Minimally Empirical Double Hybrid Functionals Trained Against the GMTKN55 Database: revDSD-PBEP86-D4, revDOD-PBE-D4, and DOD-SCAN-D4

Abstract

We present a family of minimally empirical double-hybrid DFT functionals parametrized against the very large and diverse GMTKN55 benchmark. The very recently proposed wB97M(2) empirical double hybrid (with 16 empirical parameters) has the lowest WTMAD2 (weighted mean absolute deviation over GMTKN55) ever reported at 2.19 kcal/mol. However, our xrevDSD-PBEP86-D4 functional reaches a statistically equivalent WTMAD2=2.22 kcal/mol, using just a handful of empirical parameters, and the xrevDOD-PBEP86-D4 functional reaches 2.25 kcal/mol with just opposite-spin MP2 correlation, making it amenable to reduced-scaling algorithms. In general, the D4 empirical dispersion correction is clearly superior to D3BJ. If one eschews dispersion corrections of any kind, noDispSD-SCAN offers a viable alternative. Parametrization over the entire GMTKN55 dataset yields substantial improvement over the small training set previously employed in the DSD papers.

Evaluating Transition Metal Barrier Heights with the Latest Density Functional Theory Exchange–Correlation Functionals: The MOBH35 Benchmark Database

“…194 Because, as Goerigk and Grimme noted, "DHDFs still suffer from the same 'missing dispersion energy problem' as other functionals, albeit to a smaller extent, and consequently they do also benefit from dispersion-correction schemes" 52 they added a dispersion correction to the available double-hybdrid functionals, and subsequently this was done in a more intrinsic manner by Kozuch and Martin in their DSD-BLYP and subsequent related functionals. 20,[144][145][146] Thus, it would seem that including a dispersion correction is recommended also for doublehybrid functionals. PWPB95 without any dispersion correction has the lowest MAD (1.6 kcal/mol) of all the DFT functionals evaluated, while B2K-PLYP is only slightly worse (MAD = 1.7…”

“…Finally, a wide variety of DFT functionals was evaluated to determine which perform well, ideally for both thermodynamics (i.e., MOR41) and kinetics (i.e., MOBH35). As part of this study, MOR41 was used to evaluate some of the newer functionals that were not part of Dohm et al's original study, including the latest functionals from the Martin (the revised DSD/DOD double-hybrid functionals 20 ), Truhlar (e.g., MN15, 21 MN15-L 22 ) and Head-Gordon (e.g., ωB97M-V, 23 B97M-V 24 ) groups.…”

Rotational Spectroscopy Meets Quantum Chemistry for Analyzing Substituent Effects on Non-Covalent Interactions: The Case of the Trifluoroacetophenone-Water Complex

“…Overall, this level of theory has been denoted as B3. More accurate structures and harmonic zero-point energies of the low-lying energy minima have then been obtained using the double-hybrid revDSD-PBEP86-D3(BJ) functional [ 53 ] in conjunction with the jun-cc-pVTZ (jTZ) basis set [ 54 ] (this level of theory has been denoted as rDSDjun). From a spectroscopic point of view, while equilibrium geometries straightforwardly provide equilibrium rotational constants, the prediction of the vibrational ground-state rotational constants requires the incorporation of vibrational corrections, which have been obtained from anharmonic force field calculations at the B3 level (for a detailed account, see e.g., ref.…”

Canonical and DLPNO-Based G4(MP2)XK-Inspired Composite Wave Function Methods Parametrized against Large and Chemically Diverse Training Sets: Are They More Accurate and/or Robust than Double-Hybrid DFT?

“… 47 In DHDFT, both the exchange and the correlation terms are mixtures of DFT and WFT approaches (evaluated in a basis of Kohn–Sham orbitals). Using the very large GMTKN55 (general main-group thermochemistry, kinetics, and noncovalent interactions, 55 subsets) benchmark suite, 48 with nearly 2500 main-group molecules, we found that the best DHDFT functionals, ωB97M(2) by Mardirossian and Head-Gordon 49 and revDSD-PBEP86-D4 by our group, 45 have WTMAD2 (weighted mean absolute deviation) statistics around 2.2 kcal/mol, competitive with or superior to the cWFT methods we tested. Needless to say, double hybrids are computationally much more economical, especially if RI (resolution of the identity) approximations 50 − 52 are applied.…”

“…An approach that, in practical operation, combines elements of WFT and DFT methods is the double-hybrid density functional method (DHDFT, 40 − 45 see ref ( 46 ) for a recent review), which occupies the fifth rung on Perdew’s “Jacob’s Ladder”. 47 In DHDFT, both the exchange and the correlation terms are mixtures of DFT and WFT approaches (evaluated in a basis of Kohn–Sham orbitals).…”