On the Short-Range Nature of Cooperativity in Hydrogen-Bonded Large Molecular Clusters

The variation in the hydrogen bond (HB) strength has considerable consequences on the physicochemical properties of molecular clusters. Such a variation mainly arises due to the cooperative/anti-cooperative networking effect of neighboring molecules connected by HBs. In the present work, we systematically study the effect of neighboring molecules on the strength of an individual HB and the respective cooperativity contribution toward each of them in a variety of molecular clusters. For this purpose, we propose a use of a small model of a large molecular cluster called the spherical shell-1 (SS1) model. This SS1 model is constructed by placingg the spheres of an appropriate radius centered on X and Y atoms of the X-H···Y HB under consideration. The molecules falling within these spheres constitute the SS1 model. Utilizing this SS1 model, the individual HB energies are calculated within the molecular tailoring approach-based framework and the results are compared with their actual counterparts. It is found that the SS1 is a reasonably good model of large molecular clusters, providing 81-99% of the total HB energy estimated using the actual molecular clusters. This in turn suggests that the maximum cooperativity contribution toward a particular HB is due to the fewer number of molecules (in the SS1 model) directly interacting with two molecules involved in its formation. We further demonstrate that the remaining part of the energy or cooperativity (∼1 to 19%) is captured by the molecules falling in the second spherical shell (SS2) centered on the hetero-atom of the molecules in the SS1 model. The effect of increasing size of a cluster on the strength of a particular HB, calculated by the SS1 model, is also investigated. The calculated value of the HB energy remains unchanged with the increase in the size of a cluster, emphasizing the short-ranged nature of the HB cooperativity in neutral molecular clusters.