Correlation and X-ray scattering. II. Atomic beryllium

In order to assess the importance of correlation effects with respect to the Hartree–Fock (HF) results, values of the coherent, total and incoherent scattered X-ray intensities were computed for the 1S ground state of atomic beryllium. Natural spin orbitals (NSO) and natural spin geminals (NSG) constructed from the accurate configuration interaction (CI) wavefunction of A.W. Weiss were used in the evaluation of these X-ray quantities from previously derived density matrix expressions. Values were also computed from the two-configuration wavefunction of Watson, which accounts for the 2s–2p near degeneracy effect. As expected, the CI results for the total intensity differ from their HF counterparts but the magnitudes of the absolute deviations are not as large as those observed for the coherent intensity values. Although the HF results for the coherent intensity are in reasonably good agreement with the CI values, conclusions based on the Møller–Plesset theorem must be made with caution. The largest percentage deviations between HF and CI results, however, are observed for the incoherent intensity. All calculations reported here were verified by the use of sum rules.