Nuclear quantum effects in the Van Hove Correlation functions of water

Atomistic investigations on the bulk structure of water have shown that the low mass of hydrogen induces substantial nuclear quantum effects (NQE), such as zero-point energy and tunneling, modulating the static pair distribution functions (PDFs), and lowering the energy barrier associated with proton transport. In this study, we have performed path integral molecular dynamics (PIMD) simulations with thermostatted ring polymer MD, using on-the-fly generated energies and forces from the density-functional tight-binding (DFTB) method. We aim to simulate and quantitatively understand NQEs on the dynamic structure of water through analysis of the time-dependent PDF, which is also called the Van Hove correlation function (VHF). The VHF relates molecular behavior and the macroscopic transport properties simultaneously as a function of positions and time. Our study shows that NQEs play a significant role in the correlated water motion, making it essential in the atomistic simulation to predict the correlation characteristics of water with an accuracy comparable to experiment. Remarkably, unlike static PDFs, where O-O PDF experience a negligible NQE compared to O-H and H-H PDFs, all three pairwise VHFs show slower decay of correlations in water dynamics due to NQEs.