Résumé
Equilibrium fractionation of stable isotopes is critically important in fields ranging from chemistry, including medicinal chemistry, electrochemistry, geochemistry, and nuclear chemistry, to environmental science. The dearth of reliable estimates of equilibrium fractionation factors, from experiment or from natural observations, has created a need for accurate computational approaches. Because isotope fractionation is a purely quantum mechanical phenomenon, exact calculation of fractionation factors is nontrivial. Consequently, a severe approximation is often made, in which it is assumed that the system can be decomposed into a set of independent harmonic oscillators. Reliance on this often crude approximation is one of the primary reasons that theoretical prediction of isotope fractionation has lagged behind experiment. A class of problems for which one might expect the harmonic approximation to perform most poorly is the isotopic fractionation between solid and solution phases.
In order to illustrate the errors associated with the harmonic approximation, we have considered the fractionation of Li isotopes between aqueous solution and phyllosilicate minerals, where we find that the harmonic approximation overestimates isotope fractionation factors by as much as 30% at 25 degrees C. Lithium is a particularly interesting species to examine, as natural lithium isotope signatures provide information about hydrothermal processes, carbon cycle, and regulation of the Earth's climate by continental alteration. Further, separation of lithium isotopes is of growing interest in the nuclear industry due to a need for pure Li-6 and Li-7 isotopes. Moving beyond the harmonic approximation entails performing exact quantum calculations, which can be achieved using the Feynman path integral formulation of quantum statistical mechanics. In the path integral approach, a system of quantum particles is represented as a set of classical-like ring-polymer chains, whose interparticle interactions are determined by the rules of quantum mechanics. Because a classical isomorphism exists between the true quantum system and the system of ring-polymers, classical-like methods can be applied. Recent developments of efficient path integral approaches for the exact calculation of isotope fractionation now allow the case of the aforementioned dissolved Li fractionation properties to be studied in detail. Applying this technique, we find that the calculations yield results that are in good agreement with both experimental data and natural observations. Importantly, path integral methods, being fully atomistic, allow us to identify the origins of anharmonic effects and to make reliable predictions at temperatures that are experimentally inaccessible yet are, nevertheless, relevant for natural phenomena.