Partitioning schemes for the 2-matrix and the pair density

Several schemes are discussed for partitioning the second-order reduced density matrix Γ into two parts, Γ⁰ and Γ′. The Γ⁰s are based on the independent particle model and the Γ′s are corrections due to electron correlation. The difficulties of choosing a Γ⁰ that will serve as a suitable reference point for studying electron correlation are discussed. In order to compare alternative partitioning schemes, an atomic wave function for the ¹S ground state of the Be atom in the configuration-interaction approximation was selected. A fifty-two configuration wave function was computed and contour graphs were made of the total pair density Γ(1 2) and of the “correlation pair density” Γ′(1 2) for several choices of the reference Γ⁰.