How Do DFT-DCP, DFT-NL, and DFT-D3 Compare for the Description of London-Dispersion Effects in Conformers and General Thermochemistry?

The dispersion-core-potential corrected B3LYP-DCP method (Torres and DiLabio <i>J. Phys. Chem. Lett.</i> <b>2012</b>, <i>3</i>, 1738) is for the first time thoroughly assessed and compared with the B3LYP-NL (Hujo and Grimme <i>J. Chem. Theory Comput.</i> <b>2011</b>, <i>7</i>, 3866) and B3LYP-D3 (Grimme et al. <i>J. Comput. Chem.</i> <b>2011</b>, <i>32</i>, 1456) methods for a broad range of chemical problems that particularly shed light on intramolecular London-dispersion effects in conformers and general thermochemistry. The analysis is based on a compilation of 473 reference cases, the majority of which are taken from the GMTKN30 database (Goerigk and Grimme <i>J. Chem. Theory Comput.</i> <b>2010</b>, <i>6</i>, 107; <b>2011</b>, <i>7</i>, 291). The results confirm previous findings that B3LYP-DCP indeed predicts very good binding energies for noncovalently bound complexes, particularly with small basis sets. However, problems are identified for the description of intramolecular effects in some conformers and chemical reactions, for which B3LYP-DCP sometimes gives results similar or worse than uncorrected B3LYP. Surprisingly large errors for total atomization energies reveal an unwanted influence of the DCPs on the short-range electronic structure of the investigated systems. However, a recently modified carbon potential for B3LYP-DCP (DiLabio et al. <i>Theor. Chem. Acc.</i> <b>2013</b>, <i>132</i>, 1389) was additionally tested that seems to solve most of those problems and provides improved results. An overall comparison between all tested methods shows that B3LYP-NL is the most robust and accurate approach, closely followed by B3LYP-D3. This is also true when small basis sets of double-ζ quality are applied for which those methods have not been parametrized. However, binding energies of noncovalently bound complexes can be more strongly influenced by basis-set superposition-error effects than for B3LYP-DCP. Finally, it is noted that the DFT-D3 and DFT-NL schemes are readily applicable to a large range of chemical elements and they are therefore particularly recommended for more general applications

Treating London-Dispersion Effects with the Latest Minnesota Density Functionals: Problems and Possible Solutions

It is shown that the latest Minnesota density functionals (SOGGA11, M11-L, N12, MN12-L, SOGGA11-X, M11, N12-SX, and MN12-SX) do not properly describe London-dispersion interactions. Grimme’s DFT-D3 correction can solve this problem partially; however, double-counting of medium-range electron correlation can occur. For the related M06-L functional, the alternative VV10 van der Waals kernel is tested, but it experiences similar double-counting. Most functionals give unphysical dissociation curves for the argon dimer, an indication for method-inherent problems, and further investigation is recommended. These results are further evidence that the London-dispersion problem in density functional theory approximations is unlikely to be solved by mere empirical optimization of functional parameters, unless the functionals contain components that ensure the correct asymptotic long-range behavior. London dispersion is ubiquitous, which is why the reported findings are not only important for theoreticians but also a reminder to the general chemist to carefully consider their choice of method before undertaking computational studies

Double-Hybrid Density Functionals Provide a Balanced Description of Excited ¹L_a and ¹L_b States in Polycyclic Aromatic Hydrocarbons

The time-dependent density functional theory (TD-DFT) double-hybrid methods TD-B2-PLYP and TD-B2GP-PLYP are applied to five linear and 12 nonlinear polycyclic aromatic hydrocarbons. The absolute errors compared to experiment for the two lowest-lying 1La and 1Lb excited states are evaluated and it is also tested whether the energetic order of those states and their energy difference is reproduced correctly. The results are compared to published CC2, global hybrid, and long-range corrected hybrid TD-DFT results. The two double-hybrids outmatch the other methods in terms of absolute and relative accuracy without an empirical adjustment of parameters. Although of different electronic character, both types of states are described on an equal footing by the double-hybrids. Particularly, the B2GP-PLYP functional yields very good results, which is in accordance with previous benchmarks

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 N4 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

Benchmarking Density Functional Theory Methods for Metalloenzyme Reactions: The Introduction of the MME55 Set

We present a new benchmark set of metalloenzyme model reaction energies and barrier heights that we call MME55. The set contains 10 different enzymes, representing eight transition metals, both open and closed shell systems, and system sizes of up to 116 atoms. We use four DLPNO–CCSD­(T)-based approaches to calculate reference values against which we then benchmark the performance of a range of density functional approximations with and without dispersion corrections. Dispersion corrections improve the results across the board, and triple-ζ basis sets provide the best balance of efficiency and accuracy. Jacob’s ladder is reproduced for the whole set based on averaged mean absolute (percent) deviations, with the double hybrids SOS0-PBE0-2-D3­(BJ) and revDOD-PBEP86-D4 standing out as the most accurate methods for the MME55 set. The range-separated hybrids ωB97M-V and ωB97X-V also perform well here and can be recommended as a reliable compromise between accuracy and efficiency; they have already been shown to be robust across many other types of chemical problems, as well. Despite the popularity of B3LYP in computational enzymology, it is not a strong performer on our benchmark set, and we discourage its use for enzyme energetics

Exploring CPS-Extrapolated DLPNO–CCSD(T₁) Reference Values for Benchmarking DFT Methods on Enzymatically Catalyzed Reactions

Domain-based local pair natural orbital coupled-cluster singles doubles with perturbative triples [DLPNO–CCSD(T)] is regularly used to calculate reliable benchmark reference values at a computational cost significantly lower than that of canonical CCSD(T). Recent work has shown that even greater accuracy can be obtained at only a small additional cost through extrapolation to the complete PNO space (CPS) limit. Herein, we test two levels of CPS extrapolation, CPS(5,6), which approximates the accuracy of standard TightPNO, and CPS(6,7), which surpasses it, as benchmark values to test density functional approximations (DFAs) on a small set of organic and transition-metal-dependent enzyme active site models. Between the different reference levels of theory, there are changes in the magnitudes of the absolute deviations for all functionals, but these are small and there is minimal impact on the relative rankings of the tested DFAs. The differences are more significant for the metalloenzymes than the organic enzymes, so we repeat the tests on our entire ENZYMES22 set of organic enzyme active site models [Wappett, D. A.; Goerigk, L. J. Phys. Chem. A 2019, 123, 7057–7074] to confirm that using the CPS extrapolations for the reference values has negligible impact on the benchmarking outcomes. This means that we can particularly recommend CPS(5,6) as an alternative to standard TightPNO settings for calculating reference values, increasing the applicability of DLPNO–CCSD(T) in benchmarking reaction energies and barrier heights of larger models of organic enzymes. DLPNO–CCSD(T1)/CPS(6,7) energies for ENZYMES22 are finally presented as updated reference values for the set, reflecting the recent improvements in the method

A General Database for Main Group Thermochemistry, Kinetics, and Noncovalent Interactions − Assessment of Common and Reparameterized (<i>meta</i>-)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

Calculation of Electronic Circular Dichroism Spectra with Time-Dependent Double-Hybrid Density Functional Theory

Time-dependent double-hybrid density functional theory is applied to the calculation of the electronic circular dichroism (CD) spectra of molecules. The TD-B2PLYP method is based on vertical excitation energies obtained from its hybrid-GGA part B2LYP in a conventional TD-DFT linear response treatment and a CIS(D) type perturbation correction for these excited states. A new benchmark set of six representative organic molecules with a wide variety of different electronic character is introduced for this investigation. The simulated TD-B2PLYP spectra are compared to experiment and those computed with the TD-B2LYP (i.e., no CIS(D) correction) and TD-B3LYP methods. Vertical excitation energies at the perturbatively corrected level are, in the majority of cases, more accurate than, e.g., with TD-B3LYP. Relative band positions are also reproduced better. In one example, the high-energy CD bands are not computed with sufficient accuracy, which is attributed to an instability of the perturbation correction. Due to the inclusion of a large portion of “exact” exchange (53%) in B2PLYP, the spectra feature less artificially created excited states and CD bands than with TD-B3LYP. In all six examined cases, TD-B2PLYP gives qualitatively correct spectra, whereas the hybrid functionals sometimes show a more erratic behavior. Therefore, we can recommend the use of the new double-hybrid approach for the computation of CD and the prediction of absolute configurations of chiral molecules