Many‐body exchange‐repulsion in polarizable molecular mechanics. I. orbital‐based approximations and applications to hydrated metal cation complexes

We have quantified the extent of the nonadditivity of the short‐range exchange‐repulsion energy, E exch‐rep , in several polycoordinated complexes of alkali, alkaline‐earth, transition, and metal cations. This was done by performing ab initio energy decomposition analyses of interaction energies in these complexes. The magnitude of E exch‐rep( n ‐body, n > 2) was found to be strongly cation‐dependent, ranging from close to zero for some alkali metal complexes to about 6 kcal/mol for the hexahydrated Zn 2+ complex. In all cases, the cation–water molecules, E exch‐rep(three‐body) , has been found to be the dominant contribution to many‐body exchange‐repulsion effects, higher order terms being negligible. As the physical basis of this effect is discussed, a three‐center exponential term was introduced in the SIBFA (Sum of Interactions Between Fragments Ab initio computed) polarizable molecular mechanics procedure to model such effects. The three‐body correction is added to the two‐center (two‐body) overlap‐like formulation of the short‐range repulsion contribution, E rep , which is grounded on simplified integrals obtained from localized molecular orbital theory. The present term is computed on using mostly precomputed two‐body terms and, therefore, does not increase significantly the computational cost of the method. It was shown to match closely E three‐body in a series of test cases bearing on the complexes of Ca 2+ , Zn 2+ , and Hg 2+ . For example, its introduction enabled to restore the correct tetrahedral versus square planar preference found from quantum chemistry calculations on the tetrahydrate of Hg 2+ and [Hg(H 2 O) 4 ] 2+ . © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011