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

Abstract

We present a number of near-exact, nonrelativistic, Born-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 thermochemistry 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 thermochemistry and hydrogen-transfer barriers, while also yielding excellent performance for nucleophilic substitutions. By optimizing for best overall performance on both thermochemistry 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.

Fast, accurate evaluation of exact exchange: The occ-RI-K algorithm

“…While PARI-K yields impressive accuracy in its own right, the accuracy of occ-RI-K is clearly superior. The errors per electron in the absolute energies of all molecules in the test set are quite 73,74 0.00 0.00 Butanediol65 75 0.00 0.00 BzDC215 76 0.00 0.00 CT20 77 0.00 0.00 DIE60 78 0.00 0.00 DS14 79 0.00 0.01 EA13 80 0.01 0.01 EIE22 81 0.00 0.00 FmH2O10 82,83 0.01 0.16 ACONF 84,85 0.00 0.01 BHPERI 85,86 0.00 0.00 CYCONF 85,87 0.00 0.00 G21EA 85,88 0.00 0.00 G21IP 85,88 0.00 0.00 NBPRC 85 0.00 0.02 WATER27 85,89 0.00 0.03 NHTBH38 85,90 0.01 0.02 HTBH38 85,91 0.00 0.01 BH76RC 85 0.00 0.00 DBH24 86 0.00 0.01 H2O6Bind8 83,92 0.00 0.05 HB15 93 0.00 0.01 HSG 94,95 0.00 0.00 HW30 96 0.00 0.01 HW6Cl 82,83 0.00 0.04 HW6F 82,83 0.00 0.04 IP13 80 0.00 0.00 NBC10 95 0.01 0.01 NC15 97 0.00 0.00 Pentane14 98 0.00 0.01 RG10 99 0.00 0.00 S22 …”

Double-hybrid density functionals: merging wavefunction and density approaches to get the best of both worlds

“…Table 1 gathers a summary of existing expression within this category [57][58][59][60][61][62][63][64][65][66][67][68]; broadly speaking, they differ in: (i) the kernel used to represent the exchange-correlation effects (i.e., B2-PLYP vs. mPW2-PLYP); (ii) the training set used to obtain the value of the {w EXX , w PT2 } weights, which is also related to the nature of the target set and the purpose of the parame- Table 1, it is readily seen how the weight of EXX is always considerably high, compared with the moderate weight for the perturbative term or with corresponding weight in hybrid models, and that a recently highlighted [69] condition such as w PT2 ≤ w EXX 2 , is almost invariably fulfilled independently of the final composition of these DH forms. These features are expected to largely drive the successful performance of the methods studied so far, as we will see next.…”

Quadratic integrand double-hybrid made spin-component-scaled

“…A plethora of investigations already attempted to tune the pair of {a x , a c } parameters entering into Equation (1) via fully empirical [8][9][10][11][12][13] or theoretical [14][15][16][17][18][19] routes. Following this latter line of design, we recently derived these parameters in a nonempirical fashion from the adiabatic connection model, 20 using a quadratic polynomial of the coupling integrand parameter and fixing its coefficients through some known limit conditions.…”