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).