Some aspects of diagrammatic perturbation theory

Many-body perturbation theory, or the linked cluster diagrammatic representation of Rayleigh-Schrödinger perturbation theory, is demonstrated to arise from the variational configuration interaction procedure by elementary considerations of Löwdin's partitioning approach to perturbation theory. As a consequence, variational upper bounds to the energy, which arise from the inclusion of some “unlinked” terms, may be obtained from odd-order MBPT calculations and are useful for certain applications. A brief discussion of low-order correlation diagrams for second-order properties is also presented.