Benchmarking Compound Methods (CBS-QB3, CBS-APNO, G3, G4, W1BD) against the Active Thermochemical Tables: A Litmus Test for Cost-Effective Molecular Formation Enthalpies

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Abstract

The theoretical atomization energies of some 45 CxHyOz molecules present in the Active Thermochemical Tables compilation and of particular interest to the combustion chemistry community have been computed using five composite model chemistries as titled. The species contain between 1–8 “heavy” atoms, and a few are conformationally diverse with up to nine conformers. The enthalpies of formation at 0 and 298.15 K are then derived via the atomization method and compared against the recommended values. In general, there is very good agreement between our averaged computed values and those in the ATcT; those for 1,3-cyclopentadiene exceptionally differ considerably, and we show from isodesmic reactions that the true value for 1,3-cyclopentadiene is closer to 134 kJ mol–1 than the reported 101 kJ mol–1. If one is restricted to using a single method, statistical measures indicate that the best methods are in the rank order G3 ≈ G4 > W1BD > CBS-APNO > CBS-QB3. The CBS-x methods do on average predict ΔfH⊖(298.15 K) within ≈5 kJ mol–1 but are prone to occasional lapses. There are statistical advantages to be gained from using a number of methods in tandem, and all possible combinations have been tested. We find that the average formation enthalpy coming from using CBS-APNO/G4, CBS-APNO/G3, and G3/G4 show lower mean signed and mean unsigned errors, and lower standard and root-mean-squared deviations, than any of these methods in isolation. Combining these methods also leads to the added benefit of providing an uncertainty rooted in the chemical species under investigation. In general, CBS-APNO and W1BD tend to underestimate the formation enthalpies of target species, whereas CBS-QB3, G3, and G4 have a tendency to overestimate the same. Thus, combining CBS-APNO with a G3/G4 combination leads to an improvement in all statistical measures of accuracy and precision, predicting the ATcT values to within 0.14 ± 4.21 kJ mol–1, thus rivalling “chemical accuracy” (±4.184 kJ mol–1) without the excessive cost associated with higher-level methods such as W1BD.

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