Many-body perturbation theory applied to electron pair correlation energies. I. Closed-shell first-row diatomic hydrides

Diagrammatic many-body perturbation theory is formulated through third order and applied to LiH, BH, and HF with various sizes of two-center Slater orbital basis sets. The most extensive calculations use 46 orbitals to recover 94, 95, and 97% of the experimental correlation energy for the three molecules, respectively, when the perturbation expansion is carried through third order with pair restrictions and including selections of higher-order diagrams via denominator shifts. A detailed analysis of the ’’pair’’ correlation energies relative to SCF occupied orbitals is given, including both inter- and intrapair contributions for the different spin cases.