Analysis of an Accurate Beryllium Ground-State Wave Function

Abstract

The total energy of an accurate beryllium ground-state wave function is decomposed into energies of its natural-spin geminals. These are further subdivided into kinetic, electron-nuclear attraction, and electron-electron interaction energy contributions. Similar subdivisions for a Hartree-Fock wave function are presented. It is pointed out that it is unreasonable to expect natural-spin geminals to be populated on the basis of their energies. The important energy implications of singlet-triplet degeneracies in a two-matrix are also discussed. The correlation energy is analyzed at the geminal level, and it is shown that the electron-nuclear attraction part of the correlation energy is negative and not negligible. For the beryllium ground state the Coulomb correlation energy is about four times greater than the Fermi correlation energy. It is pointed out that the Hartree-Fock wave function for beryllium contains too much Fermi correlation.