An Analysis of Recent BLYP and PBE-Based Range-Separated Double-Hybrid Density Functional Approximations for Main-Group Thermochemistry, Kinetics and Noncovalent Interactions

Abstract

<div> <div> <div> <p>We investigate the effects of range separation of the exchange energy on electronic ground-state properties for recently published double-hybrid density functionals (DHDFs) with the extensive GMTKN55 database for general main-group thermochemistry, kinetics and noncovalent interactions. We include the semi-empirical range-separated DHDFs ωB2PLYP and ωB2GP-PLYP developed by our group for excitation energies, together with their ground-state-parametrized variants, which we denote herein as ωB2PLYP18 and ωB2GP-PLYP18. We also include the non-empirical range-separated DHDFs RSX-0DH and RSX-QIDH. For all six DHDFs, damping parameters for the DFT-D3 dispersion correction (and for its DFT-D4 variant) are presented. We comment on when the range-separated functionals can be more beneficial than their global counterparts, and conclude that range separation alone is no guarantee for overall improved results. We observe that the BLYP-based functionals generally outperform the PBE-based functionals. We finally note that the best-performing double-hybrid density functionals for GMTKN55 are still the semi-empirical range-separated double hybrids ωDSD3-PBEP86-D4 and ωDSD72-PBEP86-D4, the former of which includes a third-order perturbative correlation term in addition to the more conventional second- order perturbation that DHDFs are based upon.</p> </div> </div> </div>

Time-Dependent Long-Range-Corrected Double-Hybrid Density Functionals with Spin-Component and Spin-Opposite Scaling: A Comprehensive Analysis of Singlet–Singlet and Singlet–Triplet Excitation Energies

“…The unscaled RSX-QIDH yields the highest RMSD of 0.38 eV, confirming other studies that this LC-DHDFA is often less accurate than its global PBE-QIDH counterpart. 32,41 When focussing solely on local-valence excitations, we notice similar trends as for the two previously discussed sets with most of the SCS and SOS variants being positioned at the top and RMSDs ranging from 0.13 eV (SOS-PBE-QIDH and SOS-ωPBEPP86) to 0.16 eV (SOS-RSX-QIDH, SCS-RS-PBE-P86, SCS-ωB2GP-PLYP, and ωB88PP86). Note that the unscaled RS-DH methods perform equally well with RMSDs of 0.16− 0.17 eV, values that they share with B2PLYP, B2GP-PLYP, SCS-RSX-QIDH, SOS-B2GP-PLYP21, SOS-RS-PBE-P86, and SOS-ωB2GP-PLYP.…”

“…31 Indeed, the label "nonempirical" should not be misunderstood as a synonym for quality or reliability, which was later demonstrated for DHDFAs applied to ground-state properties, where semiempirical DHDFAs by far outperformed nonempirical ones. 10,32 Several studies have been conducted since Grimme and Neese's initial idea, and TD(A)-DHDFAs have been shown to be the most accurate DFAs for excited-state calculations and absorption spectra, 18,28,33−41 even rivaling standard WFT methods. 34,39−41 While we refer the reader to a recently published detailed review on TD(A)-DHDFAs, 42 we highlight only some of the advantages of those over the conventional TD(A)-DFT approaches: a better description of electronic circular dichroism (ECD) spectra, 33 more accurate vertical singlet−singlet 18,28,34,39−43 and singlet−triplet 18,41 excitations in organic moleculeswhere TD(A)-DHDFAs even outperformed the approximate coupled-cluster singles doubles WFT approach 44,45 [(SCS-)CC2] 34 a more balanced description of the problematic first two excited states in polycyclic aromatic hydrocarbons (PAHs), 35,40 and no misleading results from artificial "ghost states".…”

Stability of the polyynic form of C18, C22, C26, and C30nanorings: a challenge tackled by range-separated double-hybrid density functionals

“…The DH models have been introduced and thoroughly tested by several groups in last years, improving the accuracy and range of applications of DFT to those challenging systems for which a GH method was insufficiently accurate. [47][48][49][50][51][52][53][54] More recently, the range-separation strategy was also extended highly successfully to these DH methods, [55][56][57] with different approaches followed to find the optimal value of the o parameter: fitting to large datasets 58,59 or to excited-state energies, 60 or simply by forcing to exactly reproduce the energy of the H atom as a model system free of one-electron self-interaction error. [61][62][63] Another strategy trying to improve the accuracy of a DH functional borrows the scaling of the opposite-and same-spin correlation energies of the PT2 term by a different factor, inspired by the spin-scaling for SCS-MP2, or even neglecting the former contribution, as for SOS-MP2, in analogy with eqn (1).…”

Explicitly correlated double hybrid DFT: a comprehensive analysis of the basis set convergence on the GMTKN55 database

“…GMTKN55 has previously been used for both evaluation and parametrization of double hybrids as well as composite wavefunction methods. 6,[8][9][10][56][57][58] We will show below that for double hybrids applied to GMTKN55, F12 accelerates basis set convergence to the point that even spd basis sets are quite close to the complete basis set limit, and that spdf basis sets effectively reach it.…”