A set of standard enthalpies of formation for benchmarking, calibration, and parametrization of electronic structure methods

Implications for the Hydrogenation of Propyne and Propene with Parahydrogen due to the in situ Transformation of Rh2C to Rh0/C

NMR spectroscopy studies using parahydrogen-induced polarization have previously established the existence of the pairwise hydrogen addition route in the hydrogenation of unsaturated hydrocarbons over heterogeneous catalysts, including those based on rhodium (Rh0). This pathway requires the incorporation of both hydrogen atoms from one hydrogen molecule to the same product molecule. However, the underlying mechanism for such pairwise hydrogen addition must be better understood. The involvement of carbon, either in the form of carbonaceous deposits on the surface of a catalyst or as a metal carbide phase, is known to modify catalytic properties significantly and thus could also affect the pairwise hydrogen addition route. Here, we explored carbon's role by studying the hydrogenation of propene and propyne with parahydrogen on a Rh2C catalyst and comparing the results with those for a Rh0/C catalyst obtained from Rh2C via H2 pretreatment. While the catalysts Rh2C and Rh0/C differ notably in the rate of conversion of parahydrogen to normal hydrogen as well as in terms of hydrogenation activity, our findings suggest that the carbide phase does not play a significant role in the pairwise H2 addition route on rhodium catalysts.

Toward Accurate Quantum Mechanical Thermochemistry: (1) Extensible Implementation and Comparison of Bond Additivity Corrections and Isodesmic Reactions

Obtaining accurate enthalpies of formation of chemical species, ΔHf, often requires empirical corrections that connect the results of quantum mechanical (QM) calculations with the experimental enthalpies of elements in their standard state. One approach is to use atomization energy corrections followed by bond additivity corrections (BACs), such as those defined by Petersson et al. or Anantharaman and Melius. Another approach is to utilize isodesmic reactions (IDRs) as shown by Buerger et al. We implement both approaches in Arkane, an open-source software that can calculate species thermochemistry using results from various QM software packages. In this work, we collect 421 reference species from the literature to derive ΔHf corrections and fit atomization energy corrections and BACs for 15 commonly used model chemistries. We find that both types of BACs yield similar accuracy, although Anantharaman- and Melius-type BACs appear to generalize better. Furthermore, BACs tend to achieve better accuracy than IDRs for commonly used model chemistries, and IDRs can be less robust because of the sensitivity to the chosen reference species and reactions. Overall, Anantharaman- and Melius-type BACs are our recommended approach for achieving accurate QM corrections for enthalpies.

DFT exchange: sharing perspectives on the workhorse of quantum chemistry and materials science

In this paper, the history, present status, and future of density-functional theory (DFT) is informally reviewed and discussed by 70 workers in the field, including molecular scientists, materials scientists, method developers and practitioners. The format of the paper is that of a roundtable discussion, in which the participants express and exchange views on DFT in the form of 302 individual contributions, formulated as responses to a preset list of 26 questions. Supported by a bibliography of 777 entries, the paper represents a broad snapshot of DFT, anno 2022.

A Data Resource for Prediction of Gas-Phase Thermodynamic Properties of Small Molecules

The thermodynamic properties of a substance are key to predicting its behavior in physical and chemical systems. Specifically, the enthalpy of formation and entropy of a substance can be used to predict whether reactions involving that substance will proceed spontaneously under conditions of constant temperature and pressure, and if they do, what the heat and work yield of those reactions would be. Prediction of enthalpy and entropy of substances is therefore of value for substances for which those parameters have not been experimentally measured. We developed a database of 2869 experimental values of enthalpy of formation and 1403 values for entropy for substances composed of stable small molecules, derived from the literature. We developed a model for predicting enthalpy of formation and entropy from semiempirical quantum mechanical calculations of energy and atom counts, and applied the model to a comprehensive database of 16,417 small molecules. The database of small-molecule thermodynamic properties will be useful for predicting the outcome of any process that might involve the generation or destruction of volatile products, such as atmospheric chemistry, volcanism, or waste pyrolysis. Additionally, the collected experimental thermodynamic values will be of value to others developing models to predict enthalpy and entropy.

Assessing Density Functional Theory for Chemically Relevant Open-Shell Transition Metal Reactions

Due to the principle lack of systematic improvement possibilities of density functional theory, careful assessment of the performance of density functional approximations (DFAs) on well-designed benchmark sets, for example, for reaction energies and barrier heights, is crucial. While main-group chemistry is well covered by several available sets, benchmark data for transition metal chemistry is sparse. This is especially the case for larger, chemically relevant molecules. Addressing this issue, we recently introduced the MOR41 benchmark which covers chemically relevant reactions of closed-shell complexes. In this work, we extend these efforts to single-reference open-shell systems and introduce the "reactions of open-shell single-reference transition metal complexes" (ROST61) benchmark set. ROST61 includes accurate coupled-cluster reference values for 61 reaction energies with a mean reaction energy of -42.8 kcal mol^-1. Complexes with 13-93 atoms covering 20 d-block elements are included, but due to the restriction to single-reference open-shell systems, important elements such as iron or platinum could not be taken into account, or only to a small extent. We assess the performance of 31 DFAs in combination with three London dispersion (LD) correction schemes. Further, DFT-based composite methods, MP2, and a few semiempirical quantum chemical methods are evaluated. Consistent with the results for the MOR41 closed-shell benchmark, we find that the ordering of DFAs according to Jacob's ladder is preserved and that adding an LD correction is crucial, clearly improving almost all tested methods. The recently introduced r²SCAN-3c composite method stands out with a remarkable mean absolute deviation (MAD) of only 2.9 kcal mol^-1, which is surpassed only by hybrid DFAs with low amounts of Fock exchange (e.g., 2.3 kcal mol^-1 for TPSS0-D4/def2-QZVPP) and double-hybrid (DH) DFAs but at a significantly higher computational cost. The lowest MAD of only 1.6 kcal mol^-1 is obtained with the DH DFA PWPB95-D4 in the def2-QZVPP basis set approaching the estimated accuracy of the reference method. Overall, the ROST61 set adds important reference data to a sparsely sampled but practically relevant area of chemistry. At this point, it provides valuable orientation for the application and development of new DFAs and electronic structure methods in general.

The origin of the regiospecificity of acrolein dimerization

Acrolein dimerization is a intriguing case since the reaction does not occur to form the electronically preferred regioisomeric adduct. Various explanations have been suggested to rationalize this experimental regioselectivity, however, none of these arguments had been convincing enough. In this work, the hetero Diels-Alder acrolein dimerization was theoretically investigated using DFT and MP2 methods. The influence of nucleophilic/electrophilic interactions and non-covalent interactions (NCI) in the regiospecificity of the reaction were analyzed. Our results show that the NCI at the transition state are the key factor controlling the regiospecificity in this reaction. Besides, we found that the choice of calculation method can have an effect on the prediction of the mechanism in the reaction, as all DFT methods forecast a one-step hetero Diels-Alder acrolein dimerization, while MP2 predicts a stepwise description for the lower energy reaction channel.

Critical benchmarking of popular composite thermochemistry models and density functional approximations on a probabilistically pruned benchmark dataset of formation enthalpies

First-principles calculation of the standard formation enthalpy, ΔH_f° (298 K), in such a large scale as required by chemical space explorations, is amenable only with density functional approximations (DFAs) and certain composite wave function theories (cWFTs). Unfortunately, the accuracies of popular range-separated hybrid, "rung-4" DFAs, and cWFTs that offer the best accuracy-vs-cost trade-off have until now been established only for datasets predominantly comprising small molecules; their transferability to larger systems remains vague. In this study, we present an extended benchmark dataset of ΔH_f° for structurally and electronically diverse molecules. We apply quartile-ranking based on boundary-corrected kernel density estimation to filter outliers and arrive at probabilistically pruned enthalpies of 1694 compounds (PPE1694). For this dataset, we rank the prediction accuracies of G4, G4(MP2), ccCA, CBS-QB3, and 23 popular DFAs using conventional and probabilistic error metrics. We discuss systematic prediction errors and highlight the role an empirical higher-level correction plays in the G4(MP2) model. Furthermore, we comment on uncertainties associated with the reference empirical data for atoms and the systematic errors stemming from these that grow with the molecular size. We believe that these findings will aid in identifying meaningful application domains for quantum thermochemical methods.

Domain-based local pair natural orbital methods within the correlation consistent composite approach

Ab initio composite approaches have been utilized to model and predict main group thermochemistry within 1 kcal mol^-1 , on average, from well-established reliable experiments, primarily for molecules with less than 30 atoms. For molecules of increasing size and complexity, such as biomolecular complexes, composite methodologies have been limited in their application. Therefore, the domain-based local pair natural orbital (DLPNO) methods have been implemented within the correlation consistent composite approach (ccCA) framework, namely DLPNO-ccCA, to reduce the computational cost (disk space, CPU (central processing unit) time, memory) and predict energetic properties such as enthalpies of formation, noncovalent interactions, and conformation energies for organic biomolecular complexes including one of the largest molecules examined via composite strategies, within 1 kcal mol^-1 , after calibration with 119 molecules and a set of linear alkanes. © 2019 Wiley Periodicals, Inc.

THERMOCHEMISTRY OF ORGANIC, HETEROORGANIC, AND INORGANIC MOLECULES AND THEIR FRAGMENTS: "QUANTUM-CHEMICAL CALCULATIONS OF THERMOCHEMICAL PARAMETERS: MOLECULES AND THEIR FRAGMENTS"

Analysis of theoretical enthalpies of formation for about 300 molecules and their fragments (free radicals, biradicals, and ions) was performed to show that the results of semiempirical, DFT, and ab initio methods must be taken with great caution. A brief review of the authors' alternative empirical methodologies for calculation of enthalpies of formation for molecules (enthalpic shift procedure) and free radicals (enthalpies of isodesmic reactions) is given.

Computational tests of quantum chemical models for structures, vibrational frequencies, and heats of formation of molecules with phosphorus and sulfur atoms

The Gaussian-n, complete basis set, and Weizmann-1 quantum chemical models for heats of formation are applied to a set of molecules with relevance to the combustion or pyrolysis of chemical warfare materials. Most of these models generate standard deviations from experiment that are less than 2 kcal/mol. The structures and vibrational frequencies that are generated in the course of these calculations are in good agreement with experimental data. Detailed comparisons with respect to structural types indicate that the present computational models are likely to generate useful data for complex models of combustion and pyrolysis of chemical warfare materials.

QUANTUM-CHEMICAL PREDICTION OF FORMATION ENTHALPY OF CYCLOALKANE

Based on the s-homodesmotic model and the seven different density functional theory (DFT) methods, we calculate standard formation enthalpy of cycloalkane of up to 10 carbons. Among the 21 different combinations, the scheme using MPWB1K method and working reactions when s = 2 achieves the experimental accuracy with RMSD of 8.49 kJ/mol. Also, credibility of this scheme is proved by discussion on influence from different aspects.

Accurate reaction enthalpies and sources of error in DFT thermochemistry for aldol, Mannich, and alpha-aminoxylation reactions

Enthalpies for bond-forming reactions that are subject to organocatalysis have been predicted using the high-accuracy CBS-QB3 model chemistry and six DFT functionals. Reaction enthalpies were decomposed into contributions from changes in bonding and other intramolecular effects via the hierarchy of homodesmotic reactions. The order of the reaction exothermicities (aldol < Mannich approximately alpha-aminoxylation) arises primarily from changes in formal bond types mediated by contributions from secondary intramolecular interactions. In each of these reaction types, methyl substitution at the beta- and gamma-positions stabilizes the products relative to the unsubstituted case. The performance of six DFT functionals (B3LYP, B3PW91, B1B95, MPW1PW91, PBE1PBE, and M06-2X), MP2, and SCS-MP2 has been assessed for the prediction of these reaction enthalpies. Even though the PBE1PBE and M06-2X functionals perform well for the aldol and Mannich reactions, errors roughly double when these functionals are applied to the alpha-aminoxylation reactions. B3PW91 and B1B95, which offer modest accuracy for the aldol and Mannich reactions, yield reliable predictions for the two alpha-aminoxylation reactions. The excellent performance of the M06-2X and PBE1PBE functionals for aldol and Mannich reactions stems from the cancellation of sizable errors arising from inadequate descriptions of the underlying bond transformations and intramolecular interactions. SCS-MP2/cc-pVTZ performs most consistently across these three classes of reactions, although the reaction exothermicities are systematically underestimated by 1-3 kcal mol(-1). Conventional MP2, when paired with the cc-pVTZ basis set, performs somewhat better than SCS-MP2 for some of these reactions, particularly the alpha-aminoxylations. Finally, the merits of benchmarking DFT functionals for the set of simple chemically meaningful transformations underlying all bond-forming reactions are discussed.

Polyfunctional methodology for improved DFT thermochemical predictions

Statistical error distributions for enthalpies of formation as predicted by 18 different density functionals have been analyzed using a test set of 675 molecules. Systematic errors, dependent on the number of valence electrons, have been identified for some functionals. A simple empirical correction makes a significant improvement in the prediction error for these single functionals. Linear combinations of enthalpy estimates from different density functionals are identified that exploit the error correlations among the functionals and allow for further improvements in the accuracy of thermodynamic predictions. A good compromise between accuracy and computational efforts is achieved by the BLUE (best linear unbiased estimator) combination of three functionals, B3LYP, BLYP, and VSXC (polyfunctional 3 or PF3). The PF3 method has a mean absolute deviation (MAD) from experiment of 2.4 kcal/mol on the G3 set of 271 molecules. This can be compared to the MAD of 4.9 kcal/mol for B3LYP and 1.2 kcal/mol for the more costly G3 method. On the larger set of 675 molecules, the MAD for PF3 is 3.0 kcal/mol. Opportunities for further improvements in the accuracy of this method are discussed.

Computational s-Block Thermochemistry with the Correlation Consistent Composite Approach

The correlation consistent composite approach (ccCA) is a model chemistry that has been shown to accurately compute gas-phase enthalpies of formation for alkali and alkaline earth metal oxides and hydroxides (Ho, D. S.; DeYonker, N. J.; Wilson, A. K.; Cundari, T. R. J. Phys. Chem. A 2006, 110, 9767). The ccCA results contrast to more widely used model chemistries where calculated enthalpies of formation for such species can be in error by up to 90 kcal mol-1. In this study, we have applied ccCA to a more general set of 42 s-block molecules and compared the ccCA DeltaHf values to values obtained using the G3 and G3B model chemistries. Included in this training set are water complexes such as Na(H2O)n+ where n = 1 - 4, dimers and trimers of ionic compounds such as (LiCl)2 and (LiCl)3, and the largest ccCA computation to date: Be(acac)2, BeC10H14O4. Problems with the G3 model chemistries seem to be isolated to metal-oxygen bonded systems and Be-containing systems, as G3 and G3B still perform quite well with a 2.7 and 2.6 kcal mol-1 mean absolute deviation (MAD), respectively, for gas-phase enthalpies of formation. The MAD of the ccCA is only 2.2 kcal mol-1 for enthalpies of formation (DeltaHf) for all compounds studied herein. While this MAD is roughly double that found for a ccCA study of >350 main group (i.e., p-block) compounds, it is commensurate with typical experimental uncertainties for s-block complexes. Some molecules where G3/G3B and ccCA computed DeltaHf values deviate significantly from experiment, such as (LiCl)3, NaCN, and MgF, are inviting candidates for new experimental and high-level theoretical studies.

The correlation-consistent composite approach: application to the G3/99 test set

The correlation-consistent composite approach (ccCA), an ab initio composite technique for computing atomic and molecular energies, recently has been shown to successfully reproduce experimental data for a number of systems. The ccCA is applied to the G3/99 test set, which includes 223 enthalpies of formation, 88 adiabatic ionization potentials, 58 adiabatic electron affinities, and 8 adiabatic proton affinities. Improvements on the original ccCA formalism include replacing the small basis set quadratic configuration interaction computation with a coupled cluster computation, employing a correction for scalar relativistic effects, utilizing the tight-d forms of the second-row correlation-consistent basis sets, and revisiting the basis set chosen for geometry optimization. With two types of complete basis set extrapolation of MP2 energies, ccCA results in an almost zero mean deviation for the G3/99 set (with a best value of -0.10 kcal mol(-1)), and a 0.96 kcal mol(-1) mean absolute deviation, which is equivalent to the accuracy of the G3X model chemistry. There are no optimized or empirical parameters included in the computation of ccCA energies. Except for a few systems to be discussed, ccCA performs as well as or better than Gn methods for most systems containing first-row atoms, while for systems containing second-row atoms, ccCA is an improvement over Gn model chemistries.

Computational Methods in Organic Thermochemistry. 2. Enthalpies and Free Energies of Formation for Functional Derivatives of Organic Hydrocarbons

Standard state enthalpies and free energies of formation for nitrogen-, oxygen-, sulfur-, fluorine-, chlorine-, and silicon-containing compounds can be computed with reasonable accuracy (usually within four and often two kJ/mol) using the G3 and G3MP2 model chemistries. In several of the families, compounds with as many as 10 carbon atoms have been computed. Larger errors are found in the free energies of these longer chain molecules which can be reduced by compensating for the presence of multiple conformers having a significant population at 298.15 K. In some instances, those substances showing large deviations are found to have experimental energies that may be erroneous.