BH9, a New Comprehensive Benchmark Data Set for Barrier Heights and Reaction Energies: Assessment of Density Functional Approximations and Basis Set Incompleteness Potentials

Comparing coupled cluster and composite quantum chemical methods for computing activation energies and reaction enthalpies of radical propagation reactions

Accurate determination of activation energies and reaction enthalpies is essential for understanding the propagation step in free radical polymerization, as it significantly affects polymer chain length and structure. In this study, we compare DLPNO-CCSD(T) to canonical CCSD(T) for 17 radical addition activation energies and 18 reaction enthalpies from Radom and Fischer's test set. Additionally, we compare the computationally efficient composite methods G3(MP2)-RAD and CBS-RAD against CCSD(T)/aug-cc-pVTZ and DLPNO-CCSD(T)/CBS methods. Compared to the CCSD(T)/aug-cc-pVTZ reference, our results indicate that DLPNO-CCSD(T)/CBS with unrestricted Hartree-Fock (UHF) or UB3LYP reference orbitals and NormalPNO parameters consistently achieves chemical accuracy, with mean absolute deviations of 3.5 kJ mol-1 for activation energies and 1.5 kJ mol-1 for reaction enthalpies. Comparing the two composite methods shows that CBS-RAD agrees most closely with coupled cluster reaction enthalpies, while G3(MP2)-RAD tracks the activation energies most closely.

Automatic Orbital Pair Selection for Multilevel Local Coupled-Cluster Based on Orbital Maps

We present an automatic, orbital-map based orbital-pair selection scheme for multilevel local coupled-cluster approaches that exploits the locality of chemical reactions by focusing on the part of the molecule directly involved in the reaction. The previously introduced pair-selected multilevel extension to domain-based local pair natural orbital coupled-cluster with singles, doubles, and semicanonical perturbative triples [DLPNO-CCSD(T0)] partitions the orbital pairs according to relative changes in pair correlation energies [Bensberg, M.; Neugebauer, J. Orbital pair selection for relative energies in the domain-based local pair natural orbital coupled-cluster method. J. Chem. Phys. 2022, 157, 064102. 10.1063/5.0100010]. To this end, maps between localized orbitals are required which in turn require maps between the atoms of structures along reaction paths. So far, these atom maps have been manually determined, which can be a (human) time-consuming procedure. Here, we present an automatic atom mapping algorithm based on the principle of minimum chemical distance that incorporates orientation dependence through dihedral angles. A similar strategy is then introduced to obtain orbital maps, which proves advantageous over the previously used direct orbital selection. Along with a modified orbital pair prescreening, this results in an improved variant of the pair-selected multilevel DLPNO-CCSD(T0) method. The performance of this approach is demonstrated for various reaction types showing a significant efficiency gain and accurate results due to beneficial, systematic error cancellation. The presented method operates in a black-box manner due to its fully automatized algorithms with only the need to specify a single target-accuracy parameter. Additionally, we demonstrate that basis set extrapolation techniques can be applied. In this context, the approach shows deficiencies for the use of large basis sets, especially with diffuse basis functions, which can be traced back to the semicanonical triples correction.

Constructing Accurate and Efficient General-Purpose Atomistic Machine Learning Model with Transferable Accuracy for Quantum Chemistry

Density functional theory (DFT) has been a cornerstone in computational science, providing powerful insights into structure-property relationships for molecules and materials through first-principles quantum-mechanical (QM) calculations. However, the advent of atomistic machine learning (ML) is reshaping the landscape by enabling large-scale dynamics simulations and high-throughput screening at DFT-equivalent accuracy with drastically reduced computational cost. Yet, the development of general-purpose atomistic ML models as surrogates for QM calculations faces several challenges, particularly in terms of model capacity, data efficiency, and transferability across chemically diverse systems. This work introduces a novel extension of the polarizable atom interaction neural network (namely, XPaiNN) to address these challenges. Two distinct training strategies have been employed, one direct-learning and the other Δ-ML on top of a semiempirical QM method. These methodologies have been implemented within the same framework, allowing for a detailed comparison of their results. The XPaiNN models, in particular the one using Δ-ML, not only demonstrate competitive performance on standard benchmarks, but also demonstrate the effectiveness against other ML models and QM methods on comprehensive downstream tasks, including noncovalent interactions, reaction energetics, barrier heights, geometry optimization and reaction thermodynamics, etc. This work represents a significant step forward in the pursuit of accurate and efficient atomistic ML models of general-purpose, capable of handling complex chemical systems with transferable accuracy.

Accurately Predicting Barrier Heights for Radical Reactions in Solution Using Deep Graph Networks

Quantitative estimates of reaction barriers and solvent effects are essential for developing kinetic mechanisms and predicting reaction outcomes. Here, we create a new data set of 5,600 unique elementary radical reactions calculated using the M06-2X/def2-QZVP//B3LYP-D3(BJ)/def2-TZVP level of theory. A conformer search is done for each species using TPSS/def2-TZVP. Gibbs free energies of activation and of reaction for these radical reactions in 40 common solvents are obtained using COSMO-RS for solvation effects. These balanced reactions involve the elements H, C, N, O, and S, contain up to 19 heavy atoms, and have atom-mapped SMILES. All transition states are verified by an intrinsic reaction coordinate calculation. We next train a deep graph network to directly estimate the Gibbs free energy of activation and of reaction in both gas and solution phases using only the atom-mapped SMILES of the reactant and product and the SMILES of the solvent. This simple input representation avoids computationally expensive optimizations for the reactant, transition state, and product structures during inference, making our model well-suited for high-throughput predictive chemistry and quickly providing information for (retro-)synthesis planning tools. To properly measure model performance, we report results on both interpolative and extrapolative data splits and also compare to several baseline models. During training and testing, the data set is augmented by including the reverse direction of each reaction and variants with different resonance structures. After data augmentation, we have around 2 million entries to train the model, which achieves a testing set mean absolute error of 1.16 kcal mol-1 for the Gibbs free energy of activation in solution. We anticipate this model will accelerate predictions for high-throughput screening to quickly identify relevant reactions in solution, and our data set will serve as a benchmark for future studies.

Study of Sterically Crowded Alkanes: Assessment of Non-Empirical Density Functionals Including Double-Hybrid (Cost-Effective) Methods

We theoretically study here the homolytic dissociation reactions of sterically crowded alkanes of increasing size, carrying three different (bulky) substituents such as tert-butyl, adamantyl, and [1.1.1]propellanyl, employing a family of parameter-free functionals ranging from semi-local, to hybrid and double-hybrid models. The study is complemented with the interaction between a pair of HC(CH3)3 molecules at repulsive and attractive regions, as an example of a system composed by a pair of weakly bound sterically crowded alkanes. We also assessed the effect of incorporating reliable dispersion corrections (i. e., D4 or NL) for all the functionals assessed, as well as the use of a tailored basis set (DH-SVPD) for non-covalent interactions, which provides the best trade-off between accuracy and computational cost for a seemingly extended applications to branched or crowded systems. Overall, the PBE-QIDH/DH-SVPD and r2SCAN-QIDH/DH-SVPD methods represent an excellent compromise providing relatively low, and thus very competitive, errors at a fraction of the cost of other quantum-chemical methods in use.

State-of-the-art local correlation methods enable affordable gold standard quantum chemistry for up to hundreds of atoms

In this feature, we review the current capabilities of local electron correlation methods up to the coupled cluster model with single, double, and perturbative triple excitations [CCSD(T)], which is a gold standard in quantum chemistry. The main computational aspects of the local method types are assessed from the perspective of applications, but the focus is kept on how to achieve chemical accuracy (i.e., <1 kcal mol-1 uncertainty), as well as on the broad scope of chemical problems made accessible. The performance of state-of-the-art methods is also compared, including the most employed DLPNO and, in particular, our local natural orbital (LNO) CCSD(T) approach. The high accuracy and efficiency of the LNO method makes chemically accurate CCSD(T) computations accessible for molecules of hundreds of atoms with resources affordable to a broad computational community (days on a single CPU and 10-100 GB of memory). Recent developments in LNO-CCSD(T) enable systematic convergence and robust error estimates even for systems of complicated electronic structure or larger size (up to 1000 atoms). The predictive power of current local CCSD(T) methods, usually at about 1-2 order of magnitude higher cost than hybrid density functional theory (DFT), has become outstanding on the palette of computational chemistry applicable for molecules of practical interest. We also review more than 50 LNO-based and other advanced local-CCSD(T) applications for realistic, large systems across molecular interactions as well as main group, transition metal, bio-, and surface chemistry. The examples show that properly executed local-CCSD(T) can contribute to binding, reaction equilibrium, rate constants, etc. which are able to match measurements within the error estimates. These applications demonstrate that modern, open-access, and broadly affordable local methods, such as LNO-CCSD(T), already enable predictive computations and atomistic insight for complicated, real-life molecular processes in realistic environments.

Growth mechanism of aromatic prebiotic molecules: insights from different processes of ion-molecule reactions in benzonitrile-ammonia and benzonitrile-methylamine clusters

Benzonitrile (BN, C6H5CN) has been detected in the cold molecular cloud Taurus molecular cloud-1 (TMC-1) in 2018, which is suggested to be a precursor in the formation of more complex nitrogen-containing aromatic interstellar compounds. In this study, we utilized mass-selected infrared (IR) photodissociation spectroscopy and quantum chemical calculations to investigate the structures and gaseous ion-molecule reactions of benzonitrile-ammonia (BN-NH3) and benzonitrile-methylamine (BN-MA) clusters. The spectral observations indicate that the cyclic hydrogen bonding structure predominates in both neutral clusters. After VUV (118 nm) single-photon ionization, a new C-N covalent bond formed between BN and NH3 in the (BN-NH3)+ cluster. However, proton sharing constitutes the primary structure of the (BN-MA)+ cluster. The two nitrogen-containing interstellar molecules react with BN to yield distinct products due to difference in charge distribution and molecular polarity in the ionized clusters. The reactions of BN with other molecules contribute to our understanding of the growth mechanisms of complex interstellar molecules.

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.

Nitrile Imine Cyclizations and Rearrangements: N-Phenyl-C-styrylnitrile Imine and N-Phenyl-C-phenylethynylnitrile Imine

The formation and rearrangements of nitrile imines are of ongoing synthetic and theoretical interest. In this paper, we report a computational investigation at the M06/6-311 + G(d,p) level of the formation and rearrangement of propargylic N-phenyl-C-styrylnitrile imine 3 from 2-phenyl-5-styryltetrazole 1 by flash vacuum pyrolysis (FVP). Nitrile imine 3 cyclizes to 3aH-3-styrylindazole 4, which is also generated by H-shifts in the FVP of 3-styrylindazole 8. Tautomerization of 4 and N2-elimination afford cyclohexadienylidene 14, which by cyclization followed by H-shifts yields the primary pyrolysis product, 3-phenylindene 5. An alternate path via 7aH-3-styrylindazole, phenyl(styryl)diazomethane, and phenyl(styryl)carbene is potentially possible. The analogous pyrolysis of 2-phenyl-5-phenylethynyltetrazole 1' afforded cyclopenta[fg]fluorene and cyclopenta[def]phenanthrene via N-phenyl-C-phenylethynylnitrile imine 3' and 3aH-3-phenylethynylindazole 4'. In both cases, 3 and 3', rearrangement to diazocyclohexadienes and cyclohexadienylidenes (e.g., 14) is energetically preferred over alternate aryldiazomethane and arylcarbene intermediates.

How Much Electron Donation Is There In Transition Metal Complexes? A Computational Study

The "dative" covalent interactions between metals and ligands in coordination compounds, i.e., metal-to-ligand and ligand-to-metal donation, are manifestations of electron delocalization and subject to errors in approximate calculations. This work addresses the extent of dative bonding/donation in a series of closed-shell transition metal complexes. Several Kohn-Sham density functionals, representing different "rungs" of approximations, along with post-Hartree-Fock methods are assessed in comparison to CCSD(T). Two widely used nonhybrid and global hybrid density functionals (B3LYP, PBE0) tend to produce notably too strong donation. Global hybrids with elevated fractions of exact exchange (40 to 50%) and the range-separated exchange functional CAM-B3LYP tend to perform better for the description of the donation. The performance of a double-hybrid functional is found to be quite satisfactory, correcting errors seen in MP2 calculations. A fast approximate coupled-cluster model (DLPNO-CCSD) also gives a reasonable description of the donation, with a tendency to underestimate its extent.

Diffusion Monte Carlo method for barrier heights of multiple proton exchanges and complexation energies in small water, ammonia, and hydrogen fluoride clusters

Proton exchange reactions are of key importance in many processes in water. However, it is nontrivial to achieve reliable barrier heights for multiple proton exchanges and complexation energies in hydrogen-bonded systems theoretically. Performance of the fixed-node diffusion quantum Monte Carlo (FN-DMC) with the single-Slater-Jastrow trial wavefunction on total energies, barrier heights of multiple proton exchanges, and complexation energies of small water, ammonia, and hydrogen fluoride clusters is investigated in this study. Effects of basis sets and those of locality approximation (LA), T-move approximation (T-move), and determinant localization approximation (DLA) schemes in dealing with the nonlocal part of pseudopotentials on FN-DMC results are evaluated. According to our results, diffuse basis functions are important in achieving reliable barrier heights and complexation energies with FN-DMC, although the cardinal number of the basis set is more important than diffuse basis functions on total energies of these systems. Our results also show that the time step bias with DLA and LA is smaller than T-move; however, the time step bias of DMC energies with respect to time steps using the T-move is roughly linear up to 0.06 a.u., while this is not the case with LA and DLA. Barrier heights and complexation energies with FN-DMC using these three schemes are always within chemical accuracy. Taking into account the fact that T-move and DLA are typically more stable than LA, FN-DMC calculations with the T-move or DLA scheme and basis sets containing diffuse basis functions are suggested for barrier heights of multiple proton exchanges and complexation energies of hydrogen-bonded clusters.

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.

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.

Easy and accurate computation of energy barriers for carbocation solvation: an expeditious tool to face carbocation chemistry

An expeditious procedure for the challenging computation of the free energy barriers (ΔG≠) for the solvation of carbocations is presented. This procedure is based on Marcus Theory (MT) and the popular B3LYP/6-31G(d)//PCM method, and it allows the easy, accurate and inexpensive prediction of these barriers for carbocations of very different stability. This method was validated by the fair mean absolute error (ca. 1.5 kcal mol-1) achieved in the prediction of 19 known experimental barriers covering a range of ca. 50 kcal mol-1. Interestingly, the new procedure also uses an original method for the calculation of the required inner reorganization energy (Λi) and free energy of reaction (ΔG). This procedure should pave the way to face computationally the pivotal issue of carbocation chemistry and could be easily extended to any bimolecular organic reaction.

Assessment of DLPNO-MP2 Approximations in Double-Hybrid DFT

The unfavorable scaling (N5) of the conventional second-order Møller-Plesset theory (MP2) typically prevents the application of double-hybrid (DH) density functionals to large systems with more than 100 atoms. A prominent approach to reduce the computational demand of electron correlation methods is the domain-based local pair natural orbital (DLPNO) approximation that is successfully used in the framework of DLPNO-CCSD(T). Its extension to MP2 [Pinski P.; Riplinger, C.; Valeev, E. F.; Neese, F. J. Chem. Phys. 2015, 143, 034108.] paved the way for DLPNO-based DH (DLPNO-DH) methods. In this work, we assess the accuracy of the DLPNO-DH approximation compared to conventional DHs on a large number of 7925 data points for thermochemistry and 239 data points for structural features, including main-group and transition-metal systems. It is shown that DLPNO-DH-DFT can be applied successfully to perform energy calculations and geometry optimizations for large molecules at a drastically reduced computational cost. Furthermore, PNO space extrapolation is shown to be applicable, similar to its DLPNO-CCSD(T) counterpart, to reduce the remaining error.

CHNO - Formylnitrene, Cyanic, Isocyanic, Fulminic, and Isofulminic Acids and their Interrelationships at DFT and CASPT2 Levels of Theory

Fulminic and cyanic acids played a decisive role in the conception of isomerism 200 years ago. Cyanic (HOCN), isocyanic (HNCO), and fulminic (HCNO) acids have been detected in several interstellar sources, but isofulminic acid (HONC) is little known. Here we examine the interrelationships between the four acids and formylnitrene, HC(O)N, at the CASPT2 and three DFT levels. Formylnitrene has a triplet ground state, T0, a closed shell singlet (CSS), S0, and an open-shell singlet (OSS), S1, lying ∼7 and 27 kcal/mol above T0, respectively. The CSS is weakly stabilized by a 12 kcal/mol bond between the N and the O atoms. A conical intersection 12 kcal/mol above T0 permits easy T0-S0 interchange. Formyl azide and formylnitrene (T0 and S0) are isomerized thermally to HNCO. HOCN is best obtained via dissociation of the nitrene (or of HNCO) to H• + NCO• radicals ∼46 kcal/mol above the T0 nitrene. Isofulminic acid, HONC, isomerizes readily to cyanic acid, HOCN, in thermal and photochemical reactions. Fulminic acid, HCNO, can isomerize to HNCO via CSS formylnitrene. Easy tautomerization prevents the preparation of HOCN in quantity. The barrier to isomerization is strongly reduced in small hydrogen-bonded aggregates so that trace amounts of HOCN can exist in equilibrium with HNCO.

Stereo-electronic factors influencing the stability of hydroperoxyalkyl radicals: transferability of chemical trends across hydrocarbons and ab initio methods

The hydroperoxyalkyl radicals (˙QOOH) are known to play a significant role in combustion and tropospheric processes, yet their direct spectroscopic detection remains challenging. In this study, we investigate molecular stereo-electronic effects influencing the kinetic and thermodynamic stability of a ˙QOOH along its formation path from the precursor, alkylperoxyl radical (ROO˙), and the depletion path resulting in the formation of cyclic ether + ˙OH. We focus on reactive intermediates encountered in the oxidation of acyclic hydrocarbon radicals: ethyl, isopropyl, isobutyl, tert-butyl, neopentyl, and their alicyclic counterparts: cyclohexyl, cyclohexenyl, and cyclohexadienyl. We report reaction energies and barriers calculated with the highly accurate method Weizmann-1 (W1) for the channels: ROO˙ ⇌ ˙QOOH, ROO˙ ⇌ alkene + ˙OOH, ˙QOOH ⇌ alkene + ˙OOH, and ˙QOOH ⇌ cyclic ether + ˙OH. Using W1 results as a reference, we have systematically benchmarked the accuracy of popular density functional theory (DFT), composite thermochemistry methods, and an explicitly correlated coupled-cluster method. We ascertain inductive, resonance, and steric effects on the overall stability of ˙QOOH and computationally investigate the possibility of forming more stable species. With new reactions as test cases, we probe the capacity of various ab initio methods to yield quantitative insights on the elementary steps of combustion.

Gas-phase formation of glycolonitrile in the interstellar medium

Our automated reaction discovery program, AutoMeKin, has been utilized to investigate the formation of glycolonitrile (HOCH2CN) in the gas phase under the low temperatures of the interstellar medium (ISM). The feasibility of a proposed pathway depends on the absence of barriers above the energy of reactants and the availability of the suggested precursors in the ISM. Based on these criteria, several radical-radical reactions and a radical-molecule reaction have been identified as viable formation routes in the ISM. Among the radical-radical reactions, OH + CH2CN appears to be the most relevant, considering the energy of the radicals and its ability to produce glycolonitrile in a single step. However, our analysis reveals that this reaction produces hydrogen isocyanide (HNC) and formaldehyde (CH2O), with rate coefficients ranging from (7.3-11.5) × 10-10 cm3 molecule-1 s-1 across the temperature range of 10-150 K. Furthermore, the identification of this remarkably efficient pathway for HNC elimination from glycolonitrile significantly broadens the possibilities for any radical-radical mechanism proposed in our research to be considered as a feasible pathway for the formation of HNC in the ISM. This finding is particularly interesing given the persistently unexplained overabundance of hydrogen isocyanide in the ISM. Among the radical-molecule reactions investigated, the most promising one is OH + CH2CHNH, which forms glycolonitrile and atomic hydrogen with rate coefficients in the range (0.3-6.6) × 10-10 cm3 molecule-1 s-1 within the 10-150 K temperature range. Our calculations indicate that the formation of both hydrogen isocyanide and glycolonitrile is efficient under the harsh conditions of the ISM.

Comprehensive exploration of graphically defined reaction spaces

Existing reaction transition state (TS) databases are comparatively small and lack chemical diversity. Here, this data gap has been addressed using the concept of a graphically-defined model reaction to comprehensively characterize a reaction space associated with C, H, O, and N containing molecules with up to 10 heavy (non-hydrogen) atoms. The resulting dataset is composed of 176,992 organic reactions possessing at least one validated TS, activation energy, heat of reaction, reactant and product geometries, frequencies, and atom-mapping. For 33,032 reactions, more than one TS was discovered by conformational sampling, allowing conformational errors in TS prediction to be assessed. Data is supplied at the GFN2-xTB and B3LYP-D3/TZVP levels of theory. A subset of reactions were recalculated at the CCSD(T)-F12/cc-pVDZ-F12 and ωB97X-D2/def2-TZVP levels to establish relative errors. The resulting collection of reactions and properties are called the Reaction Graph Depth 1 (RGD1) dataset. RGD1 represents the largest and most chemically diverse TS dataset published to date and should find immediate use in developing novel machine learning models for predicting reaction properties.

Benchmark of general-purpose machine learning-based quantum mechanical method AIQM1 on reaction barrier heights

Artificial intelligence-enhanced quantum mechanical method 1 (AIQM1) is a general-purpose method that was shown to achieve high accuracy for many applications with a speed close to its baseline semiempirical quantum mechanical (SQM) method ODM2*. Here, we evaluate the hitherto unknown performance of out-of-the-box AIQM1 without any refitting for reaction barrier heights on eight datasets, including a total of ∼24 thousand reactions. This evaluation shows that AIQM1's accuracy strongly depends on the type of transition state and ranges from excellent for rotation barriers to poor for, e.g., pericyclic reactions. AIQM1 clearly outperforms its baseline ODM2* method and, even more so, a popular universal potential, ANI-1ccx. Overall, however, AIQM1 accuracy largely remains similar to SQM methods (and B3LYP/6-31G* for most reaction types) suggesting that it is desirable to focus on improving AIQM1 performance for barrier heights in the future. We also show that the built-in uncertainty quantification helps in identifying confident predictions. The accuracy of confident AIQM1 predictions is approaching the level of popular density functional theory methods for most reaction types. Encouragingly, AIQM1 is rather robust for transition state optimizations, even for the type of reactions it struggles with the most. Single-point calculations with high-level methods on AIQM1-optimized geometries can be used to significantly improve barrier heights, which cannot be said for its baseline ODM2* method.

Influence of the complete basis set approximation, tight weighted-core, and diffuse functions on the DLPNO-CCSD(T1) atomization energies of neutral H,C,O-compounds

The impact of complete basis set extrapolation schemes (CBS), diffuse functions, and tight weighted-core functions on enthalpies of formation predicted via the DLPNO-CCSD(T1) reduced Feller-Peterson-Dixon approach has been examined for neutral H,C,O-compounds. All tested three-point (TZ/QZ/5Z) extrapolation schemes result in mean unsigned deviation (MUD) below 2 kJ mol^-1 relative to the experiment. The two-point QZ/5Z and TZ/QZ CBS 1 / l max 3 extrapolation schemes are inferior to their inverse power counterpart ( 1 / l max + 1 / 2 4 ) by 1.3 and 4.3 kJ mol^-1 . The CBS extrapolated frozen core atomization energies are insensitive (within 1 kJ mol^-1 ) to augmentation of the basis set with tight weighted core functions. The core-valence correlation effects converge already at triple-ζ, although double-ζ/triple-ζ CBS extrapolation performs better and is recommended. The effect of diffuse function augmentation converges slowly, and cannot be reproduced with double- ζ or triple- ζ calculations as these are plagued with basis set superposition and incompleteness errors.

Molecular Understanding and Practical In Silico Catalyst Design in Computational Organocatalysis and Phase Transfer Catalysis-Challenges and Opportunities

Through the lens of organocatalysis and phase transfer catalysis, we will examine the key components to calculate or predict catalysis-performance metrics, such as turnover frequency and measurement of stereoselectivity, via computational chemistry. The state-of-the-art tools available to calculate potential energy and, consequently, free energy, together with their caveats, will be discussed via examples from the literature. Through various examples from organocatalysis and phase transfer catalysis, we will highlight the challenges related to the mechanism, transition state theory, and solvation involved in translating calculated barriers to the turnover frequency or a metric of stereoselectivity. Examples in the literature that validated their theoretical models will be showcased. Lastly, the relevance and opportunity afforded by machine learning will be discussed.

ωB97X-3c: A composite range-separated hybrid DFT method with a molecule-optimized polarized valence double-ζ basis set

A new composite density functional theory (DFT) method is presented. It is based on ωB97X-V as one of the best-performing density functionals for the GMTKN55 thermochemistry database and completes the family of "3c" methods toward range-separated hybrid DFT. This method is consistently available for all elements up to Rn (Z = 1-86). Its further key ingredients are a polarized valence double-ζ (vDZP) Gaussian basis set, which was fully optimized in molecular DFT calculations, in combination with large-core effective core potentials and a specially adapted D4 dispersion correction. Unlike most existing double-ζ atomic orbital sets, vDZP shows only small basis set superposition errors (BSSEs) and can compete with standard sets of triple-ζ quality. Small residual BSSE effects are efficiently absorbed by the D4 damping scheme, which overall eliminates the need for an explicit treatment or empirical corrections for BSSE. Thorough tests on a variety of thermochemistry benchmark sets show that the new composite method, dubbed ωB97X-3c, is on par with or even outperforms standard hybrid DFT methods in a quadruple-zeta basis set at a small fraction of the computational cost. Particular strengths of this method are the description of non-covalent interactions and barrier heights, for which it is among the best-performing density functionals overall.

Mechanistic views and computational studies on transition-metal-catalyzed reductive coupling reactions

Transition-metal-catalyzed reductive coupling reactions have been considered as a powerful tool to convert two electrophiles into value-added products. Numerous related reports have shown the fascinating potential. Mechanistic studies, especially theoretical studies, can provide important implications for the design of novel reductive coupling reactions. In this review, we summarize the representative advancements in theoretical studies on transition-metal-catalyzed reductive coupling reactions and systematically elaborate the mechanisms for the key steps of reductive coupling reactions. The activation modes of electrophiles and the deep insights of selectivity generation are mechanistically discussed. In addition, the mechanism of the reduction of high-oxidation-state catalysts and further construction of new chemical bonds are also described in detail.

Electrochemical PINOylation of Methylarenes: Improving the Scope and Utility of Benzylic Oxidation through Mediated Electrolysis

A mediated electrosynthetic method has been developed for selective benzylic oxidation of methylarenes. Phthalimide-N-oxyl (PINO) radical generated by proton-coupled electrochemical oxidation of N-hydroxypthalimide serves as a hydrogen atom-transfer (HAT) mediator and as a radical trap for the benzylic radicals generated in situ. This mediated electrolysis method operates at much lower anode potentials relative to direct electrolysis methods for benzylic oxidation initiated by single-electron transfer (SET). A direct comparison of SET and mediated-HAT electrolysis methods with a common set of substrates shows that the HAT reaction exhibits a significantly improved substrate scope and functional group compatibility. The PINOylated products are readily converted into the corresponding benzylic alcohol or benzaldehyde derivative under photochemical conditions, and the synthetic utility of this method is highlighted by the late-stage functionalization of the non-steroidal anti-inflammatory drug celecoxib.

Benefits of Range-Separated Hybrid and Double-Hybrid Functionals for a Large and Diverse Data Set of Reaction Energies and Barrier Heights

To better understand the thermochemical kinetics and mechanism of a specific chemical reaction, an accurate estimation of barrier heights (forward and reverse) and reaction energies is vital. Because of the large size of reactants and transition state structures involved in real-life mechanistic studies (e.g., enzymatically catalyzed reactions), density functional theory remains the workhorse for such calculations. In this paper, we have assessed the performance of 91 density functionals for modeling the reaction energies and barrier heights on a large and chemically diverse data set (BH9) composed of 449 organic chemistry reactions. We have shown that range-separated hybrid functionals perform better than the global hybrids for BH9 barrier heights and reaction energies. Except for the PBE-based range-separated nonempirical double hybrids, range separation of the exchange term helps improve the performance for barrier heights and reaction energies. The 16-parameter Berkeley double hybrid, ωB97M(2), performs remarkably well for both properties. However, our minimally empirical range-separated double hybrid functionals offer marginally better accuracy than ωB97M(2) for BH9 barrier heights and reaction energies.

Azulene-Naphthalene, Naphthalene-Naphthalene, and Azulene-Azulene Rearrangements

The mechanism(s) of thermal rearrangement of azulenes have been enigmatic for several decades. Herein, we have employed density functional theory (DFT) calculations at the M06-2X/6-311+G(d,p) level together with single-point calculations at the CCSD(T) level to assess possible mechanisms of the experimentally observed azulene and naphthalene automerizations. Of the two mechanisms proposed for naphthalene automerization, it is found that the benzofulvene (BF) route is favored over the naphthvalene mechanism by ∼6 kcal/mol and is energetically lower than the norcaradiene-vinylidene mechanism (NVM) for the azulene-naphthalene rearrangement (E_a ∼ 76.5 (74.6) kcal/mol). Moreover, contrary to older reports, we observe that a pathway involving indenylcarbene intermediates is a viable, alternate mechanism. Therefore, the naphthalene automerization is expected to take place during azulene pyrolysis, especially under conditions of low-pressure FVP, where it will be aided by chemical activation. Furthermore, thermal azulene-azulene isomerization is feasible through vinylidene-acetylene-vinylidene (VAV), dehydrotriquinacene (DTQ), and azulvalene (AV) pathways with activation energies lying below that required for the azulene-naphthalene conversion, i.e., the NVM. These results, together with the previously published NVM, provide reasonable explanations for most of the products of the thermal azulene-naphthalene rearrangement.

Tackling an accurate description of molecular reactivity with double-hybrid density functionals

In this Communication, we assess a panel of 18 double-hybrid density functionals for the modeling of the thermochemical and kinetic properties of an extended dataset of 449 organic chemistry reactions belonging to the BH9 database. We show that most of DHs provide a statistically robust performance to model barrier height and reaction energies in reaching the “chemical accuracy.” In particular, we show that nonempirical DHs, such as PBE0-DH and PBE-QIDH, or minimally parameterized alternatives, such as ωB2PLYP and B2K-PLYP, succeed to accurately model both properties in a balanced fashion. We demonstrate, however, that parameterized approaches, such as ωB97X-2 or DSD-like DHs, are more biased to only one of both properties.

Small-Basis Set Density-Functional Theory Methods Corrected with Atom-Centered Potentials

Density functional theory (DFT) is currently the most popular method for modeling noncovalent interactions and thermochemistry. The accurate calculation of noncovalent interaction energies, reaction energies, and barrier heights requires choosing an appropriate functional and, typically, a relatively large basis set. Deficiencies of the density-functional approximation and the use of a limited basis set are the leading sources of error in the calculation of noncovalent and thermochemical properties in molecular systems. In this article, we present three new DFT methods based on the BLYP, M06-2X, and CAM-B3LYP functionals in combination with the 6-31G* basis set and corrected with atom-centered potentials (ACPs). ACPs are one-electron potentials that have the same form as effective-core potentials, except they do not replace any electrons. The ACPs developed in this work are used to generate energy corrections to the underlying DFT/basis-set method such that the errors in predicted chemical properties are minimized while maintaining the low computational cost of the parent methods. ACPs were developed for the elements H, B, C, N, O, F, Si, P, S, and Cl. The ACP parameters were determined using an extensive training set of 118655 data points, mostly of complete basis set coupled-cluster level quality. The target molecular properties for the ACP-corrected methods include noncovalent interaction energies, molecular conformational energies, reaction energies, barrier heights, and bond separation energies. The ACPs were tested first on the training set and then on a validation set of 42567 additional data points. We show that the ACP-corrected methods can predict the target molecular properties with accuracy close to complete basis set wavefunction theory methods, but at a computational cost of double-ζ DFT methods. This makes the new BLYP/6-31G*-ACP, M06-2X/6-31G*-ACP, and CAM-B3LYP/6-31G*-ACP methods uniquely suited to the calculation of noncovalent, thermochemical, and kinetic properties in large molecular systems.

Thermal Rearrangement of Azulenes to Naphthalenes: A Deeper Insight into the Mechanisms

The thermal rearrangement of azulene to naphthalene has been the subject of several experimental and computational studies. Here, we reexamine the proposed mechanisms at the DFT level. The use of different functionals showed that the HF-exchange contribution significantly affects reaction energies and barrier heights. Accordingly, all proposed pathways were investigated with the optimal method, M06-2X/6-311+G(d,p), which confirms the norcaradiene-vinylidene mechanism (A) as the dominant unimolecular route (E_a ≈ 76 kcal/mol) able to account for the major products of pyrolyses using ¹³C- or substituent-labeled azulenes. Moreover, a facile vinylidene-acetylene interconversion will scramble the terminal carbon atoms in the vinylidene. Several other potential intramolecular reaction mechanisms (B-E) are ruled out because of higher activation energies (>84 kcal/mol) and failure to reproduce the results obtained with substituted and ¹³C-labeled azulenes and benzazulenes. These experimental results also demonstrate that the proposed free radical or H atom-induced intermolecular methylene walk and spiran mechanisms cannot be major contributors, especially under flash vacuum pyrolysis conditions.