On the contribution of higher-order excitations to correlation energies: The ground state of the water molecule

Using the results of a configuration interaction calculation reported by Rosenberg and Shavitt, we derive an approximation to the correlation energy which may be associated with the sum to infinite order of all linked diagrams involving singly- and doubly-excited states. This result is compared with that obtained by calculation of the energy through third-order. The fourth-order linked diagrams involving quadruply-excited states are computed. It is shown that there is a considerable degree of cancellation between the fourth-order linked diagram energy terms involving doubly-excited intermediate states only and those which contain quadruply-excited states.