Isotope substitution is extensively used to investigate the microscopic behavior of hydrogen bonded systems such as liquid water. The changes in structure and stability of these systems upon isotope substitution arise entirely from the quantum mechanical nature of the nuclei. Here, we provide a fully ab initio determination of the isotope exchange free energy and fractionation ratio of hydrogen and deuterium in water treating exactly nuclear quantum effects and explicitly modeling the quantum nature of the electrons. This allows us to assess how quantum effects in water manifest as isotope effects, and unravel how the interplay between electronic exchange and correlation and nuclear quantum fluctuations determine the structure of the hydrogen bond in water.
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