Letter pubs.acs.org/JCTC
Many-Body Energy Decomposition with Basis Set Superposition Error Corrections István Mayer* and Imre Bakó Institute of Organic Chemistry, Research Centre for Natural Sciences, Hungarian Academy of Sciences, P. O. Box 286, H-1519 Budapest, Hungary ABSTRACT: The problem of performing many-body decompositions of energy is considered in the case when BSSE corrections are also performed. It is discussed that the two different schemes that have been proposed go back to the two different interpretations of the original Boys−Bernardi counterpoise correction scheme. It is argued that from the physical point of view the “hierarchical” scheme of Valiron and Mayer should be preferred and not the scheme recently discussed by Ouyang and Bettens, because it permits the energy of the individual monomers and all the two-body, three-body, etc. energy components to be free of unphysical dependence on the arrangement (basis functions) of other subsystems in the cluster.
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There are no problems with these requirements in the case of the usual “straightforward” quantum chemical calculations, but one finds out that only one of these two requirements can be fulfilled if corrections are performed for the basis set superposition error (BSSE). In what follows we shall briefly recall the two different interpretations23 of the classical Boys−Bernardi “counterpoise” (CP) correction scheme4 that essentially differ in preferring either condition a) or condition b) and discuss that the BSSEcorrected many-body decomposition scheme proposed by Valiron and Mayer2 from the one side and the scheme used by Ouyang and Bettens5 from the other represent direct generalizations of these two approaches. (The recent appearance of the paper ref 5 has motivated our present Letter.) However, contrary to the classical (two-body) CP case, these schemes do not simply represent different interpretations, but they also lead to different results in the total cluster formation energy if there are more than two subsystems. We shall argue that the “hierarchical” scheme of Valiron and Mayer2 is to be preferred from the physical point of view.
he properties of clusters consisting of a large number of subsystems (and those of liquids, etc., the clusters model) are determined by different pairwise interactions of the constituting subsystems, their three-body interactions, and so on. (The three-body, four-body, etc. energy terms sometimes are called “collective effects”.) For that reason it is often useful to consider the decomposition of the total cluster energy into one-body, two-body, three-body,..., N-body energy contributions:1 Etot =
(2) + ∑ ∑ EA + ∑ εAB A
A
