With an eye towards applications in environmental sciences, the factors impacting the accuracy of calculating equilibrium isotopic fractionation α are considered. α is calculated from the reduced partition function relation β via the vibrational frequencies. Density-fitting (DF, or resolution of the identity – RI) is a popular tool to help reduce the cost of DFT energy calculations, and its impact on the accuracy of calculating vibration frequencies was determined to be negligible provided one uses a sufficiently large auxiliary density-fitting basis set. Using a set of high-accuracy fractionations for a series of small molecules, the accuracy of several density-functional theory (DFT) exchange–correlation functionals in calculating β was considered. Based on these results, a selection of functionals was tested against two benchmark databases of isotopic fractionations that were generated, one for D/H fractionation (HEIF11) and one for heavy-atom fractionation (CNOEIF35). It was found that, with the def2-TZVP basis set, O3LYP had the lowest mean absolute deviation (21‰ and 3.9‰, respectively), but the GGA/meta-GGA functionals τHCTHD3BJ, τHCTH and HCTH have almost similar performances (22‰ and 4.1‰, respectively, for τHCTHD3BJ). In this work we provide a roadmap to predict for equilibrium isotopic fractionations of large organic molecules, and constrain their potential uncertainties.
Density Fitting Isotopic Fractionation - SI