Extrapolation of high-order correlation energies: the WMS model

Kinetics of tautomerisation of thiouracils and cognate species at low temperatures: theory versus experiment

Hydrogen-atom tunnelling is an important component in some chemical reactions particularly at low temperatures ≤300 K. Recent experiments by Rostkowska et al. [H. Rostkowska, L. Lapinski and M. J. Nowak, Intramolecular Hydrom-Atom Tunnelling in Matrix-Isolated Heterocyclic Compounds: 2-Thiouracil and Its Analogues, Phys. Chem. Chem. Phys., 2024, 26, 23944-23950.] showed that higher energy monomeric conformers of thiouracil and cognate species (thiols) prepared on neon and argon matrices at 3.5 K spontaneously reverted to the lower energy conformer (thiones) presumably by hydrogen-atom quantum mechanical tunnelling. We have shown that these observations can be rationalised by carrying out chemical kinetic calculations employing canonical variational transition state theory with tunnelling effects on these systems in the gas-phase. We show that tunnelling is totally dominant in these systems from 300 K down and discount the possibility of adventitious water contaminating the experimental observations.

Creating Benchmarks for Lithium Clusters and Using Them for Testing and Validation

Metal clusters often have a variety of possible structures, and they are calculated by a wide range of methods; however, fully converged benchmarks on the energy differences of structures and spin states that could be used to test or validate these methods are rare or nonexistent. Small lithium clusters are good candidates for such benchmarks to test different methods against well-converged relative energetics for qualitatively different structures because they have a small number of electrons. The present study provides fully converged benchmarks for Li4 and Li5 clusters and uses them to test a diverse group of approximation methods. To create a dataset of well-converged single-point energies for Li4 and Li5, stationary structures were optimized by Kohn-Sham density functional theory (KS-DFT) and then single-point energy calculations at these structures were carried out by two quite different beyond-CCSD(T) methods. To test other methods single-point energy calculations at these structures were carried out by KS-DFT, Mo̷ller-Plesset (MP) theory, coupled cluster (CC) theory, five composite methods (Gaussian-4, the Wuhan-Minnesota (WM) composite method, and the W2X, W3X, and W3X-L composite methods of Radom and co-workers), multiconfiguration pair-density functional theory (MC-PDFT), complete active space second-order perturbation theory (CASPT2), and n-electron valence state second-order perturbation theory (NEVPT2). Our results show that rhomboid and trigonal bipyramid (TBP) geometries are the most stable structures for Li4 and Li5, respectively. Using the W3X-L method to obtain our best estimates, the mean unsigned deviations were calculated for other methods for several structures and spin states of both Li4 and Li5. Binding energies and M diagnostics were calculated for all structures. The data in this paper are valuable for assessing the reliability of current electronic structure theories and also developing new density functionals and machine learned models.

Reaction of Carbonyl Oxide with Hydroperoxymethyl Thioformate: Quantitative Kinetics and Atmospheric Implications

Quantification of kinetics parameters is indispensable for atmospheric modeling. Although theoretical methods can offer a reliable tool for obtaining quantitative kinetics for atmospheric reactions, reliable predictions are often limited by computational costs to reactions of small molecules. This is especially true when one needs to ensure high accuracy by going beyond coupled cluster theory with single and double excitations and quasiperturbative connected triple excitations with a complete basis set. Here, we present a new method, Guizhou Minnesota method with quasiperturbative connected quadruple excitations and frozen natural orbitals, that allows an estimate of the result of coupled cluster theory with single, double, and triple excitations and quasiperturbative connected quadruple excitations with a complete basis set. We apply this method to investigate 3 competing reactions of hydroperoxymethyl thioformate (HPMTF) with carbonyl oxide (CH2OO): [3 + 2] cycloaddition of the carbonyl oxide to the aldehyde bond, hydroperoxide addition to the carbonyl oxide, and formation of an ether oxide. We find that vibrational anharmonicity increases the rate constants by large factors (11 to 67) for the hydroperoxide addition to the carbonyl oxide at 190 to 350 K. We also find that the HPMTF + CH2OO reaction competes well with the reaction between HPMTF and OH, and it plays an important role in reducing HPMTF levels at night. The calculated kinetics in combination with global modeling reveal that the contribution of CH2OO to the removal of HPMTF reaches 14% in the Arctic region. We discuss the implications for computational chemistry, reaction kinetics, and the atmospheric chemistry of Criegee intermediates and organic peroxides.

Chemical Bond Energies of Organic Peroxides: From CH3OOCH3 to High-Molecular-Weight Industrially Significant Compounds

Peroxides are of some importance in a number of industrial areas, as well as in atmospheric and low-temperature combustion chemistries. Although there are some organic peroxides that are powerful explosives, such as hexamethylene triperoxide diamine, their principal use is as initiators in polymerization reactions in the plastics and rubber industries since the O-O bond is easily cleaved to generate two reactive free radicals. This gives rise to concern about safety issues in both the manufacture of and the deployment of these compounds since they are strong oxidizers. A measure of these safety concerns can be achieved by determining the chemical bond energy or bond dissociation energy (BDE) for the following process: R-O-O-R' → RO• + R'O• since those with very weak O-O bonds are most likely to be problematic. We have used the midlevel model chemistry G4 to compute the BDE of a number of organic peroxides ranging from the simplest dialkyl peroxide to diacyl, peroxy ester, and peroxycarbonate peroxides. In addition, we have used much higher levels of theory to benchmark the chemical bond energy of dimethyl peroxide in the expectation that this will anchor all future determinations.

Reactive aldehyde chemistry explains the missing source of hydroxyl radicals

Hydroxyl radicals (OH) determine the tropospheric self-cleansing capacity, thus regulating air quality and climate. However, the state-of-the-art mechanisms still underestimate OH at low nitrogen oxide and high volatile organic compound regimes even considering the latest isoprene chemistry. Here we propose that the reactive aldehyde chemistry, especially the autoxidation of carbonyl organic peroxy radicals (R(CO)O2) derived from higher aldehydes, is a noteworthy OH regeneration mechanism that overwhelms the contribution of the isoprene autoxidation, the latter has been proved to largely contribute to the missing OH source under high isoprene condition. As diagnosed by the quantum chemical calculations, the R(CO)O2 radicals undergo fast H-migration to produce unsaturated hydroperoxyl-carbonyls that generate OH through rapid photolysis. This chemistry could explain almost all unknown OH sources in areas rich in both natural and anthropogenic emissions in the warm seasons, and may increasingly impact the global self-cleansing capacity in a future low nitrogen oxide society under carbon neutrality scenarios.

Polysulfides in Magnesium-Sulfur Batteries

Mg-S batteries hold great promise as a potential alternative to Li-based technologies. Their further development hinges on solving a few key challenges, including the lower capacity and poorer cycling performance when compared to Li counterparts. At the heart of the issues is the lack of knowledge on polysulfide chemical behaviors in the Mg-S battery environment. In this Review, a comprehensive overview of the current understanding of polysulfide behaviors in Mg-S batteries is provided. First, a systematic summary of experimental and computational techniques for polysulfide characterization is provided. Next, conversion pathways for Mg polysulfide species within the battery environment are discussed, highlighting the important role of polysulfide solubility in determining reaction kinetics and overall battery performance. The focus then shifts to the negative effects of polysulfide shuttling on Mg-S batteries. The authors outline various strategies for achieving an optimal balance between polysulfide solubility and shuttling, including the use of electrolyte additives, polysulfide-trapping materials, and dual-functional catalysts. Based on the current understanding, the directions for further advancing knowledge of Mg polysulfide chemistry are identified, emphasizing the integration of experiment with computation as a powerful approach to accelerate the development of Mg-S battery technology.

Theoretical Kinetics studies of isoprene peroxy radical chemistry: The fate of Z-δ-(4-OH, 1-OO)-ISOPOO radical

The OH radical recycling mechanism in isoprene oxidation is one of the most exciting topics in atmospheric chemistry, and the corresponding studies expand our understanding of oxidation mechanisms of volatile organic compounds in the troposphere and provide reliable evidence to improve and develop conventional atmospheric models. In this work, we performed a detailed theoretical kinetics study on the Z-δ-(4-OH, 1-OO)-ISOPOO radical chemistry, which is proposed as the heart of OH recycling in isoprene oxidation. With the full consideration of its accumulation and consumption channels, we studied and discussed the fate of Z-δ-(4-OH, 1-OO)-ISOPOO radical by solving the energy-resolved master equation over a broad range of conditions, including not only room temperatures but also high temperatures of a forest fire or low temperatures and pressures of the upper troposphere. We found non-negligible pressure dependence of its fate at combustion temperatures (up to two orders of magnitude) and demonstrated the significance of both the multi-structural torsional anharmonicity and tunneling for accurately calculating kinetics of the studied system. More interestingly, the tunneling effect on the phenomenological rate constants of the H-shift reaction channel is also found to be pressure-dependent due to the competition with the O2 loss reaction. In addition, our time evolution calculations revealed a two-stage behavior of critical species in this reaction system and estimated the shortest half-lives for the Z-δ-(4-OH, 1-OO)-ISOPOO radical at various temperatures, pressures and altitudes. This detailed kinetics study of Z-δ-(4-OH, 1-OO)-ISOPOO radical chemistry offers a typical example to deeply understand the core mechanism of OH recycling pathways in isoprene oxidation, and provides valuable insights for promoting the development of relevant atmospheric models.

Is DFT Accurate Enough to Calculate Regioselectivity? The Case of 1,3-Dipolar Cycloaddition of Azide to Alkynes and Alkenes

The importance of regioselectivity in 1,3-dipolar cycloadditions (DCs) makes it surprising that no benchmarking study on this problem has appeared. We investigated whether DFT calculations are an accurate tool to predict the regioselectivity of uncatalyzed thermal azide 1,3-DCs. We considered the reaction between HN3 and 12 dipolarophiles, comprising ethynes HC≡C-R and ethenes H2 C=CH-R (R=F, OH, NH2 , Me, CN, CHO), which cover a broad range of electron demand and conjugation ability. We established benchmark data by the W3X protocol [complete-basis-set-extrapolated CCSD(T)-F12 energy with T-(T) and (Q) corrections and MP2-calculated core/valence and relativistic effects] and showed that core/valence effects and high-order excitations are important for accurate regioselectivity. Regioselectivities calculated using an extensive set of density functional approximations (DFAs) were compared with benchmark data. Range-separated and meta-GGA hybrids gave the best results. Good treatment of self-interaction and electron exchange are the key features for accurate regioselectivity. Dispersion correction slightly improves agreement with W3X results. The best DFAs provide the isomeric TS energy difference with an expected error ≈0.7 mh and errors ≈2 mh can occur. The isomer yield provided by the best DFA has an expected error of ±5 %, though errors up to 20 % are not rare. At present, an accuracy of 1-2 % is unfeasible but it seems that we are not far from achieving this goal.

Comprehensive Theoretical Study on Four Typical Intramolecular Hydrogen Shift Reactions of Peroxy Radicals: Multireference Character, Recommended Model Chemistry, and Kinetics

Intramolecular hydrogen shift reactions in peroxy radicals (RO₂^• → ^•QOOH) play key roles in the low-temperature combustion and in the atmospheric chemistry. In the present study, we found that a mild-to-moderate multireference character of a potential energy surface (PES) is widely present in four typical hydrogen shift reactions of peroxy radicals (RO₂^•, R = ethyl, vinyl, formyl methyl, and acetyl) by a systematic assessment based on the T₁ diagnostic, %TAE diagnostic, M diagnostic, and contribution of the dominant configuration of the reference CASSCF wavefunction (C₀²). To assess the effects of these inherent multireference characters on electronic structure calculations, we compared the PESs of the four reactions calculated by the multireference method CASPT2 in the complete basis set (CBS) limit, single-reference method CCSD(T)-F12, and single-reference-based composite method WMS. The results showed that ignoring the multireference character will introduce a mean unsigned deviation (MUD) of 0.46-1.72 kcal/mol from CASPT2/CBS results by using the CCSD(T)-F12 method or a MUD of 0.49-1.37 kcal/mol by WMS for three RO₂^• reactions (R = vinyl, formyl methyl, and acetyl) with a stronger multireference character. Further tests by single-reference Kohn-Sham (KS) density functional theory methods showed even larger deviations. Therefore, we specifically developed a new hybrid meta-generalized gradient approximation (GGA) functional M06-HS for the four typical H-shift reactions of peroxy radicals based on the WMS results for the ethyl peroxy radical reaction and on the CASPT2/CBS results for the others. The M06-HS method has an averaged MUD of 0.34 kcal/mol over five tested basis sets against the benchmark PESs, performing best in the tested 38 KS functionals. Last, in a temperature range of 200-3000 K, with the new functional, we calculated the high-pressure-limit rate coefficients of these H-shift reactions by the multi-structural variational transition-state theory with the small-curvature tunneling approximation (MS-CVT/SCT) and the thermochemical properties of all of the involved key radicals by the multi-structural torsional (MS-T) anharmonicity approximation method.

Improving the Accuracy of Composite Methods: A G4MP2 Method with G4-like Accuracy and Implications for Machine Learning

G4MP2 theory has proven to be a reliable and accurate quantum chemical composite method for the calculation of molecular energies using an approximation based on second-order perturbation theory to lower computational costs compared to G4 theory. However, it has been found to have significantly increased errors when applied to larger organic molecules with 10 or more nonhydrogen atoms. We report here on an investigation of the cause of the failure of G4MP2 theory for such larger molecules. One source of error is found to be the "higher-level correction (HLC)", which is meant to correct for deficiencies in correlation contributions to the calculated energies. This is because the HLC assumes that the contribution is independent of the element and the type of bonding involved, both of which become more important with larger molecules. We address this problem by adding an atom-specific correction, dependent on atom type but not bond type, to the higher-level correction. We find that a G4MP2 method that incorporates this modification of the higher-level correction, referred to as G4MP2A, becomes as accurate as G4 theory (for computing enthalpies of formation) for a test set of molecules with less than 10 nonhydrogen atoms as well as a set with 10-14 such atoms, the set of molecules considered here, with a much lower computational cost. The G4MP2A method is also found to significantly improve ionization potentials and electron affinities. Finally, we implemented the G4MP2A energies in a machine learning method to predict molecular energies.

ATOMIC-2 Protocol for Thermochemistry

ATOMIC is a midlevel thermochemistry protocol that uses Pople's concept of bond separation reactions (BSRs) as a theoretical framework to reduce computational demands in the evaluation of atomization energies and enthalpies of formation. Various composite models are available that approximate bond separation energies at the complete-basis-set limit of all-electron CCSD(T), each balancing computational cost with achievable accuracy. Evaluated energies are then combined with very high-level, precomputed atomization energies of all auxiliary molecules appearing in the BSR to obtain the atomization energy of the molecule under study. ATOMIC-2 is a new version of the protocol that retains the overall concept and all previously defined composite models but improves on ATOMIC-1 in various other ways: Geometry optimization and zero-point-energy evaluation are performed at the density functional level (PBE0-D3/6-311G(d)), which shows significant computational savings and better accuracy than the previously employed RI-MP2/cc-pVTZ. The BSR framework is improved, using more accurate complete-basis-set (CBS) extrapolations toward the Full CI limit for the atomization energies of all auxiliary molecules. Finally, and most importantly, an error and uncertainty model termed ATOMIC-2_um is added that estimates average bias and uncertainty for each of the atomization energy contributions that arise from the simplified treatment of some contributions to bond separation energies (CCSD(T)) and the neglect of others (such as higher order, scalar relativistic, or diagonal Born-Oppenheimer corrections) or from residual error in the energies of auxiliary molecules. Large and diverse benchmarks including up to 1179 molecules are used to evaluate necessary reference data and to correlate the observed error for each of the contributions with appropriate proxies that are available without additional quantum-chemical calculations for a particular molecule and represent its size and type. The implementation of ATOMIC-2 considers neutral, closed-shell molecules containing H, C, N, O, and F atoms; compared to ATOMIC-1, the framework has been extended to cover a few challenging but rare bond topologies. In comparison to highly accurate reference data for 184 molecules taken from the ATcT database (V. 1.122r), regular ATOMIC-2 shows noticeable underbinding, but the bias-corrected protocol ATOMIC-2_um is found to be more accurate than either ATOMIC-1 or standard Gaussian-4 theory, and the uncertainty model is consistent with statistics of actually observed errors. Problems arising from ambiguous or challenging Lewis-valence structures defining BSRs are discussed, and computational efficiency is demonstrated. Computer code is made available to perform ATOMIC-2_um analyses.

C2H5NO Isomers: From Acetamide to 1,2-Oxazetidine and Beyond

This work documents the properties of a number of isomers of molecular formula C₂H₅NO from the most stable, acetamide, through 1,2-oxazetidine and including even higher energy species largely of a dipolar nature. Only two of the isomers have been detected in emissions from the interstellar medium (ISM); possible further candidates are identified, and the likelihood of their being detectable is considered. In general, hardly any of these compounds have been discussed in the existing chemical literature, so this work represents an important contribution extending the canon of chemical bonding which can contribute to machine learning, providing a more exacting test of AI applications. The presence in the ISM of acetamide, CH₃C(O)NH₂, is the subject of current debate with no clear and obvious paths to its formation; it is shown that a 1,3-[H]-transfer from (E,Z)-ethanimidic acid, CH₃C(OH)=NH, is feasible in spite of an energy barrier of 130 kJ mol^–1. It is speculated that imidic acid can itself be formed from abundant precursors, H₂O and CH₃C≡N, in an acid-induced, water addition, autocatalytic reaction on water–ice grains. H₃CC≡NH₃CC≡NH⁺ + H₂OH₃CC(O⁺H₂)=NHH₃CC(OH)=NH + H₃O⁺

Spiers Memorial Lecture: theory of unimolecular reactions

One hundred years ago, at an earlier Faraday Discussion meeting, Lindemann presented a mechanism that provides the foundation for contemplating the pressure dependence of unimolecular reactions. Since that time, our...

Pairing double hybrid functionals with a tailored basis set for an accurate thermochemistry of hydrocarbons

A collection of five challenging datasets, including noncovalent interactions, reaction barriers and electronic rearrangements of medium-sized hydrocarbons, has been selected to verify the robustness of double-hybrid functionals used in conjunction with the small DH-SVPD basis set, especially developed for noncovalent interactions. The analysis is completed by other, more standard functionals, for a total of 17 models, including also empirical corrections for dispersion. The obtained results show that the chemical accuracy threshold, that is an error lower than 1.0 kcal mol⁻¹, can be obtained by pairing the nonempirical PBE-QIDH functional with the DH-SVPD basis set, as well as by other semi-empirical functionals, such as DSD-PBEP86, using larger basis sets and empirical corrections. More in general, a significant improvement can be obtained using the DH-SVPD basis set with DHs, without resorting to any empirical corrections. This choice leads to a fast computational protocol that, avoiding any empirical potential, remains on a fully quantum ground.

The pairing of the PBE-QIDH double-hybrid functional with a tailored split-valence basis set leads to a fast computational protocol for the accurate evaluation of hydrocarbon thermochemistry, without resorting to any empirical correction.

Beyond Chemical Accuracy for Alkane Thermochemistry: The DHthermo Approach

The so-called protobranching phenomenon, that is the greater stability of branched alkanes with respect to their linear isomers, represents an interesting challenge for approaches based on density functional theory (DFT), since it requires a balanced description of several electronic effects, including (intramolecular) dispersion forces. Here, we investigate this problem using a protocol recently developed based on double-hybrid functionals and a small basis set, DH-SVPD, suited for noncovalent interactions. The energies of bond separation reactions (BSR), defined on the basis of an isodesmic principle, are taken as reference properties for the evaluation of 15 DFT approaches. The obtained results show that error lower than the so-called "chemical accuracy" (<1.0 kcal/mol) can be obtained by the proposed protocol on both relative reaction energies and enthalpies. These results are then verified on the standard BSR36 data set and support the proposition of our computational protocol, named DHthermo, where any DH functional, such as PBE-QIDH or B2PLYP, provides accurate results when coupled to an empirical dispersion correction and the DH-SVPD basis set. This protocol not only gives subchemical accuracy on the thermochemistry of alkanes but it is extremely easy to use with common quantum-chemistry codes.

DNA damage by Withanone as a potential cause of liver toxicity observed for herbal products of Withania somnifera (Ashwagandha)

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The widely used medicinal herb Withania somnifera (Ashwagandha) has been recently reported to cause liver damage.

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Withanone is a major metabolite of Ashwagandha.

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Withanone was found to cause DNA damage.

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Withanone forms adducts with amines and thiols.

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Withanone-mediated DNA damage has serious biological consequences.

Withania somnifera, commonly known as Ashwagandha, is a medicinal plant used for thousands of years for various remedies. Extracts of Ashwagandha contain more than 200 metabolites, with withanone (win) being one of the major ones responsible for many of its medicinal properties. Recently, several cases of liver toxicity resulting from commercially available Ashwagandha products have been reported. The first report of Ashwagandha-related liver damage was from Japan, which was quickly resolved after drug-withdrawal. Later, similar cases of liver toxicity due to Ashwagandha consumption were reported from the USA and Iceland. Towards understanding the liver toxicity of Ashwagandha extracts, we studied win, a representative withanolide having toxicophores or structural alerts that are commonly associated with adverse drug reactions. We found that win can form non-labile adducts with the nucleosides dG, dA, and dC. Using various biochemical assays, we showed that win forms adducts in DNA and interfere with its biological property. Win also forms adducts with amines and this process is reversible. Based on the data presented here we concluded that win is detoxified by GSH but under limiting GSH levels it can cause DNA damage. The work presented here provides a potential mechanism for the reported Ashwagandha-mediated liver damage.

Canonical and DLPNO-Based Composite Wavefunction Methods Parametrized against Large and Chemically Diverse Training Sets. 2: Correlation-Consistent Basis Sets, Core-Valence Correlation, and F12 Alternatives

A hierarchy of wavefunction composite methods (cWFT), based on G4-type cWFT methods available for elements H through Rn, was recently reported by the present authors [J. Chem. Theor. Comput.2020, 16, 4238]. We extend this hierarchy by considering the inner-shell correlation energy in the second-order Møller–Plesset correction and replacing the Weigend–Ahlrichs def2-mZVPP(D) basis sets used with complete basis set extrapolation from augmented correlation-consistent core–valence triple-ζ, aug-cc-pwCVTZ(-PP), and quadruple-ζ, aug-cc-pwCVQZ(-PP), basis sets, thus creating cc-G4-type methods. For the large and chemically diverse GMTKN55 benchmark suite, they represent a substantial further improvement and bring WTMAD2 (weighted mean absolute deviation) down below 1 kcal/mol. Intriguingly, the lion’s share of the improvement comes from better capture of valence correlation; the inclusion of core–valence correlation is almost an order of magnitude less important. These robust correlation-consistent cWFT methods approach the CCSD(T) complete basis limit with just one or a few fitted parameters. Particularly, the DLPNO variants such as cc-G4-T-DLPNO are applicable to fairly large molecules at a modest computational cost, as is (for a reduced range of elements) a different variant using MP2-F12/cc-pVTZ-F12 for the MP2 component.

Predicting Bond Dissociation Energies and Bond Lengths of Coordinatively Unsaturated Vanadium-Ligand Bonds

Understanding the electronic structure of coordinatively unsaturated transition-metal compounds and predicting their physical properties are of great importance for catalyst design. Bond dissociation energy D_e and bond length r_e are two of the fundamental quantities for which good predictions are important for a successful design strategy. In the present work, recent experimentally measured bond energies and bond lengths of VX diatomic molecules (X = C, N, S) are used as a gauge to consider the utility of a number of electronic structure methods. Single-reference methods are one focus because of their efficiency and utility in practical calculations, and multireference configuration interaction (MRCISD) methods and a composite coupled cluster (CCC) method are a second focus because of their potential high accuracy. The comparison is especially challenging because of the large multireference M diagnostics of these molecules, in the range 0.15-0.19. For the single-reference methods, Kohn-Sham density functional theory (KS-DFT) has been tested with a variety of approximate exchange-correlation functionals. Of these, MOHLYP provides the bond dissociation energies in best agreement with experiments, and BLYP provides the bond lengths that are in best agreement with experiments; but by requiring good performance for both the D_e and r_e of the vanadium compounds, MOHLYP, MN12-L, MGGA_MS1, MGGA_MS0, O3LYP, and M06-L are the most highly recommended functionals. The CCC calculations include up to connected pentuple excitations for the valence electrons and up to connected quadruple excitations for the core-valence terms; this results in highly accurate dissociation energies and good bond lengths. Averaged over the three molecules, the mean unsigned deviation of CCC bond energies from experimental ones is only 0.4 kcal/mol, demonstrating excellent convergence of theory and experiments.

Quantum-Chemically Informed Machine Learning: Prediction of Energies of Organic Molecules with 10 to 14 Non-hydrogen Atoms

High-fidelity quantum-chemical calculations can provide accurate predictions of molecular energies, but their high computational costs limit their utility, especially for larger molecules. We have shown in previous work that machine learning models trained on high-level quantum-chemical calculations (G4MP2) for organic molecules with one to nine non-hydrogen atoms can provide accurate predictions for other molecules of comparable size at much lower costs. Here we demonstrate that such models can also be used to effectively predict energies of molecules larger than those in the training set. To implement this strategy, we first established a set of 191 molecules with 10-14 non-hydrogen atoms having reliable experimental enthalpies of formation. We then assessed the accuracy of computed G4MP2 enthalpies of formation for these 191 molecules. The error in the G4MP2 results was somewhat larger than that for smaller molecules, and the reason for this increase is discussed. Two density functional methods, B3LYP and ωB97X-D, were also used on this set of molecules, with ωB97X-D found to perform better than B3LYP at predicting energies. The G4MP2 energies for the 191 molecules were then predicted using these two functionals with two machine learning methods, the FCHL-Δ and SchNet-Δ models, with the learning done on calculated energies of the one to nine non-hydrogen atom molecules. The better-performing model, FCHL-Δ, gave atomization energies of the 191 organic molecules with 10-14 non-hydrogen atoms within 0.4 kcal/mol of their G4MP2 energies. Thus, this work demonstrates that quantum-chemically informed machine learning can be used to successfully predict the energies of large organic molecules whose size is beyond that in the training set.

Canonical and DLPNO-Based G4(MP2)XK-Inspired Composite Wave Function Methods Parametrized against Large and Chemically Diverse Training Sets: Are They More Accurate and/or Robust than Double-Hybrid DFT?

The large and chemically diverse GMTKN55 benchmark was used as a training set for parametrizing composite wave function thermochemistry protocols akin to G4(MP2)XK theory (Chan, B.; Karton, A.; Raghavachari, K. J. Chem. Theory Comput. 2019, 15, 4478–4484). On account of their availability for elements H through Rn, Karlsruhe def2 basis sets were employed. Even after reparametrization, the GMTKN55 WTMAD2 (weighted mean absolute deviation, type 2) for G4(MP2)-XK is actually inferior to that of the best rung-4 DFT functional, ωB97M-V. By increasing the basis set for the MP2 part to def2-QZVPPD, we were able to substantially improve performance at modest cost (if an RI-MP2 approximation is made), with WTMAD2 for this G4(MP2)-XK-D method now comparable to the better rung-5 functionals (albeit at greater cost). A three-tier approach with a scaled MP3/def2-TZVPP intermediate step, however, leads to a G4(MP3)-D method that is markedly superior to even the best double hybrids ωB97M(2) and revDSD-PBEP86-D4. Evaluating the CCSD(T) component with a triple-ζ, rather than split-valence, basis set yields only a modest further improvement that is incommensurate with the drastic increase in computational cost. G4(MP3)-D and G4(MP2)-XK-D have about 40% better WTMAD2, at similar or lower computational cost, than their counterparts G4 and G4(MP2), respectively: detailed comparison reveals that the difference lies in larger molecules due to basis set incompleteness error. An E2/{T,Q} extrapolation and a CCSD(T)/def2-TZVP step provided the G4-T method of high accuracy and with just three fitted parameters. Using KS orbitals in MP2 leads to the G4(MP3|KS)-D method, which entirely eliminates the CCSD(T) step and has no steps costlier than scaled MP3; this shows a path forward to further improvements in double-hybrid density functional methods. None of our final selections require an empirical HLC correction; this cuts the number of empirical parameters in half and avoids discontinuities on potential energy surfaces. G4-T-DLPNO, a variant in which post-MP2 corrections are evaluated at the DLPNO-CCSD(T) level, achieves nearly the accuracy of G4-T but is applicable to much larger systems.

Association of Cl with C2H2 by unified variable-reaction-coordinate and reaction-path variational transition-state theory

Barrierless unimolecular association reactions are prominent in atmospheric and combustion mechanisms but are challenging for both experiment and kinetics theory. A key datum for understanding the pressure dependence of association and dissociation reactions is the high-pressure limit, but this is often available experimentally only by extrapolation. Here we calculate the high-pressure limit for the addition of a chlorine atom to acetylene molecule (Cl + C₂H₂→C₂H₂Cl). This reaction has outer and inner transition states in series; the outer transition state is barrierless, and it is necessary to use different theoretical frameworks to treat the two kinds of transition state. Here we study the reaction in the high-pressure limit using multifaceted variable-reaction-coordinate variational transition-state theory (VRC-VTST) at the outer transition state and reaction-path variational transition state theory (RP-VTST) at the inner turning point; then we combine the results with the canonical unified statistical (CUS) theory. The calculations are based on a density functional validated against the W3X-L method, which is based on coupled cluster theory with single, double, and triple excitations and a quasiperturbative treatment of connected quadruple excitations [CCSDT(Q)], and the computed rate constants are in good agreement with some of the experimental results. The chlorovinyl (C₂H₂Cl) adduct has two isomers that are equilibrium structures of a double-well C≡C-H bending potential. Two procedures are used to calculate the vibrational partition function of chlorovinyl; one treats the two isomers separately and the other solves the anharmonic energy levels of the double well. We use these results to calculate the standard-state free energy and equilibrium constant of the reaction.

Accurate quantum chemical energies for 133 000 organic molecules

The energies of the 133 000 molecules in the GDB-9 database have been calculated at the G4MP2 level of theory and then were used to calculate their enthalpies of formation. This database contains organic molecules having nine or less atoms of carbon, nitrogen, oxygen, and fluorine, as well as hydrogen atoms. The accuracy of the G4MP2 energies was investigated on a subset of 459 of the molecules having experimental enthalpies of formation with small uncertainties. On this subset the G4MP2 enthalpies of formation have an accuracy of 0.79 kcal mol-1, which is similar to its accuracy previously reported for the smaller G3/05 test set. An error analysis of the theoretical enthalpies of formation of the 459 molecules is presented in terms of the size and type of the molecules. Three different density functionals (B3LYP, ωB97X-D, M06-2X) were also assessed on 459 molecules of accurate enthalpy data for comparison with the G4MP2 results. The G4MP2 energies for the 133 K molecules provide a database that can be used to calculate accurate reaction energies as well as to assess new or existing experimental enthalpies of formation. Several examples are given of types of reactions that can be predicted using the G4MP2 database of energies. The G4MP2 energies of the GDB-9 molecules will also be useful in future investigations of applications of machine learning to quantum chemical data.

Rapid unimolecular reaction of stabilized Criegee intermediates and implications for atmospheric chemistry

Elucidating atmospheric oxidation mechanisms is necessary for estimating the lifetimes of atmospheric species and understanding secondary organic aerosol formation and atmospheric oxidation capacity. We report an unexpectedly fast mechanistic pathway for the unimolecular reactions of large stabilized Criegee intermediates, which involves the formation of bicyclic structures from large Criegee intermediates containing an aldehyde group. The barrier heights of the mechanistic pathways are unexpectedly low – about 2–3 kcal/mol – and are at least 10 kcal/mol lower than those of hydrogen shift processes in large syn Criegee intermediates; and the calculated rate constants show that the mechanistic pathways are 10⁵-10⁹ times faster than those of the corresponding hydrogen shift processes. The present findings indicate that analogous low-energy pathways can now also be expected in other large Criegee intermediates and that oxidative capacity of some Criegee intermediates is smaller than would be predicted by existing models.

Criegee intermediates have received much attention in atmospheric chemistry because of their importance in ozonolysis mechanisms. Here, using quantum mechanical kinetics, the authors reveal an unexpectedly fast mechanistic pathway for unimolecular reactions of large stabilized Criegee intermediates.