About the nature of intermolecular three-body forces in ionic systems: The case of protonated hydrates

The three-body intermolecular energy is computed for the water/oxonium ion/water system from ab initio self-consistent-field (SCF) calculations and 170 geometrical configurations. It is decomposed into two parts: ΔE1stnonadd is obtained at the first iteration of the calculation and ΔEdelocnonadd is due to the following iterations till convergency. The nonadditive three-body energy, Eindnonadd, is computed from the perturbation theory. It is shown that all these energy components can be either attractive or repulsive according to the geometry. Edelocnonadd is often seriously different of Eindnonadd, a nonadditive ‘‘induction–exchange’’ term being sometimes as large as Eindnonadd. In most cases, this ‘‘induction–exchange’’ term is much larger than E1stnonadd, with the same sign. This suggests that these two terms can be approximated by a same expression, but because of the sign, more than one exponential term should be used. An approximation of Eindnonadd is discussed with a particular attention to the range of the validity according to the intermolecular distances.