Highly Accurate First-Principles Benchmark Data Sets for the Parametrization and Validation of Density Functional and Other Approximate Methods. Derivation of a Robust, Generally Applicable, Double-Hybrid Functional for Thermochemistry and Thermochemical Kinetics

We present a number of near-exact, nonrelativistic, Borri-Oppenheimer reference data sets for the parametrization of more approximate methods (such as DFT functionals). The data were obtained by means of the W4 ab initio computational thermochernistry protocol, which has a 95% confidence interval well below 1 kJ/mol. Our data sets include W4-08, which are total atomization energies of over 100 small molecules that cover varying degrees of nondynamical correlations, and DBH24-W4, which are W4 theory values for Truhlar's set of 24 representative barrier heights. The usual procedure of comparing calculated DFT values with experimental atomization energies is hampered by comparatively large experimental uncertainties in many experimental values and compounds errors due to deficiencies in the DFT functional with those resulting from neglect of relativity and finite nuclear mass. Comparison with accurate, explicitly nonrelativistic, ab initio data avoids these issues. We then proceed to explore the performance of B2x-PLYP-type double hybrid functionals for atomization energies and barrier heights. We find that the optimum hybrids for hydrogen-transfer reactions, heavy-atoms transfers, nucleophilic substitutions, and unimolecular and recombination reactions are quite different from one another: out of these subsets, the heavy-atom transfer reactions are by far the most sensitive to the percentages of Hartree-Fock-type exchange y and MP2-type correlation x in an (x, y) double hybrid. The (42,72) hybrid B2K-PLYP, as reported in a preliminary communication, represents the best compromise between thermochernistry and hydrogen-transfer barriers, while also yielding excellent performance for nucleophilic substitutions. By optimizing for best overall performance on both thermochernistry and the DBH24-W4 data set, however, we find a new (36,65) hybrid which we term B2GP-PLYP. At a slight expense in performance for hydrogen-transfer barrier heights and nucleophilic substitutions, we obtain substantially better performance for the other reaction types. Although both B2K-PLYP and B2GP-PLYP are capable of 2 kcal/mol quality thermochemistry, B2GP-PLYP appears to be the more robust toward nondynamical correlation and strongly polar character. We additionally find that double-hybrid functionals display excellent performance for such problems as hydrogen bonding, prototype late transition metal reactions, pericyclic reactions, prototype cumulene-polyacetylene system, and weak interactions.