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 ωB97M(2) empirical double hybrid (with 16 adjustable parameters) has the lowest WTMAD2 (weighted mean absolute deviation over GMTKN55) ever reported at 2.19 kcal/mol. However, refits of the DSD-BLYP and DSD-PBEP86 spin-component-scaled, dispersion-corrected double hybrids can achieve WTMAD2 values as low as 2.33 with the very recent D4 dispersion correction (2.42 kcal/mol with the D3(BJ) dispersion term) using just a handful of adjustable parameters. If we use full DFT correlation in the initial orbital evaluation, the xrevDSD-PBEP86-D4 functional reaches WTMAD2 = 2.23 kcal/mol, statistically indistinguishable from ωB97M(2) but using just four nonarbitrary adjustable parameters (and three semiarbitrary ones). The changes from the original DSD parametrizations are primarily due to noncovalent interaction energies for large systems, which were undersampled in the original parametrization set. With the new parametrization, same-spin correlation can be eliminated at minimal cost in performance, which permits revDOD-PBEP86-D4 and revDOD-PBE-D4 functionals that scale as N 4 or even N 3 with the size of the system. Dependence of WTMAD2 for DSD functionals on the percentage of HF exchange is roughly quadratic; it is sufficiently weak that any reasonable value in the 64% to 72% range can be chosen semiarbitrarily. DSD-SCAN and DOD-SCAN double hybrids involving the SCAN nonempirical meta-GGA as the semilocal component have also been considered and offer a good alternative if one wishes to eliminate either the empirical dispersion correction or the same-spin correlation component. noDispSD-SCAN66 achieves WTMAD2 = 3.0 kcal/mol, compared to 2.7 kcal/mol for DOD-SCAN66-D4. However, the best performance without dispersion corrections (WTMAD2 = 2.8 kcal/mol) is reached by revωB97X-2, a slight reparametrization of the Chai−Head-Gordon range-separated double hybrid. Finally, in the context of double-hybrid functionals, the very recent D4 dispersion correction is clearly superior over D3(BJ).

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?

“…For recent reviews of cWFT methods and their performance for the thermochemistry and thermochemical kinetics of organic molecules, see Karton 36 and Chan; 37 for a recent general review of both experimental and computational thermochemistry, see Ruscic and Bross. 38 One feature that cWFTs all share is the additivity approximation of the following form: 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.…”

Some observations on the performance of the most recent exchange-correlation functionals for the large and chemically diverse GMTKN55 benchmark

“…For further details see Ref. 3 The primary metric and "objective function" employed is the WTMAD2 (weighted mean absolute deviation, type 2) as defined by Goerigk et al, defined as follows:…”

“…These authors covered a great many exchangecorrelation functionals, but a number of more recent ones such as ωB97M(2) 2 went unexplored for technical reasons. In addition, a set of revised 3 DSD double hybrids has meanwhile been fitted to GMTKN55, improving substantially on the original ones. 4 The purpose of the present short paper is to summarize these data and stress the strengths and weaknesses of these methods.…”

Clam‐like Cyclotricatechylene‐based Capsules: Identifying the Roles of Protonation State and Guests as well as the Drivers for Stability and (Anti‐)Cooperativity

“…[57] It was shown to be the most accurate and robust hybrid functional and a good alternative to double-hybrid functionals for large systems in recently performed benchmark studies that were the largest of their kind. [37,[58][59][60][61] Like other vander-Waals-DFT methods, only two-body contributions to the dispersion energy are included. As we are also interested in analysing potential non-additive three-body effects, we followed the example by Risthaus and Grimme [62] and enhanced the van-der-Waals-DFT type dispersion correction with the three-body term known from Grimme's DFT-D3 correction.…”