Abstract

Precise prediction of hydrogen (H) isotope fractionations among different substances is a long-standing challenge in isotope geochemistry, as it needs treatments beyond the harmonic approximation. Path-integral molecular dynamics (PIMD) simulations have recently been proved to be valid in predicting equilibrium isotope fractionations for light elements. However, the lack of reliable force fields hinders the application of PIMD to the condensed phases. In this work, the deep potential models trained on the first-principles molecular dynamics (FPMD) data are applied to PIMD simulations to determine the D/H and 18O/16O isotope fractionation factors between brucite and water. To quantitatively assess the influence of quantum effects, the D/H and 18O/16O isotope fractionations between brucite and water are also determined under the framework of harmonic approximation.By comparing the results of the PIMD and those of harmonic calculations, we find that H and O atoms in brucite and water are strongly affected by the anharmonic effects. The accuracy of the harmonic isotope fractionations mainly depends on the cancellation percentage of the anharmonic effects on the reduced partition function ratios (RPFRs) of the two substances. The isotope fractionations predicted by PIMD simulations are close to the experimental results at high temperatures. However, at low temperatures, the predicted isotope fractionations are different from those of experiments. The discrepancies are attributed to the approximations in the density functional theory (DFT) functionals used in this work, i.e., the inaccuracy in predicting the proton positions in brucite and water. Moreover, we find that the H isotope fractionations are extremely sensitive to the change of pressure. The direction of H isotope fractionation between brucite and water (at 300 K) will be even inversed as the pressure increases to more than 3 GPa. This strong pressure sensitivity may be a common characteristic of hydrous minerals and water systems. Therefore, the extrapolated H isotope fractionations used in the studies of dehydration of subducting slabs or deep Earth H distribution based on the isotope fractionations under low pressures may need to be rechecked.

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