Benchmark Database for Ylidic Bond Dissociation Energies and Its Use for Assessments of Electronic Structure Methods

Using atomic clustering based on structural and electronic descriptors that consider surrounding environment to evaluate local properties of DFT functionals

We developed a method for evaluating the accuracies of the local properties of DFT functionals in detail using a clustering method based on machine learning and structural/electronic descriptors. We generated 36 clusters consistent with human intuition using 30,436 carbon atoms from the QM9 dataset. The results were used to evaluate 13C NMR chemical shifts calculated using 84 DFT functionals. Carbon atoms were grouped based on their similar environments, reducing errors within these groups. This enables more accurate assessment of the accuracy using a specific DFT functional. Therefore, the present atomic clustering provides more detailed insight into accuracy verification.

Revised Mechanism of C(sp3)-C(sp3) Reductive Elimination from Ni(II) with the Assistance of a Z-Type Metalloligand

Reductive elimination is a key step in Ni-catalyzed cross-couplings. Compared with processes that proceed from Ni(III) or Ni(IV) intermediates, C(sp³)-C(sp³) reductive eliminations from Ni(II) centers are challenging due to the weak oxidizing ability of Ni(II) species. In this report, we present computational evidence that supports a mechanism in which Zn coordination to the nickel center as a Z-type ligand accelerates reductive elimination. This Zn-assisted pathway is found to be lower in energy compared with direct reductive elimination from a σ-coordinated Ni(II) intermediate, providing new insights into the mechanism of Ni-catalyzed cross-coupling with organozinc nucleophiles. Mayer bond order, Hirshfield charge, Laplacian of the electron density, orbital, and interaction region indicator analyses were conducted to elucidate details of the reductive elimination process and characterize the key intermediates. Theoretical calculations indicate a significant Z-type Ni-Zn interaction that reduces the electron density around the Ni center and accelerates reductive elimination. This mechanistic study of reductive elimination in Ni(0)-catalyzed conjunctive cross-couplings of aryl iodides, organozinc reagents, and alkenes is an important case study of the involvement of Zn-assisted reductive elimination in Ni catalysis. We anticipate that the novel Zn-assisted reductive elimination mode may extend to other cross-coupling processes and explain the unique effectiveness of organozinc nucleophiles in many instances.

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.

Eliminating Delocalization Error to Improve Heterogeneous Catalysis Predictions with Molecular DFT + U

Approximate semilocal density functional theory (DFT) is known to underestimate surface formation energies yet paradoxically overbind adsorbates on catalytic transition-metal oxide surfaces due to delocalization error. The low-cost DFT + U approach only improves surface formation energies for early transition-metal oxides or adsorption energies for late transition-metal oxides. In this work, we demonstrate that this inefficacy arises due to the conventional usage of metal-centered atomic orbitals as projectors within DFT + U. We analyze electron density rearrangement during surface formation and O atom adsorption on rutile transition-metal oxides to highlight that a standard DFT + U correction fails to tune properties when the corresponding density rearrangement is highly delocalized across both metal and oxygen sites. To improve both surface properties simultaneously while retaining the simplicity of a single-site DFT + U correction, we systematically construct multi-atom-centered molecular-orbital-like projectors for DFT + U. We demonstrate this molecular DFT + U approach for tuning adsorption energies and surface formation energies of minimal two-dimensional models of representative early (i.e., TiO₂) and late (i.e., PtO₂) transition-metal oxides. Molecular DFT + U simultaneously corrects adsorption energies and surface formation energies of multilayer models of rutile TiO₂(110) and PtO₂(110) to resolve the paradoxical description of surface stability and surface reactivity of semilocal DFT.

BSE49, a diverse, high-quality benchmark dataset of separation energies of chemical bonds

We present an extensive and diverse dataset of bond separation energies associated with the homolytic cleavage of covalently bonded molecules (A-B) into their corresponding radical fragments (A. and B.). Our dataset contains two different classifications of model structures referred to as "Existing" (molecules with associated experimental data) and "Hypothetical" (molecules with no associated experimental data). In total, the dataset consists of 4502 datapoints (1969 datapoints from the Existing and 2533 datapoints from the Hypothetical classes). The dataset covers 49 unique X-Y type single bonds (except H-H, H-F, and H-Cl), where X and Y are H, B, C, N, O, F, Si, P, S, and Cl atoms. All the reference data was calculated at the (RO)CBS-QB3 level of theory. The reference bond separation energies are non-relativistic ground-state energy differences and contain no zero-point energy corrections. This new dataset of bond separation energies (BSE49) is presented as a high-quality reference dataset for assessing and developing computational chemistry methods.

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 8.5 kcal/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.

Assessing the Applicability of the Geometric Counterpoise Correction in B2PLYP/Double-ζ Calculations for Thermochemistry, Kinetics, and Noncovalent Interactions

We present a proof-of-concept study of the suitability of Kruse and Grimme’s geometric counterpoise correction (gCP) for basis set superposition errors (BSSEs) in double-hybrid density functional calculations with a double-ζ basis set. The gCP approach only requires geometrical information as an input and no orbital/density information is needed. Therefore, this correction is practically free of any additional cost. gCP is trained against the Boys and Bernardi counterpoise correction across a set of 528 noncovalently bound dimers. We investigate the suitability of the approach for the B2PLYP/def2-SVP level of theory, and reveal error compensation effects—missing London dispersion and the BSSE—associated with B2PLYP/def2-SVP calculations, and present B2PLYP-gCP-D3(BJ)/def2-SVP with the reparametrised DFT-D3(BJ) and gCP corrections as a more balanced alternative. Benchmarking results on the S66x8 benchmark set for noncovalent interactions and the GMTKN55 database for main-group thermochemistry, kinetics, and noncovalent interactions show a statistical improvement of the B2PLYP-gCP-D3(BJ) scheme over plain B2PLYP and B2PLYP-D3(BJ). B2PLYP-D3(BJ) shows significant overestimation of interaction energies, barrier heights with larger deviations from the reference values, and wrong relative stabilities in conformers, all of which can be associated with BSSE. We find that the gCP-corrected method represents a significant improvement over B2PLYP-D3(BJ), particularly for intramolecular noncovalent interactions. These findings encourage future developments of efficient double-hybrid DFT strategies that can be applied when double-hybrid calculations with large basis sets are not feasible due to system size.

Diastereoselective synthesis and conformational analysis of 4,5-difluoropipecolic acids

Stereoselectively-fluorinated analogs of pipecolic acid have been investigated through a combined theoretical and experimental approach. Three of the four possible diastereoisomers of 4,5-difluoropipecolic acid were successfully synthesized via deoxyfluorination chemistry, navigating a complex reaction network that included neighboring group participation, rearrangement, and elimination pathways. A DFT-based conformational study, supported by NMR J-based analysis, revealed that the different diastereoisomers of 4,5-difluoropipecolic acid preferentially adopt different puckers of the six-membered ring. These findings could have future relevance for the conformational control of biologically active peptides.

Extrapolation to the Limit of a Complete Pair Natural Orbital Space in Local Coupled-Cluster Calculations

The domain-based local pair natural orbital (PNO) coupled-cluster DLPNO-CCSD(T) method allows one to perform single point energy calculations for systems with hundreds of atoms while retaining essentially the accuracy of its canonical counterpart, with errors that are typically smaller than 1 kcal/mol for relative energies. Crucial to the accuracy and efficiency of the method is a proper definition of the virtual space in which the coupled-cluster equations are solved, which is spanned by a highly compact set of pair natural orbitals (PNOs) that are specific for each electron pair. The dimension of the PNO space is controlled by the T_CutPNO threshold: only PNOs with an occupation number greater than T_CutPNO are included in the correlation space of a given electron pair, whilst the remaining PNOs are discarded. To keep the error of the method small, a conservative T_CutPNO value is used in standard DLPNO-CCSD(T) calculations. This often leads to unnecessarily large PNO spaces, which limits the efficiency of the method. Herein, we introduce a new computational strategy to approach the complete PNO space limit (for a given basis set) that consists in extrapolating the results obtained with different T_CutPNO values. The method is validated on the GMTKN55 set using canonical CCSD(T) data as the reference. Our results demonstrate that a simple two-point extrapolation scheme can be used to significantly increase the efficiency and accuracy of DLPNO-CCSD(T) calculations, thus extending the range of applicability of the technique.

Accurate Hybrid Density Functionals with UW12 Correlation

In previous work, we suggested a single-parameter hybrid functional containing a novel correlation contribution based on the Unsöld approximation, UW12. This model resembles the explicitly correlated part of MP2-F12 theory and can be written as an explicit formula in terms of the single-particle reduced density matrix. Here, we further investigate hybrid functionals containing UW12 correlation and in particular look at functionals with a large fraction of exact exchange to reduce the self-interaction error. We suggest two new hybrid functionals B-LYP-osUW12 and fB-LYP-osUW12. On the test sets we use, our best hybrid functional overall (B-LYP-osUW12) is of similar accuracy to the best double hybrids considered while eliminating the need for virtual orbitals.

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.

M11plus, a Range-Separated Hybrid Meta Functional Incorporating Nonlocal Rung-3.5 Correlation, Exhibits Broad Accuracy on Diverse Databases

We present tests of the recent M11plus Minnesota density functional for a broad range of main-group and transition-metal chemistry databases, most of which were not used in in the construction of any of the Minnesota functionals. M11plus is a range-separated hybrid meta functional combining long-range nonlocal Hartree-Fock exchange with nonlocal rung-3.5 correlation. M11plus performs well for main-group thermochemistry, kinetics, and noncovalent interactions and especially well for radical species. It is numerically well behaved, it has a computational cost that is ∼1.2 to 1.5 times that of M11 in realistic calculations, and it is particularly accurate for triplet excited states, which is a difficult challenge for density functional approximations. The results show that nonlocal rung-3.5 correlation is a broadly useful ingredient for improving the performance of density functional approximations.

Role of Alkaline-Earth Metal-Catalyst: A Theoretical Study of Pyridines Hydroboration

Density functional theory (DFT) calculations have been performed to investigate the mechanism of alkaline-earth-metal-catalyzed hydroboration of pyridines with borane. In this reaction, the active catalytic species is considered to be an alkaline earth metal hydride complex when the corresponding alkaline earth metal is used as the catalyst. The theoretical results reveal that initiation of the catalytic cycle is hydride transfer to generate a magnesium hydride complex when β-diimine alkylmagnesium is used as a pre-catalyst. The magnesium hydride complex can undergo coordination of the pyridine reactant followed by hydride transfer to form a dearomatized magnesium pyridine intermediate. Coordination of borane and hydride transfer from borohydride to magnesium then give the hydroboration product and regenerate the active magnesium hydride catalyst. The rate-determining step of the catalytic cycle is hydride transfer to pyridine with a free energy barrier of 29.7 kcal/mol. Other alkaline earth metal complexes, including calcium and strontium complexes, were also considered. The DFT calculations show that the corresponding activation free energies for the rate-determining step of this reaction with calcium and strontium catalysts are much lower than with the magnesium catalyst. Therefore, calcium and strontium complexes can be used as the catalyst for the reaction, which could allow mild reaction conditions.

Theoretical Study of the Addition of Cu-Carbenes to Acetylenes to Form Chiral Allenes

Terminal alkynes have become one of the most versatile building blocks for C-C bond construction in the past few decades, and they are usually considered to convert to acetylides before further transformations. In this study, a novel direct nucleophilic addition mode for Cu(I)-catalyzed cross-coupling of terminal alkynes and N-tosylhydrazones to synthesize chiral allenes is proposed, and it was investigated by density functional theory with the M11-L density functional. Three different reaction pathways were considered and investigated. The computational results show that the proposed reaction pathway, which includes direct nucleophilic attack of protonated acetylene, deprotonation of the vinyl cation, and catalyst regeneration, is the most favorable pathway. Another possible deprotonation-carbenation-insertion pathway is shown to be unfavorable. The direct nucleophilic addition step is the rate- and enantioselectivity-determining step in the catalytic cycle. Noncovalent interaction analysis shows that the steric effect between the methyl group of the carbene moiety and the naphthalyl group of the bisoxazoline ligand is important to control the enantioselectivity. In addition, calculation of a series of chiral bisoxazoline ligands shows that a bulky group on the oxazoline ring is favorable for high enantioselectivity, which agrees with experimental observations. Moreover, copper acetylides are stable, and their generation is a favorable pathway in the absence of chiral bisoxazoline ligands.

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.

Long distance unconjugated agostic-assisted 1,5-H shift in a Ru-mediated Alder-ene type reaction: mechanism and stereoselectivity

A long distance unconjugated novel 1,5-H shift mechanism for a Ru-catalyzed Alder-ene type alkene–alkyne coupling reaction was examined by DFT.

C–H bond cleavage occurring on a Rh(v) intermediate: a theoretical study of Rh-catalyzed arene azidation

Our theoretical calculations indicated that the oxidation of Rh(iii) to Rh(v) by PhI(OAc)OTs is a facile process. Subsequent electrophilic deprotonation was shown to occur from a Rh(v) intermediate rather than a Rh(iii) intermediate.

‘Diet GMTKN55’ offers accelerated benchmarking through a representative subset approach

The GMTKN55 benchmarking protocol allows comprehensive analysis and ranking of density functional approximations with diverse chemical behaviours. This work reports diet versions of GMTKN55 which reproduce key properties of the full protocol at substantially reduced numerical cost. ‘Diet GMTKN55’ can thus be used for benchmarking expensive methods, or in combination with solid state benchmarks.

From Mechanistic Study to Chiral Catalyst Optimization: Theoretical Insight into Binaphthophosphepine-catalyzed Asymmetric Intramolecular [3 + 2] Cycloaddition

Density functional M11 was used to study the mechanism and enantioselectivity of a binaphthophosphepine-catalyzed intramolecular [3 + 2] cycloaddition reaction. The computational results revealed that this reaction proceeds through nucleophilic addition of the phosphine catalyst to the allene, which yields a zwitterionic phosphonium intermediate. The subsequent stepwise [3 + 2] annulation process, which starts with the intramolecular nucleophilic addition of the allenoate moiety to the electron-deficient olefin group, determines the enantioselectivity of the reaction. This step is followed by a ring-closing reaction and water-assisted proton-transfer process to afford the final product with concomitant regeneration of the phosphine catalyst. Theoretical predictions of the enantioselectivity for various phosphine catalysts were consistent with experimental observations, and 2D contour maps played an important role in explaining the origin of the enantioselectivity. Moreover, on the basis of our theoretical study, new binaphthophosphepine catalysts were designed and that are expecting to afford higher enantioselectivity in this cycloaddition reaction.

Comparative investigation of the reactivities between catalysts [Cp*RhCl2]2 and [Cp*IrCl2]2 in the oxidative annulation of isoquinolones with alkynes: a combined experimental and computational study

The origin of the lower reactivity of [Cp*IrCl₂]₂ relative to [Cp*RhCl₂]₂ is disclosed and the substituent effects on reactivities are discussed.

Kinetics and branching fractions of the hydrogen abstraction reaction from methyl butenoates by H atoms

We studied hydrogen abstraction reactions at various sites of unsaturated methyl esters by H atoms, including variational effects, tunneling and multi-structural torsional anharmonicity.

Reaction kinetics of hydrogen abstraction from polycyclic aromatic hydrocarbons by H atoms

We studied how the PAH structure, site, and size affect the rate constants of hydrogen abstraction reactions of PAH systematically.

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 updated and extended GMTKN55 benchmark database for more accurate and extensive energetic evaluation of density functionals and other electronic structure methods with detailed guidelines for method users.

Silane-initiated nucleation in chemically active plasmas: validation of density functionals, mechanisms, and pressure-dependent variational transition state calculations

Pressure-dependent rate constants for nucleation in nanodusty plasmas are calculated by variational transition state theory with system-specific quantum RRK theory.

Understanding the photophysical properties of chiral dinuclear Re(i) complexes and the role of Re(i) in their complexes

We have investigated the electronic structure, UV-Vis/CD spectra and the second-order NLO properties of chiral dinuclear Re(i) complexes and elucidated structure–property relationships with the aid of DFT calculations.