Double-hybrid density functionals free of dispersion and counterpoise corrections for non-covalent interactions

The p-block challenge: assessing quantum chemistry methods for inorganic heterocycle dimerizations

The elements of the p-block of the periodic table are of high interest in various chemical and technical applications like frustrated Lewis-pairs (FLP) or opto-electronics. However, high-quality benchmark data to assess approximate density functional theory (DFT) for their theoretical description are sparse. In this work, we present a benchmark set of 604 dimerization energies of 302 "inorganic benzenes" composed of all non-carbon p-block elements of main groups III to VI up to polonium. This so-called IHD302 test set comprises two classes of structures formed by covalent bonding and by weaker donor-acceptor (WDA) interactions, respectively. Generating reliable reference data with ab initio methods is challenging due to large electron correlation contributions, core-valence correlation effects, and especially the slow basis set convergence. To compute reference values for these dimerization reactions, after thorough testing, we applied a computational protocol using state-of-the-art explicitly correlated local coupled cluster theory termed PNO-LCCSD(T)-F12/cc-VTZ-PP-F12(corr.). It includes a basis set correction at the PNO-LMP2-F12/aug-cc-pwCVTZ level. Based on these reference data, we assess 26 DFT methods in combination with three different dispersion corrections and the def2-QZVPP basis set, five composite DFT approaches, and five semi-empirical quantum mechanical methods. For the covalent dimerizations, the r2SCAN-D4 meta-GGA, the r2SCAN0-D4 and ωB97M-V hybrids, and the revDSD-PBEP86-D4 double-hybrid functional are found to be the best-performing methods among the evaluated functionals of the respective class. However, since def2 basis sets for the 4th period are not associated to relativistic pseudo-potentials, we obtained significant errors in the covalent dimerization energies (up to 6 kcal mol-1) for molecules containing p-block elements of the 4th period. Significant improvements were achieved for systems containing 4th row elements by using ECP10MDF pseudopotentials along with re-contracted aug-cc-pVQZ-PP-KS basis sets introduced in this work with the contraction coefficients taken from atomic DFT (PBE0) calculations. Overall, the IHD302 set represents a challenge to contemporary quantum chemical methods. This is due to a large number of spatially close p-element bonds which are underrepresented in other benchmark sets, and the partial covalent bonding character for the WDA interactions. The IHD302 set may be helpful to develop more robust and transferable approximate quantum chemical methods in the future.

A comprehensive benchmark investigation of quantum chemical methods for carbocations

The application of various density functional approximations (DFAs) and an emphasis on popular methods without any consensus have prevailed in computational studies dedicated to carbocations. More importantly, an extensive and rigorous benchmark investigation on density functionals for the class is still lacking. To close this gap, we present a comprehensive benchmark study of quantum chemical methods on a series of classical and nonclassical carbocations, the CARBO33 dataset. We evaluate a total of 107 DFT methods from all rungs giving particular attention to double hybrid density functionals as the potential of the class has been largely undermined in the context of carbocations. To support our findings, DLPNO-CCSD(T) at the complete basis set (CBS) limit and W1-F12 are used as reference methods. Our results indicate that the composite CBS-QB3 method performs poorly and should not be adopted for target energies. Oftentimes, the tested DFAs of a lower rung perform better than several DFAs in a higher rung of Perdew's "Jacob's ladder". Nonetheless, double hybrids DSD-PBEP86-NL and ωB97X-2-D3(BJ) stand out by showing the overall best performance. Among the hybrids evaluated, about half of them show mean absolute deviation (MAD) below 1.1 kcal mol^-1, including the popular hybrids M06-2X and mPW1PW91. In this family, MN15-D3(BJ) performs particularly well (MAD = 0.77 kcal mol^-1) displaying reliable results across various tests. Highly popular B3LYP exhibited one of the worst performances (MAD = 4.74 kcal mol^-1), and we do not recommend its application to carbocations. We also assess the 24 general-purpose basis sets of single- up to quadruple-ζ quality. The best compromise between accuracy and computational cost is achieved with cc-pVTZ followed by def2-TZVP. Computations on larger structures of general interest, including terpene carbocations, are also presented for selected DFT methods confirming general trends in the results.

CHAL336 Benchmark Set: How Well Do Quantum-Chemical Methods Describe Chalcogen-Bonding Interactions?

We present the CHAL336 benchmark set-the most comprehensive database for the assessment of chalcogen-bonding (CB) interactions. After careful selection of suitable systems and identification of three high-level reference methods, the set comprises 336 dimers each consisting of up to 49 atoms and covers both σ- and π-hole interactions across four categories: chalcogen-chalcogen, chalcogen-π, chalcogen-halogen, and chalcogen-nitrogen interactions. In a subsequent study of DFT methods, we re-emphasize the need for using proper London dispersion corrections when treating noncovalent interactions. We also point out that the deterioration of results and systematic overestimation of interaction energies for some dispersion-corrected DFT methods does not hint at problems with the chosen dispersion correction but is a consequence of large density-driven errors. We conclude this work by performing the most detailed DFT benchmark study for CB interactions to date. We assess 109 variations of dispersion-corrected and dispersion-uncorrected DFT methods and carry out a detailed analysis of 80 of them. Double-hybrid functionals are the most reliable approaches for CB interactions, and they should be used whenever computationally feasible. The best three double hybrids are SOS0-PBE0-2-D3(BJ), revDSD-PBEP86-D3(BJ), and B2NCPLYP-D3(BJ). The best hybrids in this study are ωB97M-V, PW6B95-D3(0), and PW6B95-D3(BJ). We do not recommend using the popular B3LYP functional nor the MP2 approach, which have both been frequently used to describe CB interactions in the past. We hope to inspire a change in computational protocols surrounding CB interactions that leads away from the commonly used, popular methods to the more robust and accurate ones recommended herein. We would also like to encourage method developers to use our set for the investigation and reduction of density-driven errors in new density functional approximations.

What Types of Chemical Problems Benefit from Density-Corrected DFT? A Probe Using an Extensive and Chemically Diverse Test Suite

For the large and chemically diverse GMTKN55 benchmark suite, we have studied the performance of density-corrected density functional theory (HF-DFT), compared to self-consistent DFT, for several pure and hybrid GGA and meta-GGA exchange–correlation (XC) functionals (PBE, BLYP, TPSS, and SCAN) as a function of the percentage of HF exchange in the hybrid. The D4 empirical dispersion correction has been added throughout. For subsets dominated by dynamical correlation, HF-DFT is highly beneficial, particularly at low HF exchange percentages. This is especially true for noncovalent interactions where the electrostatic component is dominant, such as hydrogen and halogen bonds: for π-stacking, HF-DFT is detrimental. For subsets with significant nondynamical correlation (i.e., where a Hartree–Fock determinant is not a good zero-order wavefunction), HF-DFT may do more harm than good. While the self-consistent series show optima at or near 37.5% (i.e., 3/8) for all four XC functionals—consistent with Grimme’s proposal of the PBE38 functional—HF-BnLYP-D4, HF-PBEn-D4, and HF-TPSSn-D4 all exhibit minima nearer 25% (i.e., 1/4) as the use of HF orbitals greatly mitigates the error at 25% for barrier heights. Intriguingly, for HF-SCANn-D4, the minimum is near 10%, but the weighted mean absolute error (WTMAD2) for GMTKN55 is only barely lower than that for HF-SCAN-D4 (i.e., where the post-HF step is a pure meta-GGA). The latter becomes an attractive option, only slightly more costly than pure Hartree–Fock, and devoid of adjustable parameters other than the three in the dispersion correction. Moreover, its WTMAD2 is only surpassed by the highly empirical M06-2X and by the combinatorially optimized empirical range-separated hybrids ωB97X-V and ωB97M-V.

Double hybrid DFT calculations with Slater type orbitals

On a comprehensive database with 1,644 datapoints, covering several aspects of main-group as well as of transition metal chemistry, we assess the performance of 60 density functional approximations (DFA), among them 36 double hybrids (DH). All calculations are performed using a Slater type orbital (STO) basis set of triple-ζ (TZ) quality and the highly efficient pair atomic resolution of the identity approach for the exchange- and Coulomb-term of the KS matrix (PARI-K and PARI-J, respectively) and for the evaluation of the MP2 energy correction (PARI-MP2). Employing the quadratic scaling SOS-AO-PARI-MP2 algorithm, DHs based on the spin-opposite-scaled (SOS) MP2 approximation are benchmarked against a database of large molecules. We evaluate the accuracy of STO/PARI calculations for B3LYP as well as for the DH B2GP-PLYP and show that the combined basis set and PARI-error is comparable to the one obtained using the well-known def2-TZVPP Gaussian-type basis set in conjunction with global density fitting. While quadruple-ζ (QZ) calculations are currently not feasible for PARI-MP2 due to numerical issues, we show that, on the TZ level, Jacob's ladder for classifying DFAs is reproduced. However, while the best DHs are more accurate than the best hybrids, the improvements are less pronounced than the ones commonly found on the QZ level. For conformers of organic molecules and noncovalent interactions where very high accuracy is required for qualitatively correct results, DHs provide only small improvements over hybrids, while they still excel in thermochemistry, kinetics, transition metal chemistry and the description of strained organic systems.

Appraising spin-state energetics in transition metal complexes using double-hybrid models: accountability of SOS0-PBESCAN0-2(a) as a promising paradigm

Through a comprehensive survey, reliable double-hybrid models have been validated and proposed for spin-state energetics in transition metal complexes.

Semi-empirical or non-empirical double-hybrid density functionals: which are more robust?

The development of non-empirical double-hybrid density functionals (DHDFs) is a very active research area with the number of approaches in this field having increased rapidly. At the same time, there is a lack of published work that provides a fair assessment and comparison between non-empirical and semi-empirical DHDFs on an equal footing. Herein, we close this gap and present a thorough analysis of both classes of DHDFs on the large GMTKN55 benchmark database for general main-group thermochemistry, kinetics, and noncovalent interactions [Goerigk et al., Phys. Chem. Chem. Phys., 2017, 19, 32184-32215]. In total, 115 variations of dispersion-corrected and -uncorrected DHDFs are tested, which will be condensed to an in-depth assessment of 31 methods: 19 non-empirical and 12 semi-empirical DHDFs. As such, our study represents the largest DHDF study ever conducted and can serve as an important benchmark informing method developers and users alike. Our results show that semi-empirical DHDFs are the most robust density functional approximations and more reliable and accurate than non-empirical ones. In fact, some non-empirical approaches are even outperformed by hybrid approaches or even dispersion-corrected and -uncorrected MP2 and SCS-MP2. SOS0-PBE0-2-D3(BJ) is the only exception and the only non-empirical DHDF that we can safely recommend for general applicability. However, it is still outperformed by six semi-empirical DHDFs, of which we would like to particularly recommend the following five: ωB97X-2-D3(BJ), DSD-BLYP-D3(BJ), DSD-PBEP86-D3(BJ), B2NC-PLYP-D3(BJ), and B2GPPLYP-D3(BJ). Our findings seriously question current trends in the field and they highlight that novel strategies have to be found in order to outperform the currently best density functional theory methods on the market. We hope that our study can function as an important cornerstone inspiring such a change of direction in the field.

Dissecting the accountability of parameterized and parameter-free single-hybrid and double-hybrid functionals for photophysical properties of TADF-based OLEDs

Organic light emitting diodes (OLEDs) based on thermally activated delayed fluorescence (TADF) emitters are an attractive category of materials that have witnessed a booming development in recent years. In the present contribution, we scrutinize the accountability of parameterized and parameter-free single-hybrid (SH) and double-hybrid (DH) functionals through the two formalisms, full time-dependent density functional theory (TD-DFT) and Tamm-Dancoff approximation (TDA), for the estimation of photophysical properties like absorption energy, emission energy, zero-zero transition energy, and singlet-triplet energy splitting of TADF molecules. According to our detailed analyses on the performance of SHs based on TD-DFT and TDA, the TDA-based parameter-free SH functionals, PBE0 and TPSS0, with one-third of exact-like exchange turned out to be the best performers in comparison to other functionals from various rungs to reproduce the experimental data of the benchmarked set. Such affordable SH approximations can thus be employed to predict and design the TADF molecules with low singlet-triplet energy gaps for OLED applications. From another perspective, considering this point that both the nonlocal exchange and correlation are essential for a more reliable description of large charge-transfer excited states, applicability of the functionals incorporating these terms, namely, parameterized and parameter-free DHs, has also been evaluated. Perusing the role of exact-like exchange, perturbative-like correlation, solvent effects, and other related factors, we find that the parameterized functionals B2π-PLYP and B2GP-PLYP and the parameter-free models PBE-CIDH and PBE-QIDH have respectable performance with respect to others. Lastly, besides the recommendation of reliable computational protocols for the purpose, hopefully this study can pave the way toward further developments of other SHs and DHs for theoretical explorations in the field of OLEDs technology.

Relative energies of water nanoclusters (H2O)20: comparison of empirical and nonempirical double-hybrids with generalized energy-based fragmentation approach

The applicability of recently developed parameterized and parameter-free double-hybrids for predicting the relative energies of water nanoclusters has been examined.