Critical Benchmarking of the G4(MP2) Model, the Correlation Consistent Composite Approach and Popular Density Functional Approximations on a Probabilistically Pruned Benchmark Dataset of Formation Enthalpies

First-principles calculation of the standard formation enthalpy, $\Delta H_f^0$~(298K), in such large scale as required by chemical space explorations, is amenable only with density functional approximations (DFAs) and some composite wave function theories (cWFTs). Alas, the accuracies of popular range-separated hybrid, `rung-4' DFAs, and cWFTs that offer the best accuracy-vs.-cost trade-off have as yet been established only for datasets predominantly comprising small molecules, hence, their transferability to larger datasets remains vague. In this study, we present an extended benchmark dataset of over two-thousand values of $\Delta H_f^0$ for structurally and electronically diverse molecules. We apply quartile-ranking based on boundary-corrected kernel density estimation to filter outliers and arrive at Probabilistically Pruned Enthalpies of 1908 compounds (PPE1908). For this dataset, we rank the prediction accuracies of G4(MP2), ccCA and 23 popular DFAs using conventional and probabilistic error metrics. We discuss systematic prediction errors and highlight the role an empirical higher-level correction (HLC) plays in the G4(MP2) model. Furthermore, we comment on uncertainties associated with the reference empirical data for atoms and systematic errors introduced by these that grow with the molecular size. We believe these findings to aid in identifying meaningful application domains for quantum thermochemical methods.