Cooperative effects in extended hydrogen bonded systems involving OH groups. Ab initio studies of the cyclic S₄ water tetramer

The additional energy stabilization due to cooperative effects was calculated in extended hydrogen bonded systems OH ⃛OH ⃛OH with unidirectional (homodromic) orientation of the OH groups. Ab initio restricted Hartree Fock, MP2 and MP3 calculations with geometry optimization and BSSE correction have been performed using the GAUSSIAN 83 program package for the ground states of the linear water dimer with C s symmetry and the cyclic water tetramer with S 4 symmetry. The latter represents the smallest possible, experimentally observed cooperative structure. A new definition for a cooperativity parameter is proposed. The definition is based on the two‐body, non‐neighbour interaction energy, plus three‐ and four‐body contributions, including one‐body deformation terms in relation to the total interaction energy of the water tetramer. The advantage of this definition is its independence of the reference system, which is necessary in complicated molecular systems with an undefined number of hydrogen bonds, such as disordered or flip‐flop systems. According to this definition the energy gain based on cooperativity in the S 4 water tetramer is 29% with the MP3/6‐31G** approximation, (30% with HF/4‐31G* and 46% with HF/3‐21G). The largest contribution of 18% is due to the three‐body term on the MP3/6‐31G** level, followed by the two‐body, non‐neighbour term with 11%. The four‐body term and the deformation term are in the order of 1% and cancel each other because they have opposite sign.