Diagrammatic perturbation theory: evaluation of fourth-order energy terms involving quadruply-excited states for closed-shell systems

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Abstract
The energy terms involving quadruply-excited states that arise in fourth order in the many-body perturbation series are discussed in detail. Both linked-diagram and unlinked-diagram components are calculated for the nitrogen molecule. The unlinked diagram components, which are required to correct for the unphysical terms included in configuration interaction calculations that are restricted to double excitations, are calculated for some closed-shell diatomic hydrides at their respective equilibrium separations and for the hydrogen fluoride molecule as a function of internuclear distance.