Intermolecular bonding in water clusters from the molecular-wide and electron density-based (MOWED) perspective : a theoretical study

Abstract

Cooperativity is a strange phenomenon in water clusters, characterized by a non-linear decrease in the average electronic energy of a water molecule or hydrogen bond with an increase in cluster size. The main aim of this theoretical study was to determine the effect cooperativity has on a water cluster and how it manifests, using novel theoretical tools and methodologies. Specifically, the MOlecular Wide Electron Density (MOWED) approach was used in this study to explore water clusters. Modelled water clusters (which included 2D cyclic and various 3D conformers) displayed the expected non-linear decrease in electronic energy. A novel equation was developed and fitted to the clusters in order to predict maximum cooperativity effects and their relative rates of changes. The equation was then adapted to be able to accommodate any property for the applicable water clusters. The equation predicted a maximum stability for cyclic water clusters of –8.316 kcal/mol per water molecule. This is the limit in stability relative to the dimer that a cyclic water cluster can reach due to cooperativity. The relationship between electron delocalization and cooperative stabilization was also explored extensively. It was found that intermolecular electron delocalization increases non-linearly with increasing cluster size and can be used to explain the origins of cooperativity. Intermolecular delocalization and interaction energies were also further decomposed into atomic and fragment contributions, and notably the 3-atom oxygen fragments contributed the most to the stability of the water clusters. Visualization of electron delocalization revealed ‘highways’ that electrons travel through within the water clusters, and 1D cross-section of an H-bond showed that a substantial amount of delocalized electron density is contributed by atoms other than the three present. The investigation of electron delocalization reveals that cooperativity is truly a molecular-wide event that is driven primarily by O-atoms and directed by H-atoms. The mechanistic limits to the number of electrons that can be delocalized were also investigated and found to be primarily O-localized density. Various cooperativity–induced effects – effects that result from cooperativity – were investigated. The atomic charge for oxygen showed a contribution from delocalized electrons resulting in the increased negative charge for the oxygen atom. The total interaction energy decreased while the exchange-correlation increased and had a positive sign. However, the total classic electrostatic interactions decreased and had a larger magnitude than total interaction energy. The increase and positive sign for exchange-correlation resulted from intramolecular interactions. Overall, the total intermolecular interaction energy and both its components contributed to the stability of the water cluster. The topological properties showed a stability increase at the critical point and increased covalency with the incremental increase of water molecules. Geometrical descriptors resulted in the same conclusions as found above. Finally, similar cooperativity effects were revealed in a series of 3D hexamer clusters, where the number of water molecules remain constant but the number and nature of H-bonds increases. The same mechanism of intermolecular electron delocalization along ‘highways’ connecting neighbouring O-atoms were revealed to be the primary driver of cooperative stabilization. Unlike the cyclic structures, the primary source of delocalized electrons was shown to be intramolecular delocalization (such as O–H covalent bonds).