Direct prediction of isotopic properties from molecular dynamics trajectories: Application to sulfide, sulfate and sulfur radical ions in hydrothermal fluids

In hydrothermal fluids, disulfur (S₂^•−) and trisulfur (S₃^•−) radical anions have been observed to coexist with the major hydrogen sulfide and sulfate species. These radical ions have potentially important effects on the solubility, transport and fractionation of metals and sulfur, with consequences for ore deposit formation and, more generally, for geochemical cycles of metals and volatiles. It is therefore essential to know the intrinsic isotopic properties of these important sulfur species in order to use sulfur isotopes for tracing different geological processes. Here, the theoretical equilibrium isotopic properties of the disulfur and trisulfur radical ions are computed and compared to the hydrogen sulfide (H₂S) and sulfate ion (SO₄²⁻), using, for the first time, a first-principles molecular dynamics (MD) approach. The isotopic properties are calculated directly from molecular dynamics trajectories using the vibrational density of states and the atomic kinetic energy, and then compared to the more established method based on sampling of several snapshots. This comparison allowed us to validate the new modelling method and to assess its advantages and limitations. The predicted equilibrium isotope fractionation in terms of ³⁴S/³²S between S₂^•− and S₃^•− is small, i.e. <1‰, with a slight enrichment in the heavier isotope for S₃^•−, over the temperature range 200–500 °C. Both radical ions are slightly depleted in the heavier isotope, by 1 to 2‰, relative to aqueous H₂S. Our results help tuning sulfur isotope fractionation models used for tracing the origin and evolution of hydrothermal fluids. Our method opens large perspectives for using the rapidly growing body of MD simulation data in geosciences on structure and stability of aqueous complexes to assess in parallel element isotope fractionations from MD-generated trajectories.