Evaluating Computational Chemistry Methods for Isotopic Fractionation between CO₂(g) and H₂O(g)

Abstract

Quantum mechanical calculations can be useful in predicting equilibrium isotopic fractionations of geochemical reactions. However, these computational chemistry methods vary widely in their effectiveness in the prediction of various physical observables. Most studies employing the approach known as density functional theory (DFT) to model these observable quantities focus on predictive accuracy for energetics and geometries. In this study, several density functionals are evaluated against experimental bond lengths, harmonic vibrational frequencies, frequency shifts upon isotopic substitution, and 18 O/ 16 O isotopic fractionation between CO 2 (g) and H 2 O(g). Successful prediction of harmonic vibrational frequencies strongly correlates with successful prediction of isotopic fractionation, despite the possible introduction of errors by the harmonic approximation. Harmonic experimental frequencies, not anharmonic ones, must be used when comparing spectra and when predicting isotope fractionation. The B3LYP and X3LYP functionals perform more accurately in the evaluation of both harmonic vibrational frequencies and isotopic fractionation factors using the 6-311+G(d,p) and 6-311++G(2d,p) basis sets, achieving fractionation factor errors of 0.2−0.6‰ at 25 °C out of a total fractionation of 51‰. Error cancellation between vibrational frequencies and the harmonic approximation is crucial to their success. The above combination of exchange−correlation functionals and basis sets also well predicts the vibrational properties of interacting CO 2 and H 2 O molecules, suggesting that they may be applicable to more complex geochemical reactions involving C and O isotopic fractionations.