Hydrogen-Bond Cooperative Effects in Small Cyclic Water Clusters as Revealed by the Interacting Quantum Atoms Approach

The cooperative effects of hydrogen bonding in small water clusters (H2O)(n) (n=3-6) have been studied by using the partition of the electronic energy in accordance with the interacting quantum atoms (IQA) approach. The IQA energy splitting is complemented by a topological analysis of the electron density ((r)) compliant with the quantum theory of atoms-in-molecules (QTAIM) and the calculation of electrostatic interactions by using one- and two-electron integrals, thereby avoiding convergence issues inherent to a multipolar expansion. The results show that the cooperative effects of hydrogen bonding in small water clusters arise from a compromise between: 1)the deformation energy (i.e., the energy necessary to modify the electron density and the configuration of the nuclei of the isolated water molecules to those within the water clusters), and 2)the interaction energy (E-int) of these contorted molecules in (H2O)(n). Whereas the magnitude of both deformation and interaction energies is enhanced as water molecules are added to the system, the augmentation of the latter becomes dominant when the size of the cluster is increased. In addition, the electrostatic, classic, and exchange components of E-int for a pair of water molecules in the cluster (H2O)(n-1) become more attractive when a new H2O unit is incorporated to generate the system (H2O)(n) with the last-mentioned contribution being consistently the most important part of E-int throughout the hydrogen bonds under consideration. This is opposed to the traditional view, which regards hydrogen bonding in water as an electrostatically driven interaction. Overall, the trends of the delocalization indices, (,), the QTAIM atomic charges, the topology of (r), and the IQA results altogether show how polarization, charge transfer, electrostatics, and covalency contribute to the cooperative effects of hydrogen bonding in small water clusters. It is our hope that the analysis presented in this paper could offer insight into the different intra- and intermolecular interactions present in hydrogen-bonded systems.