Many-body perturbation theory applied to molecules: Analysis and correlation energy calculation for Li2, N2, and H3

The correlation problem is analyzed in terms of Goldstone diagrammatic perturbation theory. A hole-line expansion for the correlation energy is defined and used with matrix partitioning techniques to determine the diagrams contributing to various forms of pair theory and to configuration interaction treatments of the usual type. The presence of certain terms in the double excitation configuration interaction formulation that cancel in higher order is demonstrated. The nature of various approximations to the correlation correction is determined. To illustrate the analysis, certain of the approximations are used in correlation energy calculations with multicenter Slater basis sets on Li2, N2, and H3. Comparison with complete configuration interaction calculations are made for Li2 and H3; the diagrammatic calculation, which is much simpler than a full CI treatment, is found to be a good approximation to the latter.