GMTKN55 Database Research Articles

Assessment of a Nonlocal Correction Scheme to Semilocal Density Functional Theory Methods.

A nonlocal correction method to (semi)local density-functional theory (DFT) methods is derived that is based on a partitioning of the correlation-energy density into atom-atom contributions. Nonlocal interaction contributions, which are absent in standard DFT methods, are introduced in this method by using atomic weight functions that do not vanish exponentially as the atomic densities but with the inverse sixth power of the atomic distances. The parameters contained in these weight functions were fitted to reproduce intermolecular interaction energies for a range a small dimer systems. The new functional has then been tested both for intermolecular interactions, using the S22, S66 × 8, and IonHB databases from Hobza et al., and for other thermodynamical properties using a subset of 14 databases of the GMTKN30 database of Grimme et al. It is found that for intermolecular interactions the accuracy of the method is often higher than with standard DFT+D methods while for other properties, such as reaction energies or relative conformation energies of medium sized organic molecules, the accuracy is similar to hybrid-DFT+D methods. The nonlocal correction method has been tested also to predict the interaction energy of the water-graphene system yielding an estimated interaction energy of -2.87 kcal/mol, which is in line with previous theoretical investigations.

Performance of dispersion-corrected density functional theory for thermochemistry and non-covalent interactions

The accuracy of non-local van der Waals density functional [1] is tested for the thermochemical properties of 1200+ atoms and molecules in the GMTKN30 database. Five (hybrid)GGA functionals are augmented by the non-local (NL) part of the VV10 functional. The widely used atom-pair wise dispersion correction DFT-D3 [2] is considered for comparison. The addition of the NL dispersion energy definitely improves the results of all tested short-range functionals. Based on little empiricism and basic physical insight, DFT-NL can be recommended as robust electronic structure method. For more detailed insight into non-covalent bonding, potential energy curves [3] for five complexes with weak to medium strong hydrogen bonds have been computed with dispersion corrected DFT methods VV10, DFT-D3 and vdW-DF2 [4]. All dispersion corrected methods perform reasonably well for these hydrogen bonds. For the fluorinated complexes, the VV10 method gives remarkably good results. The vdW-DF2 method yields good interaction energies similar to the other methods, but fails to provide accurate equilibrium separations. For large-scale applications we can recommend DFT-D3 based structure optimizations with subsequent checking of interaction energies by single-point VV10 computations.

Long-range correlation energies from frequency-dependent weighted exchange-hole dipole polarisabilities

Long-range correlation energies are calculated using an approximation of the single-particle density-density response function of the system that leads to an expression requiring only occupied orbitals and eigenvalues. Dipole-dipole polarisabilities and isotropic leading-order dispersion coefficients obtained from this approximation are shown to be in a reasonable agreement with corresponding values from the experiment or dipole oscillator strength distributions. The localised polarisabilities were used to calculate a long-range correlation correction to a hybrid-generalised gradient approximation functional using a proper damping function at short ranges. It was found that the hybrid density-functional theory+dispersion method obtained in this way has a comparable accuracy than high-level ab initio wave function methods at a much lower computational cost. This has been analysed for a number of systems from the GMTKN30 database including subsets for noncovalently bound complexes, relative energies for sugar conformers and reaction energies and barrier heights of pericyclic reactions of some medium sized organic molecules.

Benchmarking Density Functional Methods against the S66 and S66x8 Datasets for Non‐Covalent Interactions

Dispersion-corrected density functional theory is assessed on the new S66 and S66x8 benchmark sets for non-covalent interactions. In total, 17 different density functionals are evaluated. Two flavors of our latest additive London-dispersion correction DFT-D3 and DFT-D3(BJ), which differ in their short-range damping functions, are tested. In general, dispersion corrections are again shown to be crucial to obtain reliable non-covalent interaction energies and equilibrium distances. The corrections strongly diminish the performance differences between the functionals, and in summary most dispersion-corrected methods can be recommended. DFT-D3 and DFT-D3(BJ) also yield similar results but for most functionals and intermolecular distances, the rational Becke-Johnson scheme performs slightly better. Particularly, the statistical analysis for S66x8, which covers also non-equilibrium complex geometries, shows that the Minnesota class of functionals is also improved by the D3 scheme. The best methods on the (meta-)GGA or hybrid- (meta-)GGA level are B97-D3, BLYP-D3(BJ), PW6B95-D3, MPW1B95-D3 and LC-ωPBE-D3. Double-hybrid functionals are the most accurate and robust methods, and in particular PWPB95-D3 and B2-PLYP-D3(BJ) can be recommended. The best DFT-D3 and DFT-D3(BJ) approaches are competitive to specially adapted perturbation methods and clearly outperform standard MP2. Comparisons between S66, S22 and parts of the GMTKN30 database show that the S66 set provides statistically well-behaved data and can serve as a valuable tool for, for example, fitting purposes or cross-validation of other benchmark databases.

Performance of the van der Waals Density Functional VV10 and (hybrid)GGA Variants for Thermochemistry and Noncovalent Interactions.

The nonlocal van der Waals density functional VV10 (Vydrov, O. A.; Van Voorhis, T. J. Chem. Phys.2010, 133, 244103) is tested for the thermochemical properties of 1200+ atoms and molecules in the GMTKN30 database in order to assess its global accuracy. Five GGA and hybrid functionals in unmodified form are augmented by the nonlocal (NL) part of the VV10 functional (one parameter adjusted). The addition of the NL dispersion energy definitely improves the results of all tested functionals. On the basis of little empiricism and basic physical insight, DFT-NL can be recommended as a fully electronic, robust electronic structure method.

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.