Comment on “Dispersion-corrected r²SCAN based double-hybrid functionals” [J. Chem. Phys. 159, 224103 (2023)] Free

Very recently, some of us¹ have introduced novel double-hybrid (DH) density functionals built on the model of the nonempirical 0-DH^2,3 or “quadratic-integrand double-hybrid” (QIDH)⁴ approximations and employing the regularized and restored exchange–correlation functional r²SCAN as semilocal meta-generalized gradient approximation (meta-GGA) ingredient.⁵ Later on, Wittman and co-workers assessed these models against various large and diverse datasets.⁶ We believe that the terminology used by Wittmann and co-workers to name some of the DH approaches of Ref. 6 is misleading and can create confusion to the reader, in particular for those interested by our longstanding quest to look for nonempirical DH approximations⁷ started in 2010 with the development of PBE0-DH.² Within this comment, we thus take the opportunity to clarify the main difference between the DHs assessed by Wittmann and co-workers⁶ and our expressions.¹ 

Originally coupled with the PBE¹¹ or TPSS¹² semilocal DFA terms, the robustness of the QIDH model has extensively been assessed with other semilocal approximations still providing excellent energy performance,¹³ and it has very recently been applied with r²SCAN for an improved estimation of noncovalent interactions.¹ The latter r²SCAN-QIDH model is thus defined as a global DH ruled by Eq. (1).

It is within this context where the work of Wittmann and co-workers should be placed, because their approach named “r²SCAN-QIDH” corresponds indeed to what it should have been correctly called “SOS1-r²2SCAN-QIDH” augmented by a D4 empirical dispersion term (i.e., SOS1-r²SCAN-QIDH-D4),^25,26 the latter correction being systematically recommended in the SOS scheme to further compensate the missing London dispersion correlation. To a larger extent, it is worth noting that this terminology is not exclusive to double hybrids but was introduced with the development of SOS-MP2 as a reference to the SOS variant of the canonical second-order Møller–Plesset perturbation theory (MP2).²⁷ These differences in the definitions of both DH approaches explain also their different performance on the diverse benchmark sets assessed in both publications.

To get a better overview of their performance comparison, we report in Table II their respective weighted mean absolute deviation (WTMAD) measures calculated with the extended def2-QZVPP basis set²⁸ from the 55 different subsets of the very large GMTKN55 database²⁹ according to the definition given in Ref. 1, as well as the mean absolute deviations (MADs) calculated on the S22 × 5,³⁰ S66 × 8,³¹ NCIBLIND10³² datasets recommended to adjust the parameters included into the D4 or NL³³ (VV10) dispersion corrections. Computations are performed with the release 5.0.3 of the Orca program package taking benefit from the computational speed-up provided by the resolution-of-the-identity.³⁴ With respect to SOS1-r²SCAN-QIDH-D4, our canonical r²SCAN-QIDH and its D4 or NL dispersion-corrected variant are 0.9 and 0.7 kcal mol⁻¹ less accurate on the overall GMTKN55 database, respectively, but remains, of course, very competitive with others on this database.^7,14–18 Going deeper into details by analyzing the basic, reaction (react.), barrier-height (BH), inter- or intra-molecular noncovalent interactions (inter. NCI or intra. NCI, respectively) datasets of GMTKN55, we observe that the deviations depicted above come from a global performance increase while going from r²SCAN-QIDH to SOS1-r²SCAN-QIDH-D4, the largest improvement being obtained for basic properties (7.14 instead of 6.09 kcal mol⁻¹, respectively). Out of that, we remark that the addition of the D4 or NL corrections to r²SCAN-QIDH is only efficient for NCI purposes, the latter corrections providing, for instance, a performance improvement of about 0.4 kcal mol⁻¹ for intermolecular NCI. They tend, however, to slightly degrade the other properties by 0.1–0.2 kcal mol⁻¹.

In short, we remove here all of the ambiguities between our canonical r²SCAN-QIDH double hybrid reported in Ref. 1 and the later one reported by Wittman and co-workers in Ref. 6. According to our terminology,^20,35 the variant by Wittman and co-workers is a dispersion-corrected spin-opposite-scaled reformulation of r²SCAN-QIDH that should be dubbed SOS1-r²SCAN-QIDH-D4 to not be confused with the canonical r²SCAN-QIDH double hybrid. The same comment can be done for r²SCAN0-DH reported in our work and SOS1-r²SCAN0-DH-D4 by Wittman and co-workers.

The supplementary material provides the definition of the WTMAD measure in Sec. SI. It also contains the MAD and MSD measures of the 55 subsets of the GMTKN55 database in Tables SII and SIII for the density-functional approximations investigated herein.

E.B. gratefully acknowledges ANR (Agence Nationale de la Recherche) for the financial support of this work through the MoMoPlasm Project No. ANR-21-CE29-0003. He also acknowledges ANR and CGI (Commissariat à l’Investissement d’Avenir) for their financial support of this research through Labex SEAM (Science and Engineering for Advanced Materials and devices), Grant Nos. ANR-10-LABX-096 and ANR-18-IDEX-0001, and acknowledges TGGC (Très Grand Centre de Calcul du CEA) for computational resources allocation (Grant No. AD010810359R2). The work in Alicante is supported by Project No. PID2023-152372NB-I00 funded by MCIN/AEI (https://doi.org/10.13039/501100011033).

The authors have no conflicts to disclose.