The correlation energy in the random phase approximation: Intermolecular forces between closed-shell systems

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Abstract
A new expression for the correlation energy within the random phase approximation (RPA) is presented. It has the following properties: it is (1) size consistent, (2) invariant to unitary transformations of degenerate orbitals, (3) correct to second order in perturbation theory, and (4) when applied to a supermolecule comprised of two interacting closed‐shells, it describes the dispersive part of the interaction at the coupled Hartree–Fock (HF) level, i.e., the van der Waals’ coefficient extracted from its long‐range behavior is identical to that obtained from the Casimir–Polder expression using the dynamic coupled Hartree–Fock polarizabilities of the isolated systems. This expression, which requires only particle–hole two‐electron integrals for its evaluation, is expected to yield considerably more accurate potential energy curves between closed‐shell systems than second‐order Moller–Plesset perturbation theory which, as is shown, describes dispersion forces at the less accurate uncoupled HF level. In addition, since it is shown how this RPA correlation energy can be obtained from the zeroth iteration of a self‐consistent RPA procedure such as that of McKoy and co‐workers, our result can be systematically improved. Finally, illustrative calculations of He and (He)2 are presented.

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