On the connection between the supermolecular Møller-Plesset treatment of the interaction energy and the perturbation theory of intermolecular forces

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Abstract
This paper presents the first rigorous analysis of the MP2 and MP3 supermolecular treatments in terms of the perturbation theory of intermolecular forces. In order to connect the two formalisms the MP energies are first expanded in terms of an auxiliary double-perturbation theory in spirit similar to the one proposed by Sadlej (1980, Molec. Phys., 39, 1249). In the next step, each term of this expansion is related to the perturbation theory of intermolecular interactions in the formulation of Szalewicz and Jeziorski (1979, Molec. Phys., 38, 191). Although the formal analysis neglects intermolecular exchange effects, a generalization of the final results is proposed so as to accommodate exchange effects. The supermolecular MP2 interaction energy contains the second-order intrasystem correlation correction to the Coulomb energy, in addition to the UCHF dispersion. The supermolecular MP3 term additionally involves the following: first-order intrasystem (apparent) correlation correction to the second-order UCHF dispersion, third-order UCHF dispersion, and third-order intramolecular correlation correction to the Coulomb energy. All terms should be accompanied by their exchange counterparts. Numerical illustration of this decomposition is provided by calculations of interaction energies in the He2 and (HF)2 systems. The correction of supermolecular values by the full counterpose procedure is shown to be essential.