Impact of Nuclear Quantum Effects on the Structural Properties of Protonated Water Clusters

Nuclear quantum effects (NQEs) play a crucial role in hydrogen-bonded systems due to quantum tunneling and proton fluctuation. Our understanding of how NQEs affect microstructures mainly focuses on bulk phases of liquids and solids but remains deficient for water clusters, including their hydrogen nuclei, hydrogen-bonded configurations, and temperature dependence. Here, we conducted ab initio molecular dynamics (MD) and path integral MD simulations to investigate the influence of NQEs on the structural properties of protonated water clusters H⁺(H₂O) (n = 3, 6, 9, 12). The results reveal that the NQEs become less evident as the cluster size increases due to the competition between NQEs and electrostatic interactions. Simulations of several H⁺(H₂O)₆ isomers at different temperatures indicate that the effect of elevated temperature on proton transfer is related to the initial structure. Interestingly, the process of proton transfer also involves the interconversion between Zundel-type and Eigen-type isomers. These findings significantly deepen our understanding of ion-water and water-water interactions, opening new avenues for the study of hydrated ion clusters and related systems.