Radial Momentum DistributionsI0(p)and Compton ProfilesJ(q). TheS1Be Atom Ground State

Abstract

The natural orbitals (NO) obtained from ${}_{}{}^1{}_{}{}^{}S$ Be atom ground-state wave functions which incorporate various amounts of the correlation energy are Fourier transformed to momentum space in order to obtain radial momentum distributions $J_0\mathrm{}\left(p\right)\mathrm{}$. Momentum distributions calculated from several analytical restricted Hartree-Fock (RHF) wave functions are also presented. Correlated and RHF Compton profile values $J\left(q\right)\mathrm{}$ are found to be in better agreement than the corresponding $I_0\mathrm{}\left(p\right)\mathrm{}$ values. In the "valence shell" portion of the $I_0\mathrm{}\left(p\right)\mathrm{}$ distribution, relative differences as large as 25% are observed between correlated and RHF values, whereas in the "core" portion of $I_0\mathrm{}\left(p\right)\mathrm{}$ the correlated and RHF values are in relatively good agreement. The virial theorem is used to explain the differences observed between correlated and RHF $I_0\mathrm{}\left(p\right)\mathrm{}$ distributions. Basis set effects are found to be negligible in comparison with correlation effects. The present calculations indicate that much of the discrepancy between correlated and RHF $I_0\mathrm{}\left(p\right)\mathrm{}$ values, at least for the ${}_{}{}^1{}_{}{}^{}S$ Be ground state, is due to the $2s-2p$ "near-degeneracy" effect. They also demonstrate that the node found when examining the long-range behavior of the RHF $1s$ orbital in position space is of a spurious nature.