General Main Group Research Articles

A remarkably simple dispersion damping scheme and the DH24 double hybrid density functional.

In recent papers, Becke et al. [J. Chem. Phys. 158, 151103 (2023)] and then Becke [J. Chem. Phys. 159, 241101 (2023)] have developed a novel double hybrid density functional, "DH23," whose terms are based on good local physics. Its 12 coefficients are trained on the GMTKN55 (general main-group thermochemistry, kinetics, and noncovalent interactions) chemical database of Goerigk et al. [Phys. Chem. Chem. Phys. 19, 32184 (2017)]. The lowest GMTKN55 "WTMAD2" error to date for any hybrid or double hybrid density functional was obtained (1.73 kcal/mol for the revDH23 variant). Here, we simplify DH23 by introducing a dispersion damping scheme involving atomic numbers only and one global parameter. The resulting new functional, "DH24," performs as well as its predecessors.

Doubling down on density-functional theory.

In a recent paper, Becke et al. [J. Chem. Phys. 158, 151103 (2023)] presented a novel double hybrid density functional, "DH23," whose terms are based on good physics. Its 12 coefficients were trained on the GMTKN55 (general main-group thermochemistry, kinetics, and noncovalent interactions) chemical database of Goerigk et al. [Phys. Chem. Chem. Phys. 19, 32184 (2017)]. The lowest GMTKN55 "WTMAD2" error to date for any hybrid or double hybrid density functional was obtained (1.76 kcal/mol). Here, we make some revisions to DH23 and test its efficacy on reference data beyond GMTKN55, namely, organometallic reaction energies and barrier heights. The results confirm that DH23 is robust outside its training set. In the process, a slightly smaller GMTKN55 WTMAD2 of 1.73 kcal/mol is achieved.

A double-hybrid density functional based on good local physics with outstanding performance on the GMTKN55 database.

In two recent papers [A. D. Becke, J. Chem. Phys. 156, 214101 (2022) and A. D. Becke, J. Chem. Phys. 157, 234102 (2022)], we compared two Kohn-Sham density functionals based on physical modeling and theory with the best density-functional power-series fits in the literature. The best error statistics reported to date for a hybrid functional on the general main-group thermochemistry, kinetics, and noncovalent interactions (GMTKN55) chemical database of Goerigk et al. [Phys. Chem. Chem. Phys. 19, 32184 (2017)] were obtained. In the present work, additional second-order perturbation-theory terms are considered. The result is a 12-parameter double-hybrid density functional with the lowest GMTKN55 WTMAD2 "weighted total mean absolute deviation" error (1.76 kcal/mol) yet seen for any hybrid or double-hybrid density-functional approximation. We call it "DH23."

Density-functional theory vs density-functional fits: The best of both.

In a recent paper [A. D. Becke, J. Chem. Phys. 156, 214101 (2022)], we compared two Kohn-Sham density functionals based on physical modeling and theory with the best density-functional power series fits in the literature. With only a handful of physically motivated pre-factors, our functionals matched, and even slightly exceeded, the performance of the best power-series functionals on the general main group thermochemistry, kinetics, and noncovalent interactions (GMTKN55) chemical database of Goerigk et al. [Phys. Chem. Chem. Phys. 19, 32184 (2017)]. This begs the question: how much can their performance be improved by adding power-series terms of our own? We address this question in the present work. First, we describe a series expansion variable that we believe contains more local physics than any other variable considered to date. Then we undertake modest, one-dimensional fits to the GMTKN55 data with our theory-based functional corrected by power-series exchange and dynamical correlation terms. We settle on 12 power-series terms (plus six parent terms) and achieve the lowest GMTKN55 "WTMAD2" error yet reported, by a substantial margin, for a hybrid Kohn-Sham density functional. The new functional is called "B22plus."

Explicitly Correlated Double-Hybrid DFT: A Comprehensive Analysis of the Basis Set Convergence on the GMTKN55 Database.

Double-hybrid density functional theory (DHDFT) offers a pathway to accuracy approaching composite wavefunction approaches such as G4 theory. However, the Görling–Levy second-order perturbation theory (GLPT2) term causes them to partially inherit the slow ∝L–3 (with L the maximum angular momentum) basis set convergence of correlated wavefunction methods. This could potentially be remedied by introducing F12 explicit correlation: we investigate the basis set convergence of both DHDFT and DHDFT-F12 (where GLPT2 is replaced by GLPT2-F12) for the large and chemically diverse general main-group thermochemistry, kinetics, and noncovalent interactions (GMTKN55) benchmark suite. The B2GP-PLYP-D3(BJ) and revDSD-PBEP86-D4 DHDFs are investigated as test cases, together with orbital basis sets as large as aug-cc-pV5Z and F12 basis sets as large as cc-pVQZ-F12. We show that F12 greatly accelerates basis set convergence of DHDFs, to the point that even the modest cc-pVDZ-F12 basis set is closer to the basis set limit than cc-pV(Q+d)Z or def2-QZVPPD in orbital-based approaches, and in fact comparable in quality to cc-pV(5+d)Z. Somewhat surprisingly, aug-cc-pVDZ-F12 is not required even for the anionic subsets. In conclusion, DHDF-F12/VDZ-F12 eliminates concerns about basis set convergence in both the development and applications of double-hybrid functionals. Mass storage and I/O bottlenecks for larger systems can be circumvented by localized pair natural orbital approximations, which also exhibit much gentler system size scaling.

Асоціації SNP rs_7927894 гена FLG та TARC/CCL17 з атопічним дерматитом у дітей

One of the main genetic factors of the development of atopic dermatitis (AD) in children are single nucleotide polymorphisms (SNP) of the filagrin gene (FLG), particularly rs_7927894 FLG. One of the mostly studied and promising AD marker chemokines (CK) is the thymusE and activation regulated chemokine (TARC/CCL17). Purpose – to detect the associations and role of different variants of SNP rs_7927894 FLG gene and TARC/CCL17 in children suffering different AD clinical proE files (CP) – isolated or combined with comorbid atopic disorders (AtD). Materials and methods. The main group comprised 39 patients aged 3 to 18 years, suffering the isolated AD or combined with comorbid AtD. The control group comprised 47 patients aged 3 to 18 years, suffering the pathology of gastrointestinal tract without clinical signs of atopy. All the patients of the main and control groups had undergone detection of the genotype variants of SNP rs_7927894 FLG gene by real-time polymerase chain reaction and detection of TARC/CCL17 serum concentrations in venous blood. The cutEoff value of statistical significance was set as p<0.05. Results. The incidence and association of genotype variants C/C, C/T and T/T SNP rs_7927894 FLG gene in patients of cohorts of the studied groups were detected as follows: C/T rs_7927894 FLG was significantly the most common in the general main group (56.4%, p<0.05), within the cohort of CP AD isolated (61.1%, p<0.05) and CP of AD combined with comorbid AtD (52.4%, p<0.05). There were detected the associations of studied SNP with AD: C/T rs_7927894 FLG is significantly directly associated with AD (r=0.291, p<0.05), C/C rs_7927894 FLG has a reverse association with a trend to significance (r=-0.194, p=0.07). Mean serum concentrations of TARC/CCL17 did not differ significantly among patients cohorts of the main and control groups, respectively: general main group — 615.8 pg/ml, main with a CP AD isolated — 651.3 pg/ml, main with a CP of AD combined with comorbid AtD — 585.4 pg/ml, control — 608.4 pg/ml (p>0.05). Associations of serum TARC/CCL17 concentrations were determined as follows: elevation trending to significance within increasing AD severity degree (r=0.290, p=0.07) and significant elevation within the AD exhacerbation period (r=0.426, p<0.05). No significant association of TARC/CCL17 as to AD patients compared to the control group was detected in our study (r=-0.027, p>0.05). Conclusions. The genotype heterozygote variant C/T rs_7927894 FLG is significantly the most common and associated with all AD CP in children — isolated and combined with comorbid AtD. Variant C/C rs_7927894 of FLG gene is significantly reversely associated with AD in children. Serum concentrations of TARC/CCL17 did not reveal any significant differences between the AD patients and nonEatopic ones. However, they significantly elevate within AD exacerbation phase and trending to significance within AD severity degree increase in children. The research was carried out in accordance with the principles of the Helsinki declaration. The study protocol was approved by the Local Ethics Committee of all participating institutions. The informed consent of the patient was obtained for conducting the studies. No conflict of interest was declared by the authors. Key words: atopic dermatitis, children, associations, polymorphism, filaggrin, thymus- and activation regulated chemokine.

Density functionals with full nonlocal exchange, nonlocal rung-3.5 correlation, and D3 dispersion: Combined accuracy for general main-group thermochemistry, kinetics, and noncovalent interactions.

We introduce the HF-R35-D3(BJ) functional combining full nonlocal exact (Hartree-Fock-like, HF) exchange, inexpensive rung-3.5 correlation constructed from nonlocal one-electron operators, and nonlocal D3 dispersion corrections. HF-R35-D3(BJ) is among the first full-exact-exchange functionals offering competitive accuracy for general main-group thermochemistry, kinetics, and noncovalent interactions. HF-R35-D3(BJ) gives weighted mean absolute deviation WTMAD-2 8.5kcal/mol across the entire GMTKN55 dataset, outperforming most dispersion-corrected semilocal functionals and approaching the accuracy of dispersion-corrected global hybrids. This requires six fitted parameters, three each in the nonlocal correlation and dispersion corrections. Full nonlocal exchange appears to help give accurate binding energies and reasonable energy orderings for water hexamers. These results motivate continued exploration of inexpensive nonlocal correlation corrections to nonlocal exchange.

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

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 semiempirical 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 nonempirical 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 DHDFs for GMTKN55 are still the semiempirical 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.

R2SCAN-D4: Dispersion corrected meta-generalized gradient approximation for general chemical applications.

We combine a regularized variant of the strongly constrained and appropriately normed semilocal density functional [J. Sun, A. Ruzsinszky, and J. P. Perdew, Phys. Rev. Lett. 115, 036402 (2015)] with the latest generation semi-classical London dispersion correction. The resulting density functional approximation r2SCAN-D4 has the speed of generalized gradient approximations while approaching the accuracy of hybrid functionals for general chemical applications. We demonstrate its numerical robustness in real-life settings and benchmark molecular geometries, general main group and organo-metallic thermochemistry, and non-covalent interactions in supramolecular complexes and molecular crystals. Main group and transition metal bond lengths have errors of just 0.8%, which is competitive with hybrid functionals for main group molecules and outperforms them for transition metal complexes. The weighted mean absolute deviation (WTMAD2) on the large GMTKN55 database of chemical properties is exceptionally small at 7.5 kcal/mol. This also holds for metal organic reactions with an MAD of 3.3 kcal/mol. The versatile applicability to organic and metal-organic systems transfers to condensed systems, where lattice energies of molecular crystals are within the chemical accuracy (errors <1 kcal/mol).

A range-separated generalized Kohn-Sham method including a long-range nonlocal random phase approximation correlation potential.

Based on our recently published range-separated random phase approximation (RPA) functional [Kreppel et al., "Range-separated density-functional theory in combination with the random phase approximation: An accuracy benchmark," J. Chem. Theory Comput. 16, 2985-2994 (2020)], we introduce self-consistent minimization with respect to the one-particle density matrix. In contrast to the range-separated RPA methods presented so far, the new method includes a long-range nonlocal RPA correlation potential in the orbital optimization process, making it a full-featured variational generalized Kohn-Sham (GKS) method. The new method not only improves upon all other tested RPA schemes including the standard post-GKS range-separated RPA for the investigated test cases covering general main group thermochemistry, kinetics, and noncovalent interactions but also significantly outperforms the popular G0W0 method in estimating the ionization potentials and fundamental gaps considered in this work using the eigenvalue spectra obtained from the GKS Hamiltonian.

Range-Separated Density-Functional Theory in Combination with the Random Phase Approximation: An Accuracy Benchmark.

A formulation of range-separated random phase approximation (RPA) based on our efficient ω-CDGD-RI-RPA [J. Chem. Theory Comput. 2018, 14, 2505] method and a large scale benchmark study are presented. By application to the GMTKN55 data set, we obtain a comprehensive picture of the performance of range-separated RPA in general main group thermochemistry, kinetics, and noncovalent interactions. The results show that range-separated RPA performs stably over the broad range of molecular chemistry included in the GMTKN55 set. It improves significantly over semilocal DFT but it is still less accurate than modern dispersion corrected double-hybrid functionals. Furthermore, range-separated RPA shows a faster basis set convergence compared to standard full-range RPA making it a promising applicable approach with only one empirical parameter.

The Nonlocal Kernel in van der Waals Density Functionals as an Additive Correction: An Extensive Analysis with Special Emphasis on the B97M-V and ωB97M-V Approaches.

The development of van der Waals density functional approximations (vdW-DFAs) has gained considerable interest over the past decade. While in a strictest sense, energy calculations with vdW-DFAs should be carried out fully self-consistently, we demonstrate conclusively for a total of 11 methods that such a strategy only increases the computational time effort without having any significant effect on energetic properties, electron densities, or orbital-energy differences. The strategy to apply a nonlocal vdW-DFA kernel as an additive correction to a fully converged conventional DFA result is therefore justified and more efficient. As part of our study, we utilize the extensive GMTKN55 database for general main-group thermochemistry, kinetics, and noncovalent interactions [ Phys. Chem. Chem. Phys. 2017, 19, 32184], which allows us to analyze the very promising B97M-V [ J. Chem. Phys. 2015, 142, 074111] and ωB97M-V [ J. Chem. Phys. 2016, 144, 214110] DFAs. We also present new DFT-D3(BJ) based counterparts of these two methods and of ωB97X-V [ J. Chem. Theory Comput 2013, 9, 263], which are faster variants with similar accuracy. Our study concludes with updated recommendations for the general method user, based on our current overview of 325 dispersion-corrected and -uncorrected DFA variants analyzed for GMTKN55. vdW-DFAs are the best representatives of the three highest rungs of Jacob's Ladder, namely, B97M-V, ωB97M-V, and DSD-PBEP86-NL.

A look at the density functional theory zoo with the advanced GMTKN55 database for general main group thermochemistry, kinetics and noncovalent interactions.

We present the GMTKN55 benchmark database for general main group thermochemistry, kinetics and noncovalent interactions. Compared to its popular predecessor GMTKN30 [Goerigk and Grimme J. Chem. Theory Comput., 2011, 7, 291], it allows assessment across a larger variety of chemical problems-with 13 new benchmark sets being presented for the first time-and it also provides reference values of significantly higher quality for most sets. GMTKN55 comprises 1505 relative energies based on 2462 single-point calculations and it is accessible to the user community via a dedicated website. Herein, we demonstrate the importance of better reference values, and we re-emphasise the need for London-dispersion corrections in density functional theory (DFT) treatments of thermochemical problems, including Minnesota methods. We assessed 217 variations of dispersion-corrected and -uncorrected density functional approximations, and carried out a detailed analysis of 83 of them to identify robust and reliable approaches. Double-hybrid functionals are the most reliable approaches for thermochemistry and noncovalent interactions, and they should be used whenever technically feasible. These are, in particular, DSD-BLYP-D3(BJ), DSD-PBEP86-D3(BJ), and B2GPPLYP-D3(BJ). The best hybrids are ωB97X-V, M052X-D3(0), and ωB97X-D3, but we also recommend PW6B95-D3(BJ) as the best conventional global hybrid. At the meta-generalised-gradient (meta-GGA) level, the SCAN-D3(BJ) method can be recommended. Other meta-GGAs are outperformed by the GGA functionals revPBE-D3(BJ), B97-D3(BJ), and OLYP-D3(BJ). We note that many popular methods, such as B3LYP, are not part of our recommendations. In fact, with our results we hope to inspire a change in the user community's perception of common DFT methods. We also encourage method developers to use GMTKN55 for cross-validation studies of new methodologies.

Benchmark tests of a strongly constrained semilocal functional with a long-range dispersion correction

The strongly constrained and appropriately normed (SCAN) semilocal density functional [J. Sun, A. Ruzsinszky, J. P. Perdew \textit{Phys. Rev. Lett.} {\bf 115}, 036402 (2015)] obeys all 17 known exact constraints for meta-generalized-gradient approximations (meta-GGA) and includes some medium range correlation effects. Long-range London dispersion interactions are still missing, but can be accounted for via an appropriate correction scheme. In this study, we combine SCAN with an efficient London dispersion correction and show that lattice energies of simple organic crystals can be improved with the applied correction by 50\%. The London-dispersion corrected SCAN meta-GGA outperforms all other tested London-dispersion corrected meta-GGAs for molecular geometries. Our new method delivers mean absolute deviations (MADs) for main group bond lengths that are consistently below 1\,pm, rotational constants with MADs of 0.2\%, and noncovalent distances with MADs below 1\%. For a large database of general main group thermochemistry and kinetics, it also delivers a weighted mean absolute deviation below 4 kcal/mol, one of the lowest for long-range corrected meta-GGA functionals. We also discuss some consequences of numerical sensitivity encountered for meta-GGAs.

Why the Standard B3LYP/6-31G* Model Chemistry Should Not Be Used in DFT Calculations of Molecular Thermochemistry: Understanding and Correcting the Problem

We analyze the error compensations that are responsible for the relatively good performance of the popular B3LYP/6-31G* model chemistry for molecular thermochemistry. We present the B3LYP-gCP-D3/6-31G* scheme, which corrects for missing London dispersion and basis set superposition error (BSSE) in a physically sound manner. Benchmark results for the general main group thermochemistry, kinetics, and noncovalent interactions set (GMTKN30) are presented. A detailed look is cast on organic reactions of several arenes with C(60), Diels-Alder reactions, and barriers to [4 + 3] cycloadditions. We demonstrate the practical advantages of the new B3LYP-gCP-D3/6-31G* scheme and show its higher robustness over standard B3LYP/6-31G*. B3LYP-gCP-D3/6-31G* is meant to fully substitute standard B3LYP/6-31G* calculations in the same black-box sense at essentially no increase in computational cost. The energy corrections are made available by a Web service ( http://www.thch.uni-bonn.de/tc/gcpd3 ) and by freely available software.

Performance of meta-GGA Functionals on General Main Group Thermochemistry, Kinetics, and Noncovalent Interactions.

Among the computationally efficient semilocal density functionals for the exchange-correlation energy, meta-generalized-gradient approximations (meta-GGAs) are potentially the most accurate. Here, we assess the performance of three new meta-GGAs (revised Tao-Perdew-Staroverov-Scuseria or revTPSS, regularized revTPSS or regTPSS, and meta-GGA made simple or MGGA_MS), within and beyond their "comfort zones," on Grimme's big test set of main-group molecular energetics (thermochemistry, kinetics, and noncovalent interactions). We compare them against the standard Perdew-Burke-Ernzerhof (PBE) GGA, TPSS, and Minnesota M06L meta-GGAs, and Becke-3-Lee-Yang-Parr (B3LYP) hybrid of GGA with exact exchange. The overall performance of these three new meta-GGA functionals is similar. However, dramatic differences occur for different test sets. For example, M06L and MGGA_MS perform best for the test sets that contain noncovalent interactions. For the 14 Diels-Alder reaction energies in the "difficult" DARC subset, the mean absolute error ranges from 3 kcal mol(-1) (MGGA_MS) to 15 kcal mol(-1) (B3LYP), while for some other reaction subsets the order of accuracy is reversed; more generally, the tested new semilocal functionals outperform the standard B3LYP for ring reactions. Some overall improvement is found from long-range dispersion corrections for revTPSS and regTPSS but not for MGGA_MS. Formal and universality criteria for the functionals are also discussed.

Benchmarking Semiempirical Methods for Thermochemistry, Kinetics, and Noncovalent Interactions: OMx Methods Are Almost As Accurate and Robust As DFT-GGA Methods for Organic Molecules.

Semiempirical quantum mechanical (SQM) methods offer a fast approximate treatment of the electronic structure and the properties of large molecules. Careful benchmarks are required to establish their accuracy. Here, we report a validation of standard SQM methods using a subset of the comprehensive GMTKN24 database for general main group thermochemistry, kinetics, and noncovalent interactions, which has recently been introduced to evaluate density functional theory (DFT) methods ( J. Chem. Theory Comput. 2010 , 6 , 107 ). For all SQM methods considered presently, parameters are available for the elements H, C, N, and O, and consequently, we have extracted from the GMTKN24 database all species containing only these four elements (excluding multireference cases). The resulting GMTKN24-hcno database has 370 entries (derived from 593 energies) compared with 715 entries (derived from 1033 energies) in the original GMTKN24 database. The current benchmark covers established standard SQM methods (AM1, PM6), more recent approaches with orthogonalization corrections (OM1, OM2, OM3), and the self-consistent-charge density functional tight binding method (SCC-DFTB). The results are compared against each other and against DFT results using standard functionals. We find that the OMx methods outperform AM1, PM6, and SCC-DFTB by a significant margin, with a substantial gain in accuracy especially for OM2 and OM3. These latter methods are quite accurate even in comparison with DFT, with an overall mean absolute deviation of 6.6 kcal/mol for PBE and 7.9 kcal/mol for OM3. The OMx methods are also remarkably robust with regard to the unusual bonding situations encountered in the "mindless" MB08-165 test set, for which all other SQM methods fail badly.

A thorough benchmark of density functional methods for general main group thermochemistry, kinetics, and noncovalent interactions

A thorough energy benchmark study of various density functionals (DFs) is carried out with the new GMTKN30 database for general main group thermochemistry, kinetics and noncovalent interactions [Goerigk and Grimme, J. Chem. Theor. Comput., 2010, 6, 107; Goerigk and Grimme, J. Chem. Theor. Comput., 2011, 7, 291]. In total, 47 DFs are investigated: two LDAs, 14 GGAs, three meta-GGAs, 23 hybrids and five double-hybrids. Besides the double-hybrids, also other modern approaches, i.e., the M05 and M06 classes of functionals and range-separated hybrids, are tested. For almost all functionals, the new DFT-D3 correction is applied in order to consistently test the performance also for important noncovalent interactions; the parameters are taken from previous works or determined for the present study. Basis set and quadrature grid issues are also considered. The general aim of the study is to work out which functionals are generally well applicable and robust to describe the energies of molecules. In summary, we recommend on the GGA level the B97-D3 and revPBE-D3 functionals. The best meta-GGA is oTPSS-D3 although meta-GGAs represent in general no clear improvement compared to numerically simpler GGAs. Notably, the widely used B3LYP functional performs worse than the average of all tested hybrids and is also very sensitive to the application of dispersion corrections. We discourage its usage as a standard method without closer inspection of the results, as it still seems to be often done nowadays. Surprisingly, long-range corrected exchange functionals do in general not perform better than the corresponding standard hybrids. However, the ωB97X-D functional seems to be a promising method. The most robust hybrid is Zhao and Truhlar's PW6B95 functional in combination with DFT-D3. If higher accuracy is required, double-hybrids should be applied. The corresponding DSD-BLYP-D3 and PWPB95-D3 variants are the most accurate and robust functionals of the entire study. Additional calculations with MP2 and and its spin-scaled variants SCS-MP2, S2-MP2 and SOS-MP2 revealed that double-hybrids in general outperform those. Only SCS-MP2 can be recommended, particularly for reaction energies. We suggest its usage when a large self-interaction error is expected that prohibits usage of double-hybrids. Perdews' metaphoric picture of Jacob's Ladder for the classification of density functionals' performance could unbiasedly be confirmed with GMTKN30. We also show that there is no statistical correlation between a functional's accuracy for atomization energies and the performance for chemically more relevant reaction energies.

Efficient and Accurate Double-Hybrid-Meta-GGA Density Functionals-Evaluation with the Extended GMTKN30 Database for General Main Group Thermochemistry, Kinetics, and Noncovalent Interactions.

We present an extended and improved version of our recently published database for general main group thermochemistry, kinetics, and noncovalent interactions [J. Chem. Theory Comput. 2010, 6, 107], which is dubbed GMTKN30. Furthermore, we suggest and investigate two new double-hybrid-meta-GGA density functionals called PTPSS-D3 and PWPB95-D3. PTPSS-D3 is based on reparameterized TPSS exchange and correlation contributions; PWPB95-D3 contains reparameterized PW exchange and B95 parts. Both functionals contain fixed amounts of 50% Fock-exchange. Furthermore, they include a spin-opposite scaled perturbative contribution and are combined with our latest atom-pairwise London-dispersion correction [J. Chem. Phys. 2010, 132, 154104]. When evaluated with the help of the Laplace transformation algorithm, both methods scale as N(4) with system size. The functionals are compared with the double hybrids B2PLYP-D3, B2GPPLYP-D3, DSD-BLYP-D3, and XYG3 for GMTKN30 with a quadruple-ζ basis set. PWPB95-D3 and DSD-BLYP-D3 are the best functionals in our study and turned out to be more robust than B2PLYP-D3 and XYG3. Furthermore, PWPB95-D3 is the least basis set dependent and the best functional at the triple-ζ level. For the example of transition metal carbonyls, it is shown that, mainly due to the lower amount of Fock-exchange, PWPB95-D3 and PTPSS-D3 are better applicable than the other double hybrids. Finally, we discuss in some detail the XYG3 functional [Proc. Nat. Acad. Sci. U.S.A. 2009, 106, 4963], which makes use of B3LYP orbitals and electron densities. We show that it is basically a highly nonlocal variant of B2PLYP and that its partially good performance is mainly due to a larger effective amount of perturbative correlation compared to other double hybrids. We finally recommend the PWPB95-D3 functional in general chemistry applications.

A General Database for Main Group Thermochemistry, Kinetics, and Noncovalent Interactions - Assessment of Common and Reparameterized (meta-)GGA Density Functionals.

We present a quantum chemistry benchmark database for general main group thermochemistry, kinetics, and noncovalent interactions (GMTKN24). It is an unprecedented compilation of 24 different, chemically relevant subsets that either are taken from already existing databases or are presented here for the first time. The complete set involves a total of 1.049 atomic and molecular single point calculations and comprises 731 data points (relative chemical energies) based on accurate theoretical or experimental reference values. The usefulness of the GMTKN24 database is shown by applying common density functionals on the (meta-)generalized gradient approximation (GGA), hybrid-GGA, and double-hybrid-GGA levels to it, including an empirical London dispersion correction. Furthermore, we refitted the functional parameters of four (meta-)GGA functionals based on a fit set containing 143 systems, comprising seven chemically different problems. Validation against the GMTKN24 and the molecular structure (bond lengths) databases shows that the reparameterization does not change bond lengths much, whereas the description of energetic properties is more prone to the parameters' values. The empirical dispersion correction also often improves for conventional thermodynamic problems and makes a functional's performance more uniform over the entire database. The refitted functionals typically have a lower mean absolute deviation for the majority of subsets in the proposed GMTKN24 set. This, however, is also often accompanied at the expense of poor performance for a few other important subsets. Thus, creating a broadly applicable (and overall better) functional by just reparameterizing existing ones seems to be difficult. Nevertheless, this benchmark study reveals that a reoptimized (i.e., empirical) version of the TPSS-D functional (oTPSS-D) performs well for a variety of problems and may meet the standards of an improved functional. We propose validation against this new compilation of benchmark sets as a definitive way to evaluate a new quantum chemical method's true performance.