Topological constraints on proton dynamics in water clusters

Interconversion of H-bond configurations is an essential element of the water cluster dynamics. Different local mechanisms form pathways between H-bond configurations-intrabond motion of all protons in an ordered cycle of H-bonds, rotation of a pair of H-bonded water molecules, as well as the classical Grotthuss mechanism in charged clusters-resulting in extended proton rearrangement networks. An outstanding problem is whether these reaction networks are connected or fall apart into disconnected fragments to set barriers to proton dynamics. Here, the topological aspect of this problem is addressed. The network connectivity for individual mechanisms and their combinations is studied analytically using basic tools of graph theory. The connectivity is proven for wide classes of water clusters, manifesting the great power of the simple mechanisms in the interconversion of H-bond configurations. The structural motifs leading to the disintegration of proton rearrangement networks are identified. The analytical conclusions are complemented by a numerical examination of characteristic clusters. The results are relevant to studies of water-based ferroelectrics. They provide a framework for the analysis of proton dynamics in water clusters.