Hierarchy of counterpoise corrections for N-body clusters: generalization of the Boys-Bernardi scheme

The counterpoise correction method of Boys and Bernardi is generalized for a consistent treatment of the basis set superposition error (BSSE) of three-body and higher many-body effects along the line used by White and Davidson for the three-body terms in an ice model. The BSSE-corrected energy terms are calculated recursively by using the hierarchy of one-, two-, three-body, etc. energy terms, and by recomputing each such contribution in basis sets of subclusters of increasing size. The scheme is illustrated by calculations on the He trimer at the RHF, MP2 and MP4 levels. The results suggest that properly BSSE-corrected cluster calculations may combin refined two-body interactions with approximate many-body corrections. The method might be useful in calculating potential surfaces of chemical reactions.