Diagrammatic perturbation theory: the contribution of triply-excited states to correlation energies

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Abstract
The energy terms involving triply excited intermediate states that arise in fourth-order in the diagrammatic many-body perturbation series for the electron correlation energy in closed-shell systems are discussed. These terms are evaluated for the neon atom using three different Slater exponential basis sets which have been employed in previous perturbation studies and limited configuration-interaction calculations. The contribution from fourth-order terms involving quadruply excited intermediate states are also presented. It is found that in fourth-order the linked-diagram triple-excitation energy is of the same order of magnitude as the unlinked-diagram quadrupole-excitation energy.