Using Cost-Effective Density Functional Theory (DFT) to Calculate Equilibrium Isotopic Fractionation for Reactions Involving Large Organic Molecules

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 τHCTH_D3BJ, τHCTH and HCTH have almost similar performances (22‰ and 4.1‰, respectively, for τHCTH_D3BJ). In this work we provide a roadmap to predict for equilibrium isotopic fractionations of large organic molecules, and constrain their potential uncertainties.