Correlation effects to the expectation values of atomic systems

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Abstract
The Hartree‐Fock and first natural spin determinants were compared as reference determinants for calculating various one‐electron properties such as ρ(0), 〈½∇〉, 〈r−2〉,…, 〈r3〉, and r−112〉. Calculations were made on various small atoms and their positive and negative ions. For nearly all the expectation values studied, the first natural spin orbital determinant gave consistently superior results. In particular, the Hartree‐Fock functions gave markedly inferior results for some long range properties such as the magnentic susceptibilities of negative ions. The major correlation error in the expectation values is primarily an orbital effect which may be accounted for by including correlation terms in the one‐particle Hamiltonian. Such approximate Brueckner or best overlap orbitals should reproduce most one‐electron expectation values accurately.