Benchmarking Compound Methods (CBS-QB3, CBS-APNO, G3, G4, W1BD) against the Active Thermochemical Tables: Formation Enthalpies of Radicals.

Abstract

The 298.15 K formation enthalpies of 38 radicals with molecular formula CxHyOz have been computed via the atomization procedure using the five title methods. The computed formation enthalpies are then benchmarked against the values recommended in the Active Thermochemical Tables (ATcT). The accuracy of the methods have been interpreted in terms of descriptive statistics, including the mean-signed error, mean-unsigned error, maximum average deviation, 2σ uncertainties, and 2×root-mean-square-deviations (2RMSD). The results highlight the following rank order of accuracy for the methods studied G4 > G3 > W1BD > CBS-APNO > CBS-QB3. The findings of this work are also considered in light of a recent companion study, which took an identical approach to quantifying the accuracies of these methods for 48 closed-shell singlet CxHyOz compounds. A similar order of accuracies and precisions were observed therein: G3 > G4 > W1BD > CBS-APNO > CBS-QB3. Both studies highlight systematic biases/deviations from the ATcT for the methods investigated, which are discussed in some detail, with methods having clear tendencies to over- or underpredict the recommended formation enthalpies for radical and/or closed-shell CxHyOz compounds. We show that one can improve the accuracy of their computation, and simultaneously reduce the uncertainty, by taking unweighted average formation enthalpies from various combinations of methods used. The reader should note that the statistical analyses preceding these conclusions also highlight that these error cancellation effects are unique for closed-shell and radical species. By extension, these error-cancellation effects can be expected to be different for various homologous series and chemical functionalities and their closed- and open-shell subgroups. Hence, further benchmarking studies are advised for other homologous series, such that the scientists and engineers (e.g., combustion/atmospheric/astrochemical) who frequently use these methods can assign reasonable uncertainties to their computations, while simultaneously optimizing their computational costs. For CxHyOz compounds, a combination of the CBS-APNO/G3/G4 methods is shown to be quite powerful when the atomization method is employed and is capable of reproducing the ATcT to within "near-chemical-accuracy", with 2RMSD (≈95% confidence interval) values of 0.0 ± 4.34 kJ mol(-1) computed for CxHyOz radicals, 0.0 ± 4.22 kJ mol(-1) for closed-shell CxHyOz compounds, with a total uncertainty of 0.0 ± 4.27 kJ mol(-1) subsequently computed considering all 85 CxHyOz compounds. Given the performance of these methods for determination of formation enthalpies when the atomization procedure is employed, we expect isodesmic reactions involving these methods to be capable of achieving chemical accuracy, as illustrated for the case of the tert-butyl radical. We also highlight that there is still disagreement between experiment and theory for this radical, despite its significance in gas-phase chemistry. Kineticists, thermodynamicists, and chemical kinetic modellers alike are warned that the popular CBS-QB3 method is found to have particularly poor performance, with a computed 2RMSD of 0.0 ± 12.51 kJ mol(-1), indicating that one should not apply this method in isolation for formation enthalpy determination unless other error-cancellation strategies are employed.