Quantum nuclear effects, despite their importance for understanding the behaviour of water, are often overlooked due to the approximations used in classical models of water. Many complex processes take place in water, among them is proton transfer—an inherently quantum phenomenon. In this work, we investigated proton transfer in small neutral, protonated, and deprotonated water clusters. We used proton transfer as a coordinate to construct a one-dimensional energy surface for each cluster. Using a quantum mechanical approach, we then determined the nuclear wave function and evaluated quantum delocalization of the proton in its hydrogen bond. To validate the one-dimensional model, we used it for predicting IR frequencies of the transfer vibrational mode. For transfers exhibiting a clear reaction barrier, we estimated the rate enhancement due to tunnelling effects using simple approximations and instanton theory. We also studied isomerization involving cyclic proton transfer through closed loops of hydrogen bonds in small water clusters. This phenomenon has attracted considerable interest in recent years because of its application in chiral catalysis and energy storage. Specifically, we characterized tunnelling effects in small single and double layered rings. Using the smallest water cluster, we have developed a model for studying tunnelling in ice.
Our results highlight the importance of including proton delocalization in hydrogen bonds. We have demonstrated that the hydrogen-bond network is strongly coupled, indicating that models considering only a single isolated hydrogen bond are frequently inadequate. In protonated clusters, we demonstrated that the excess proton can be either localized or completely delocalized along its hydrogen bond. Furthermore, we have shown that at low temperatures, tunnelling plays a dominant role in proton transfer in cyclic hydrogen-bond networks, in ice, and in proton hole transfer in deprotonated water clusters. Importantly, tunnelling remains relevant for all systems with OHO-type hydrogen bonds even at higher temperatures.
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