Prediction of equilibrium isotopic fractionation of the gypsum/bassanite/water system using first-principles calculations

The stable isotopes (¹⁸O/¹⁶O, ¹⁷O/¹⁶O and ²H/¹H) of structurally-bound water (also called hydration water) in gypsum (CaSO₄•2H₂O) and bassanite (CaSO₄•0.5H₂O) can be used to reconstruct the isotopic composition of paleo-waters. Understanding the variability of the isotope fractionation factors between the solution and the solid (α¹⁷O_{mineral-water}, α¹⁸O_{mineral-water} and αD_{mineral-water}) is crucial for applying this proxy to paleoclimatic research. Here we predict the theoretical equilibrium fractionation factors for triple oxygen and hydrogen isotopes in the gypsum-water and bassanite-water systems between 0 °C and 60 °C. We apply first-principles using density functional theory within the harmonic approximation. Our theoretical results for α¹⁸O_gypsum-water (1.00347±0.00037) are in agreement with previous experimental studies, whereas αD_gypsum-water agrees only at temperatures above 25 °C. At lower temperatures, the experimental values of αD_gypsum-water are consistently higher than theoretical values (e.g. 0.9749 and 0.9782, respectively, at 3 °C), which can be explained by kinetic effects that affect gypsum precipitation under laboratory conditions at low temperature. We predict that α¹⁸O_{bassanite-water} is similar to α¹⁸O_gypsum-water in the temperature range of 0 °C to 60 °C. Both α¹⁸O_gypsum-water and α¹⁸O_{bassanite-water} show a small temperature dependence of ∼0.0000122 per °C, which is negligible for most paleoclimate studies. The theoretical relationship between α¹⁷O_gypsum-water and α¹⁸O_gypsum-water (θ =lnα17Olnα18O) from 0 °C to 60 °C is 0.5274±0.00063. The relationship is very insensitive to temperature (0.00002 per °C). The fact that δ18O values of gypsum hydration water are greater than free water (α¹⁸O_gypsum-water >1) whereas δD values of gypsum hydration water are less than free water (αD_gypsum-water <1) is explained by phonon theory. We conclude that calculations from first-principles using density functional theory within the harmonic approximation can accurately predict fractionation factors between structurally-bound water of minerals and free water.