Equilibrium Fractionation of Non-traditional Isotopes: a Molecular Modeling Perspective

The isotopic compositions of natural materials are determined by their parent reservoirs, on the one hand, and by fractionation mechanisms, on the other hand. Under the right conditions, fractionation represents isotope partitioning at thermodynamic equilibrium. In this case, the isotopic equilibrium constant depends on temperature, and reflects the slight change of free energy between two phases when they contain different isotopes of the same chemical element. The practical foundation of the theory of mass-dependent stable isotope fractionation dates back to the mid-twentieth century, when Bigeleisen and Mayer (1947) and Urey (1947) proposed a formalism that takes advantage of the Teller–Redlich product rule (Redlich 1935) to simplify the estimation of equilibrium isotope fractionations. In this chapter, we first give a brief introduction to this isotope fractionation theory. We see in particular how the various expressions of the fractionation factors are derived from the thermodynamic properties of harmonically vibrating molecules, a surprisingly effective mathematical approximation to real molecular behavior. The central input data of these expressions are vibrational frequencies, but an approximate formula that requires only force constants acting on the element of interest can be applied to many non-traditional isotopic systems, especially at elevated temperatures. This force-constant based approach can be particularly convenient to use in concert with first-principles electronic structure models of vibrating crystal structures and aqueous solutions. Collectively, these expressions allow us to discuss the crystal chemical parameters governing the equilibrium stable isotope fractionation. Since the previous volume of Reviews in Mineralogy and Geochemistry dedicated to non-traditional stable isotopes, the number of first-principles molecular modeling studies applied to geosciences in general and to isotopic fractionation in particular, has significantly increased. After a concise introduction to computational methods based on quantum mechanics, we will focus on the modeling of isotopic properties in liquids, which represents a bigger methodological challenge than …