Dipole moment of polyhedral water clusters: mathematical relationships and their application

Polyhedral water clusters are characterized by exponential proton disorder and a complex molecular interaction. Nevertheless, a simple theory has been developed for these systems. It allows predicting classes of the most stable proton configurations that differ in the arrangement of hydrogen atoms (protons) in the hydrogen bonds. The stability for a particular configuration is evaluated on the basis of the analysis of local topological characteristics of the hydrogen bond network. However, the stability of water clusters is determined also by another, clearly non-topological global characteristic: the magnitude of the total dipole moment. In this article we show that the total dipole moment of polyhedral water clusters is proportional to the vector sum of polyhedron edges if their direction coincides with the direction of hydrogen bonds. This makes it possible not to take into account separately the contribution of free (dangling) hydrogen atoms when classifying proton configurations.