Quantum Thermochemistry: Multistructural Method with Torsional Anharmonicity Based on a Coupled Torsional Potential

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.

Efficient Generation of Torsional Energy Profiles by Multifidelity Gaussian Processes for Hindered Rotor Corrections

Accurate thermochemistry computations often require proper treatment of torsional modes. The one-dimensional hindered rotor model has proven to be a computationally efficient solution, given a sufficiently accurate potential energy surface. Methods that provide potential energies at various compromises of uncertainty and computational time demand can be optimally combined within a multifidelity treatment. In this study, we demonstrate how multifidelity modeling leads to (1) smooth interpolation along low-fidelity scan points with uncertainty estimates, (2) inclusion of high-fidelity data that change the energetic order of conformations, and (3) predicting best next-point calculations to extend an initial coarse grid. Our diverse application set comprises molecules, clusters, and transition states of alcohols, ethers, and rings. We discuss limitations for cases in which the low-fidelity computation is highly unreliable. Different features of the potential energy curve affect different quantities. To obtain "optimal" fits, we apply strategies ranging from simple minimization of deviations to developing an acquisition function tailored for statistical thermodynamics. Bayesian prediction of best next calculations can save a substantial amount of computation time for one- and multidimensional hindered rotors.

Theoretical investigation of the OH-initiated atmospheric degradation mechanism of CX2CHX (X = H, F, Cl) by advanced quantum chemical and transition state theory methods

Halogenated olefins are anthropogenic compounds with many industrial applications but at the same time raising many environmental and health concerns. Gas-phase electrophilic addition of the OH radical to the olefinic CC bond represents the primary sink for these chemicals in the atmosphere, with the degree and type of halogenation playing a significant role in their overall reactivity. In this work, we present a theoretical investigation of the reaction mechanisms and kinetics for the reactions between the OH radical and CH2CH2 (ethylene, ETH), CF2CHF (trifluoroethylene, TFE) and CCl2CHCl (trichloroethylene, TCE), simulated by state-of-the-art protocols and methods, with the aim of providing a detailed interpretation of the available experimental results, as well as new data of relevance to tropospheric chemistry. Specifically, potential energy surfaces (PESs) are obtained using the jun-Cheap (jChS) composite scheme, whereas temperature and pressure dependent rate coefficients and product distributions in the 100-600 K temperature range are calculated within the Rice-Ramsperger-Kassel-Marcus/master equation (RRKM/ME) framework. The rates for barrierless channels are obtained from variable reaction coordinate-variational transition state theory (VRC-VTST) combined with the two transition state model. While the reactions with ETH and TFE proceed mainly via the formation of addition adducts at P = 1 atm and T = 298 K, the dominant channel for TCE is the Cl-elimination reaction. Global rate constants for the two halogenated olefins, TFE and TCE, are found to be pressure-independent, contrary to the case of ETH. The computed rate constants, as well as their temperature and pressure dependence, are in remarkable agreement with the available experimental data, and they are used to derive atmospheric lifetimes (τ) for both TFE and TCE as a function of altitude (h) in the atmosphere, by taking into account variations in the rate coefficients (k (T, P)) and [OH] concentration.

Theoretical study on the H-atom abstraction reactions of pentanol + HȮ2, part I: five branched pentanol isomers

The chemical kinetic studies of hydrogen atom (H-atom) abstraction reactions by hydroperoxyl (HȮ2) radicals from five branched pentanol isomers, including 3-methyl-1-butanol, 2-methyl-1-butanol, 1,1-dimethyl-1-propanol, 1,2-dimethyl-1-propanol, and 2,2-dimethyl-1-propanol were investigated systematically through high-level ab initio calculations. Geometry optimization, frequency analysis, and zero-point energy (ZPE) corrections were performed for six reactants, twenty-three transition states (TSs), and twenty-four products at the M06-2X/6-311++G(d,p) level of theory. The intrinsic reaction coordinate calculation was performed at the same level of theory to confirm the transition state connection. The one-dimensional hindered rotor treatment for low-frequency torsional modes was also treated at the M06-2X/6-311++G(d,p) level of theory. The QCISD(T)/CBS level of theory was used to calculate the single-point energies for the species whose T1 diagnostic value was lower than 0.035. At the same time, the CASPT2/CBS level of theory was used to calculate the single-point energies for the channel in which the T1 diagnostic value of transition states was greater than 0.035. Rate constants for the H-atom abstraction reactions from the five branched pentanol isomers by HȮ2 radicals were calculated by using conventional transition state theory with asymmetric Eckart tunneling corrections in the temperature range of 500-2000 K. Rate constants and branching ratios for the title reactions and the rate rules for ten different H-atom abstraction types were investigated. Temperature-dependent thermochemistry properties for all reactants and products were calculated by the composite methods of G3/G4/CBS-QB3/CBS-APNO, which were in good agreement with the data available in the literature. Rate constants for the H-atom abstraction reactions by HȮ2 radical from branched pentanol isomers were investigated in this work as part I, and those for linear pentanol isomers will be analyzed in part II. All the calculated kinetics and thermochemistry data can be utilized in the model development for branched pentanol isomers oxidation.

Performance of Effective Harmonic Oscillator Approach for the Calculations of Vibrational Transition Energies of Large Molecules

The accuracy and performance of the effective harmonic oscillator approximation for the description of anharmonic vibrational structure calculations are tested for large molecular systems and compared with experimental values along with vibrational self-consistent field and second-order perturbation theories. The effective harmonic oscillator approach is an effective single-particle approximation where the variational parameters are the centroids and widths of the multidimensional Gaussian product functions posited as the vibrational wave functions. A comprehensive calculation for 849 transitions that include the fundamentals, two and three quanta overtone transitions, and several combination bands of three polyaromatic hydrocarbons and one DNA nucleobase with a total of 231 normal modes are assessed. A comparison of EHO results with the experimental values is done for the polyaromatic hydrocarbons, and a close agreement is found between the two results. It also offers anharmonic eigenstates and eigenfunctions that are nearly identical with vibrational self-consistent field theory. An extensive analysis on the resultant wave functions of the excited states is performed. The overall root-mean-square deviation (RMSD) between these two methods for 849 transitions understudy is only about 8.3 cm-1, suggesting the effective harmonic oscillator as a viable alternative for the reliable calculations of transition energies of large molecular systems.

The Interplay between the Temperature and Pressure on the Reaction Pathways of the Prenol Oxidation by Hydroxyl Radicals

Despite prenol emerging as a next-generation biofuel, some questions about its mechanism still need to be adequately proposed to rationalize its consumption and evaluate its efficiency in spark-ignition (SI) engines. Here, we present new insights into the reaction mechanism of prenol (3-methyl-2-buten-1-ol) with OH radicals as a function of temperature and pressure. We have determined that the different temperature and pressure conditions control the preferred products. At combustion temperatures and low pressures, OH-addition adducts are suppressed, increasing the formation of α and δ allylic radicals responsible for the auto-ignition.

Detailed Reaction Kinetics for Hydrocarbon Fuels: The Development and Application of the ReaxFFCHO-S22 Force Field for C/H/O Systems with Enhanced Accuracy

Efficient and accurate reactive force fields (e.g., ReaxFF) are pivotal for large-scale atomistic simulations to comprehend microscopic combustion processes. ReaxFF has been extensively utilized to describe chemical reactions in condensed phases, but most existing ReaxFF models rely on quantum mechanical (QM) data nearly two decades old, particularly in hydrocarbon systems, constraining their accuracy and applicability. Addressing this gap, we introduce a reparametrized ReaxFFCHO-S22 for C/H/O systems, tailored for studying the pyrolysis and combustion of hydrocarbon fuel. Our approach involves high-level QM benchmarks and large database construction for C/H/O systems, global ReaxFF parameter optimization, and molecular dynamics simulations of typical hydrocarbon fuels. Density functional theory (DFT) computations utilized the M06-2X functional at the meta-generalized gradient approximation (meta-GGA) level with a large basis set (6-311++G**). Our new ReaxFFCHO-S22 model exhibits a minimum 10% enhancement in accuracy compared to the previous ReaxFF models for a large variety of hydrocarbon molecules. This advanced ReaxFFCHO-S22 not only enables efficient large-scale studies on the microscopic chemical reactions of more complex hydrocarbon fuel but also can extend to biofuels, energetic materials, polymers, and other pertinent systems, thus serving as a valuable tool for studying chemical reaction dynamics of the large-scale hydrocarbon condensed phase at an atomistic level.

Theoretical and kinetic study of the H-atom abstraction reactions by Ḣ atom from alkyl cyclohexanes

Reaction kinetics of hydrogen atom abstraction from six alkyl cyclohexanes, methyl cyclohexane (MCH), ethyl cyclohexane (ECH), n-propyl cyclohexane (nPCH), iso-propyl cyclohexane (iPCH), sec-butyl cyclohexane (sBCH) and iso-butyl cyclohexane (iBCH), by the Ḣ atom are systematically studied in this work. The M06-2X method combined with the 6-311++G(d,p) basis set is used to perform geometry optimization, frequency analysis and zero-point energy calculations for all species. The intrinsic reaction coordinate (IRC) calculations are performed to confirm the transition states connecting the reactants and products correctly. One-dimensional hindered rotors are used to treat the low frequency torsional models with potentials scanned at the M06-2X/6-31G level of theory. Electronic single-point energy calculations for all reactants, transition states, and products are performed at the QCISD(T)/CBS level of theory. High-pressure limiting rate constants of 39 reaction channels are obtained using conventional transition state theory with asymmetric Eckart tunneling corrections in the temperature range 298.15-2000 K. Reaction rate rules for H-atom abstraction by the Ḣ atom from alkyl cyclohexanes on primary, secondary and tertiary carbon sites on both the side chain and ring are provided. The obtained rate constants are given by the Arrhenius expression in the temperature range 500-2000 K, which can be used for the combustion kinetics model development for alkyl cyclohexanes.

Comprehensive Multipath Variational Kinetics Study on Hydrogen Abstraction Reactions from Three Typical Dimethylcyclohexane Isomers by Hydroxyl Radicals: from the Electronic Structure to Model Applications

Cycloalkanes serve as an important class of chemical components in both fossil and alternative transportation fuels and have attracted considerable attention from the combustion community. Hydrogen abstractions from cycloalkanes by hydroxyl radicals initiate the fuel decomposition process and trigger off the subsequent chain reactions and thus play an important role in both combustion and atmospheric chemistry. The target of this study is to fill the vacancy in kinetics data toward the H-abstraction reactions by hydroxyl radical from three typical dimethylcyclohexane isomers through first-principles and direct dynamics. The rate constants involving 18 elementary reactions in total were accurately determined by the multipath canonical variational transition state theory with the multidimensional small-curvature correction for tunneling (MP-CVT/SCT), over a broad temperature range of 200-2000 K. The significant roles of multistructural torsional anharmonicity and recrossing effects were stressed per abstraction site, while the quantum tunneling effect was found to be slight at temperatures of interest in combustion. The discrepancies observed among different reaction systems at a similar abstraction site highlight the fuel molecular effects on site-specific rate constants. The comparison results of total rate constants given by different dynamics approaches prove the importance of considering the torsional anharmonicity, recrossing, and tunneling effects, and the robust feature of the simplified MS-CVT/SCT. The calculated total constants for dimethylcyclohexane isomers by OH are consistent with those measured for methylcyclohexane and 1,4-dimethylcyclohexane at low temperatures. The branching ratio analysis confirms the predominant role of the tertiary abstraction at low-to-intermediate temperatures and its growing competition with distinct secondary abstractions as temperature increases. The calculated rate constants were eventually fitted into the analytical expressions and incorporated into the kinetic models to learn about the influences on modeling performance.

Quantitative kinetics reveal that reactions of HO2 are a significant sink for aldehydes in the atmosphere and may initiate the formation of highly oxygenated molecules via autoxidation

Large aldehydes are widespread in the atmosphere and their oxidation leads to secondary organic aerosols. The current understanding of their chemical transformation processes is limited to hydroxyl radical (OH) oxidation during daytime and nitrate radical (NO3) oxidation during nighttime. Here, we report quantitative kinetics calculations of the reactions of hexanal (C5H11CHO), pentanal (C4H9CHO), and butanal (C3H7CHO) with hydroperoxyl radical (HO2) at atmospheric temperatures and pressures. We find that neither tunneling nor multistructural torsion anharmonicity should be neglected in computing these rate constants; strong anharmonicity at the transition states is also important. We find rate constants for the three reactions in the range 3.2-7.7 × 10-14 cm3 molecule-1 s-1 at 298 K and 1 atm, showing that the HO2 reactions can be competitive with OH and NO3 oxidation under some conditions relevant to the atmosphere. Our findings reveal that HO2-initiated oxidation of large aldehydes may be responsible for the formation of highly oxygenated molecules via autoxidation. We augment the theoretic studies with laboratory flow-tube experiments using an iodide-adduct time-of-flight chemical ionization mass spectrometer to confirm the theoretical predictions of peroxy radicals and the autoxidation pathway. We find that the adduct from HO2 + C5H11CHO undergoes a fast unimolecular 1,7-hydrogen shift with a rate constant of 0.45 s-1. We suggest that the HO2 reactions make significant contributions to the sink of aldehydes.

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.

Quantitative kinetics of the atmospheric reaction between isocyanic acid and hydroxyl radicals: post-CCSD(T) contribution, anharmonicity, recrossing effects, torsional anharmonicity, and tunneling

Hydroxyl radicals (OH) are the most important atmospheric oxidant, initiating atmospheric reactions for the chemical transformation of volatile organic compounds. Here, we choose the HNCO + OH reaction as a prototype reaction because it contains the fundamental reaction processes for OH radicals: H-abstraction reaction by OH and OH addition reaction. However, its kinetics are unknown under atmospheric conditions. We investigate the reaction of HNCO with OH by using the GMM(P).L method close to the accuracy of single, double, triple, and quadruple excitations and noniterative quintuple excitations with a complete basis set (CCSDTQ(P)/CBS) as benchmark results and a dual-level strategy for kinetics calculations. The calculated rate constant of HNCO + OH is in good agreement with the experimental data available at the temperatures between 620 and 2500 K. We find that the rate constant cannot be correctly obtained by using experimental data to extrapolate the atmospheric temperature ranges. We find that the post-CCSD(T) contribution is very large for the barrier height with the value of -0.85 kcal mol-1 for the H-abstraction reaction, while the previous investigations were done up to the CCSD(T) level. Moreover, we also find that recrossing effects, tunneling, torsional anharmonicity, and anharmonicity are important for obtaining quantitative kinetics in the OH + HNCO reaction.

Theoretical Kinetic Study on Hydrogen Abstraction Reactions from n-Pentane by NO2

The interaction of fuel with NOx chemistry is important for the construction of the reaction mechanism and engine application. In this work, the reaction pathways of nC5H12 + NO2 were studied by high-level electronic structure calculations (DLPNO-CCSD(T)-F12/cc-pVTZ-F12//B2PLYPD3/cc-pVTZ). The rate constants were calculated by using the multistructural canonical transition-state theory with the Eckart tunneling method (TST/MS-T/ET). The studied condition is in a wide temperature range of 298-2400 K. The influence of MS-T anharmonicity and tunneling effect will be clarified for these site-specific H-abstraction pathways. The result reflects the large deviation introduced by the treatment of MS-T anharmonicity, especially at a high temperature. For the same type of reactions, the rate constants of H-abstraction both occurring at the secondary carbon are not almost identical. The branching ratios show that abstraction from the secondary site forming cis-HONO (R2c) contributes 36-78% to nC5H12 consumption in the temperature range of 298-2400 K. The current results show that the multistructural torsional anharmonicity has a crucial influence on the accurate estimation of branching ratios.

Exploring torsional conformer space with physical prior mean function-driven meta-Gaussian processes

We present a novel approach for systematically exploring the conformational space of small molecules with multiple internal torsions. Identifying unique conformers through a systematic conformational search is important for obtaining accurate thermodynamic functions (e.g., free energy), encompassing contributions from the ensemble of all local minima. Traditional geometry optimizers focus on one structure at a time, lacking transferability from the local potential-energy surface (PES) around a specific minimum to optimize other conformers. In this work, we introduce a physics-driven meta-Gaussian processes (meta-GPs) method that not only enables efficient exploration of target PES for locating local minima but, critically, incorporates physical surrogates that can be applied universally across the optimization of all conformers of the same molecule. Meta-GPs construct surrogate PESs based on the optimization history of prior conformers, dynamically selecting the most suitable prior mean function (representing prior knowledge in Bayesian learning) as a function of the optimization progress. We systematically benchmarked the performance of multiple GP variants for brute-force conformational search of amino acids. Our findings highlight the superior performance of meta-GPs in terms of efficiency, comprehensiveness of conformer discovery, and the distribution of conformers compared to conventional non-surrogate optimizers and other non-meta-GPs. Furthermore, we demonstrate that by concurrently optimizing, training GPs on the fly, and learning PESs, meta-GPs exhibit the capacity to generate high-quality PESs in the torsional space without extensive training data. This represents a promising avenue for physics-based transfer learning via meta-GPs with adaptive priors in exploring torsional conformer space.

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.

Kinetics of Sulfur Trioxide Reaction with Water Vapor to Form Atmospheric Sulfuric Acid

Although experimental methods can be used to obtain the quantitative kinetics of atmospheric reactions, experimental data are often limited to a narrow temperature range. The reaction of SO3 with water vapor is important for elucidating the formation of sulfuric acid in the atmosphere; however, the kinetics is uncertain at low temperatures. Here, we calculate rate constants for reactions of sulfur trioxide with two water molecules. We consider two mechanisms: the SO3···H2O + H2O reaction and the SO3 + (H2O)2 reaction. We find that beyond-CCSD(T) contributions to the barrier heights are very large, and multidimensional tunneling, unusually large anharmonicity of high-frequency modes, and torsional anharmonicity are important for obtaining quantitative kinetics. We find that at lower temperatures, the formation of the termolecular precursor complexes, which is often neglected, is rate-limiting compared to passage through the tight transition states. Our calculations show that the SO3···H2O + H2O mechanism is more important than the SO3 + (H2O)2 mechanism at 5-50 km altitudes. We find that the rate ratio between SO3···H2O + H2O and SO3 + (H2O)2 is greater than 20 at altitudes between 10 and 35 km, where the concentration of SO3 is very high.

Unimolecular Reactions of E-Glycolaldehyde Oxide and Its Reactions with One and Two Water Molecules

The kinetics of Criegee intermediates are important for atmospheric modeling. However, the quantitative kinetics of Criegee intermediates are still very limited, especially for those with hydroxy groups. Here, we calculate rate constants for the unimolecular reaction of E-glycolaldehyde oxide [E-hydroxyethanal oxide, E-(CH₂OH)CHOO], for its reactions with H₂O and (H₂O)₂, and for the reaction of the E-(CH₂OH)CHOO…H₂O complex with H₂O. For the highest level of electronic structure, we use W3X-L//CCSD(T)-F12a/cc-pVDZ-F12 for the unimolecular reaction and the reaction with water and W3X-L//DF-CCSD(T)-F12b/jun-cc-pVDZ for the reaction with 2 water molecules. For the dynamics, we use a dual-level strategy that combines conventional transition state theory with the highest level of electronic structure and multistructural canonical variational transition state theory with small-curvature tunneling with a validated density functional for the electronic structure. This dynamical treatment includes high-frequency anharmonicity, torsional anharmonicity, recrossing effects, and tunneling. We find that the unimolecular reaction of E-(CH₂OH)CHOO depends on both temperature and pressure. The calculated results show that E-(CH₂OH)CHOO…H₂O + H₂O is the dominant entrance channel, while previous investigations only considered Criegee intermediates + (H₂O)₂. In addition, we find that the atmospheric lifetime of E-(CH₂OH)CHOO with respect to 2 water molecules is particularly short with a value of 1.71 × 10^-6 s at 0 km, which is about 2 orders of magnitude shorter than those usually assumed for Criegee intermediate reactions with water dimer. We also find that the OH group in E-(CH₂OH)CHOO enhances its reactivity.

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.

Identification of Torsional Modes in Complex Molecules Using Redundant Internal Coordinates: The Multistructural Method with Torsional Anharmonicity with a Coupled Torsional Potential and Delocalized Torsions

Identification of internal-rotation modes in the normal-mode analysis of complex molecules is important for accurately describing the thermodynamic properties and kinetics of complex molecules when it is necessary to treat the anharmonicity of torsions and the multiconformer anharmonicity caused by the internal rotations. However, identifying and distinguishing torsional modes are very challenging because they are coupled to one another. In this work, we present a new strategy to automatically identify torsional vibrations and separate them from the other vibrational modes. By combining a redundant-internal-coordinate auto-generation procedure with torsional projection techniques, we automate the procedure of identifying and separating the coupled torsions, and we show that we can obtain robust and consistent results with various reasonable definitions of redundant-internal-coordinate sets. This model has been implemented in a new development version of the MSTor program to reduce the user input needed for multistructural and torsional anharmonicity (MS-T) calculations. The new method is called multistructural and torsional anharmonicity with a coupled torsional potential and delocalized torsions ([MS-T(CD)]. As example applications, we consider MS-T(CD) calculations on three molecules (2-hexyl radical, n-propylbenzene, and 5-hydroperoxy-6-oxohexanoylperoxy radical) that have multiple rotors and that provide challenges to choosing good sets of nonredundant-internal coordinates, and we compare the performance of the new strategy to five other torsion identification methods. The new strategy is demonstrated to be efficient in separating the torsional and nontorsional elements in the Hessian matrix, as well as in providing reasonable projected nontorsional frequencies to be used for calculations of partition function and thermochemistry.

Theoretical-Computational Modeling of Gas-State Thermodynamics in Flexible Molecular Systems: Ionic Liquids in the Gas Phase as a Case Study

A theoretical-computational procedure based on the quasi-Gaussian entropy (QGE) theory and molecular dynamics (MD) simulations is proposed for the calculation of thermodynamic properties for molecular and supra-molecular species in the gas phase. The peculiarity of the methodology reported in this study is its ability to construct an analytical model of all the most relevant thermodynamic properties, even within a wide temperature range, based on a practically automatic sampling of the entire conformational repertoire of highly flexible systems, thereby bypassing the need for an explicit search for all possible conformers/rotamers deemed relevant. In this respect, the reliability of the presented method mainly depends on the quality of the force field used in the MD simulations and on the ability to discriminate in a physically coherent way between semi-classical and quantum degrees of freedom. The method was tested on six model systems (n-butane, n-butane, n-octanol, octadecane, 1-butyl-3-methylimidazolium hexafluorophosphate and 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ionic pairs), which, being experimentally characterized and already addressed by other theoretical-computational methods, were considered as particularly suitable to allow us to evaluate the method's accuracy and efficiency, bringing out advantages and possible drawbacks. The results demonstrate that such a physically coherent yet relatively simple method can represent a further valid computational tool that is alternative and complementary to other extremely efficient computational methods, as it is particularly suited for addressing the thermodynamics of gaseous systems with a high conformational complexity over a large range of temperature.

Lowering of Reaction Rates by Energetically Favorable Hydrogen Bonding in the Transition State. Degradation of Biofuel Ketohydroperoxides by OH

Ketohydroperoxides (KHPs) are oxygenates with carbonyl and hydroperoxy functional groups, and they are generated under combustion and atmospheric conditions. Their fate is crucial for secondary organic aerosol formation in the troposphere and for the ignition processes of biofuels in advanced combustion engines. We investigated the thermodynamics and kinetics of nine hydrogen abstraction reactions from four ether KHPs by OH. We find that the rate constants are strongly affected by entropic effects whose estimation requires a consideration of higher-energy conformers of the transition state. A density functional was selected for these reactions by comparison to coupled cluster calculations, and it was used for calculations by multistructural canonical transition-state theory with multidimensional tunneling over the temperature range of 200-2000 K. We find that the effect of multistructural torsional anharmonicity is very large and quite different for the various ether KHP reactions. A leading cause of the structural dependence is the dominance of entropic factors due to the lack of hydrogen bonding in some of the higher-energy conformers of the transition states. Four of the reactions involve abstraction from the α-carbon (the carbon vicinal to the hydroperoxide group); they exhibit nonmonotonic temperature dependence with complex fuel-specific dependence. The rate constants for abstraction from a non-α-carbon of a given KHP can be faster than the ones for abstraction from an α-carbon; in two cases, this is due to entropy, and in one case, the non-α-carbon abstraction has a lower energy barrier. Tunneling and recrossing effects are also found to be important.

Prenol as a Next-Generation Biofuel or Additive: A Comprehension of the Hydrogen Abstraction Reactions by a H Atom

Thermal rate coefficients for the hydrogen abstraction reactions of prenol (3-methyl-2-butenol) by a hydrogen atom were calculated with the multipath canonical variational theory with small-curvature tunneling (MP-CVT/SCT). The conformational search was performed with a dual-level approach, and the multistructural torsional anharmonicity effects were corrected through the rovibrational partition function calculated with the multistructural method based on a coupled torsional potential (MS-T(C)). This methodology allows us to estimate the thermal rate constants in the temperature range of 200-2500 K and fit them into two analytical expressions. Differences between the number of conformations on the torsional potential energy surfaces for prenol and the transition state decrease the thermal rate constants for the H-abstraction at the α carbon. An opposite behavior was detected for the abstractions on the δ site. The product branching ratios were calculated using single-structure and multipath approaches. The product distributions from the former are shown to be inadequate for studying the mechanism under combustion conditions. The values estimated from MP-CVT/SCT rate coefficients indicated that the radicals from (R_α) and (R_δ)/(R_δ') are formed in considerable amounts. These species are fundamental in comprehending the inhibition and promotion of the autoignition phenomena.

Fast Predictions of Reaction Barrier Heights: Toward Coupled-Cluster Accuracy

Quantitative estimates of reaction barriers are essential for developing kinetic mechanisms and predicting reaction outcomes. However, the lack of experimental data and the steep scaling of accurate quantum calculations often hinder the ability to obtain reliable kinetic values. Here, we train a directed message passing neural network on nearly 24,000 diverse gas-phase reactions calculated at CCSD(T)-F12a/cc-pVDZ-F12//ωB97X-D3/def2-TZVP. Our model uses 75% fewer parameters than previous studies, an improved reaction representation, and proper data splits to accurately estimate performance on unseen reactions. Using information from only the reactant and product, our model quickly predicts barrier heights with a testing MAE of 2.6 kcal mol^-1 relative to the coupled-cluster data, making it more accurate than a good density functional theory calculation. Furthermore, our results show that future modeling efforts to estimate reaction properties would significantly benefit from fine-tuning calibration using a transfer learning technique. We anticipate this model will accelerate and improve kinetic predictions for small molecule chemistry.

An integrated protocol to study hydrogen abstraction reactions by atomic hydrogen in flexible molecules: application to butanol isomers

This work presents a protocol designed to study hydrogen abstraction reactions by atomic hydrogen in molecules with multiple conformations.

Pressure-Dependent Kinetics of o-Xylene Reaction with OH Radical

OH-initiated oxidation reactions of o-xylene are widely concerned both in combustion and atmospheric chemistry. In this work, the kinetics of o-xylene reaction with OH radical has been studied systematically in...

Coupled Anharmonic Thermochemistry from Stratified Monte Carlo Integration

This study presents configuration integral Monte Carlo integration (CIMCI), a new semiclassical method for handling fully coupled anharmonicity in gas-phase thermodynamics that promises to be black boxable, to be applicable to all kinds of anharmonicity, and to scale better at higher dimensionality than other methods for handling gas-phase molecular anharmonicity. The method does so using automatically and recursively stratified, simultaneous Monte Carlo (MC) integration of multiple functions, following a modified version of the standard MISER scheme that converges at a rate of about the square of naïve MC integration. For the small systems analyzed by this study where proper reference data is available (H₂O and H₂O₂), the method's anharmonic entropy corrections match reference data better than those of other black box anharmonic methods, e.g., vibrational perturbation theory (VPT2) and the McClurg hindered rotor model used with automatic detection of rotors; for H₂O₂ and NH₂OH, the method is also in general agreement with one-dimensional hindered rotor treatments at low temperatures. This holds even when sampling with CIMCI is done with primitive force fields, e.g., UFF, while the competing methods are used with proper, comprehensive potentials, e.g., the M06-2X metahybrid density-functional theory (DFT) functional.

TorsiFlex: an automatic generator of torsional conformers. Application to the twenty proteinogenic amino acids

In this work, we introduce TorsiFlex, a user-friendly software written in Python 3 and designed to find all the torsional conformers of flexible acyclic molecules in an automatic fashion. For the mapping of the torsional potential energy surface, the algorithm implemented in TorsiFlex combines two searching strategies: preconditioned and stochastic. The former is a type of systematic search based on chemical knowledge and should be carried out before the stochastic (random) search. The algorithm applies several validation tests to accelerate the exploration of the torsional space. For instance, the optimized structures are stored and this information is used to prevent revisiting these points and their surroundings in future iterations. TorsiFlex operates with a dual-level strategy by which the initial search is carried out at an inexpensive electronic structure level of theory and the located conformers are reoptimized at a higher level. Additionally, the program takes advantage of conformational enantiomerism, when possible. As a case study, and in order to exemplify the effectiveness and capabilities of this program, we have employed TorsiFlex to locate the conformers of the twenty proteinogenic amino acids in their neutral canonical form. TorsiFlex has produced a number of conformers that roughly doubles the amount of the most complete work to date.

Differences in the torsional anharmonicity between reactant and transition state: the case of 3-butenal + H abstraction reactions

Thermal rate coefficients for the hydrogen-abstraction reactions of 3-butenal by a hydrogen atom were obtained applying multipath canonical variational theory with small-curvature tunneling (MP-CVT/SCT). Torsional anharmonicity due to the hindered rotors was taken into account by calculating the rovibrational partition function using the extended two-dimensional torsional (E2DT) method. For comparison, rovibrational partition functions were also estimated using the multistructural method with torsional anharmonicity based on a coupled torsional potential (MS-T(C)). By contrast, with (E)-2-butenal reactions, the abstraction reactions of 3-butenal proceed via five reaction channels (R1)-(R5). In a conformational search, 45 distinguishable structures of transition states were found, including enantiomers, which were separated into six conformational reaction channels (CRCs). The individual reactive paths were constructed, the recrossing and semiclassical transmission coefficients estimated, and the multipath rate constants were obtained. High torsional barriers between the wells of CRC2/CRC6 indicate a harmonic behavior. Consequently, a difference between the torsional anharmonicity of 3-butenal and the transition states is responsible for the increase in the thermal rate constants for channel (R2). Analysis of the contributions of each conformer of the transition state shows an important contribution of the high-energy rotamers in the total flux of (R1)-(R5). After fitting the rate constants in a four-parameter equation, the activation energy estimation showed a strong temperature dependence.

Multistructural Variational Reaction Kinetics of the Simplest Unsaturated Methyl Ester: H-Abstraction from Methyl Acrylate by H, OH, CH3, and HO2 Radicals

The H-abstraction reaction kinetics of methyl acrylate (MA) + H/OH/CH₃/HO₂ radicals have been investigated theoretically in the present work. For these reactions, the reaction energies and barrier heights are first computed using several density functionals and compared to the coupled cluster CCSD(T)-F12/jun-cc-pVTZ benchmark calculations. The M062X/maug-cc-pVTZ method shows the best performance with the smallest mean unsigned deviation (MUD) of 0.42 kcal mol^-1. Combined with the electronic structure calculations using the M062X/maug-cc-pVTZ method, the multistructural canonical variational transition-state theory (MS-CVT) with small-curvature tunneling (SCT) is employed to calculate the reaction rate constants at 500-2000 K. The variational effect is between 0.56 and 1.0, the multistructural torsional anharmonicity factor ranges from 0.004 to 4.57, and the tunneling coefficient is in the range of 0.5-4.70. Notably, given the existence of reactant complexes (RCs) between reactants and transition states for the reaction systems MA + OH/HO₂, we further compare the rate constants under the low-pressure limit (LPL) kinetic model, which treats the reaction as a single-step process and neglects RCs, and the pre-equilibrium model, which takes RCs into account in the reaction and treats the reaction as a two-step process. The rate constants calculated by these two models are similar within the combustion temperature range, and apparent differences occur at lower temperatures. In addition, we determine the branching ratios as a function of temperature and find that the methyl site (S3) abstractions by OH and H radicals are dominant in the low- and high-temperature ranges, respectively. Moreover, we update the kinetic model with the calculated H-abstraction rate constants to simulate the ignition delay times of MA. The simulations of the updated model are in good agreement with experimental results. The accurate reaction kinetics determined in this work are useful for the understanding and prediction of consumption branching fractions and ignition properties of the unsaturated methyl esters.

Early Chemistry of Nicotine Degradation in Heat-Not-Burn Smoking Devices and Conventional Cigarettes: Implications for Users and Second- and Third-Hand Smokers

Nicotine exposure results in health risks not only for smokers but also for second- and third-hand smokers. Unraveling nicotine's degradation mechanism and the harmful chemicals that are produced under different conditions is vital to assess exposure risks. We performed a theoretical study to describe the early chemistry of nicotine degradation by investigating two important reactions that nicotine can undergo: hydrogen abstraction by hydroxyl radicals and unimolecular dissociation. The former contributes to the control of the degradation mechanism below 800 K due to a non-Arrhenius kinetics, which implies an enhancement of reactivity as temperature decreases. The latter becomes important at higher temperatures due to its larger activation energy. This change in the degradation mechanism is expected to affect the composition of vapors inhaled by smokers and room occupants. Conventional cigarettes, which operate at temperatures higher than 1000 K, are more prone to yield harmful pyridinyl radicals via nicotine dissociation, while nicotine in electronic cigarettes and vaporizers, with operating temperatures below 600 K, will be more likely degraded by hydroxyl radicals, resulting in a vapor with a different composition. Although low-temperature nicotine delivery devices have been claimed to be less harmful due to their nonburning operating conditions, the non-Arrhenius kinetics that we observed for the degradation mechanism below 873 K suggests that nicotine degradation may be more rapidly initiated as temperature is reduced, indicating that these devices may be more harmful than it is commonly assumed.

A kinetics study on hydrogen abstraction reactions of cyclopentane by hydrogen, methyl, and ethyl radicals

Hydrogen abstraction reactions of (cyclo)alkanes by radicals play a fundamental role in both combustion and atmospheric chemistry. In this work, we select three common radicals in the pyrolysis of hydrocarbon fuels: hydrogen radical (H[combining dot above]), methyl radical (ĊH₃), and ethyl radical (ĊH₂CH₃) to investigate the kinetics of their hydrogen abstraction reactions with cyclopentane. The rate constants over a broad temperature range of 150-3000 K are calculated by using the multi-structural variational transition state theory in the small-curvature tunneling approximation (MS-CVT/SCT), by which the multi-structural torsional (MS-T) anharmonicity of partition functions, variational effects, and corner-cutting tunneling are all included in dynamics calculations. We stress the particular importance of considering the MS-T anharmonicity in the rate constant calculation for the reaction with the ethyl radical compared to those with hydrogen and methyl radicals. The MS-T anharmonicity significantly accelerates the reaction with the ethyl radical in the whole temperature range, and in particular, it increases the rate constant by a factor of >-9 at 1000 K. We also found that the tunneling effect drastically increases the rate constants at low-temperatures by up to 3-5 orders of magnitudes. The calculated reaction rate constants have an order of .

Calculation of absolute molecular entropies and heat capacities made simple

We propose a fully-automated composite scheme for the accurate and numerically stable calculation of molecular entropies by efficiently combining density-functional theory (DFT), semi-empirical methods (SQM), and force-field (FF) approximations. The scheme is systematically expandable and can be integrated seamlessly with continuum-solvation models. Anharmonic effects are included through the modified rigid-rotor-harmonic-oscillator (msRRHO) approximation and the Gibbs-Shannon formula for extensive conformer ensembles (CEs), which are generated by a metadynamics search algorithm and are extrapolated to completeness. For the first time, variations of the ro-vibrational entropy over the CE are consistently accounted-for through a Boltzmann-population average. Extensive tests of the protocol with the two standard DFT approaches B97-3c and B3LYP-D3 reveal an unprecedented accuracy with mean deviations <1 cal mol-1 K-1 (about <1-2%) for the total gas phase molecular entropy of medium-sized molecules. Even for the hardship case of extremely flexible linear alkanes (C14H30-C16H34), errors are only about 3 cal mol-1 K-1. Comprehensive tests indicate a relatively strong variation of the conformational entropy on the underlying level of theory for typical drug molecules, inferring the complex potential energy surfaces as the main source of error. Furthermore, we show some application examples for the calculation of free energy differences in typical chemical reactions.

Kinetics and mechanism of OH-mediated degradation of three pentanols in the atmosphere

Pentanols as potential biofuels have attracted considerable interest, and thus it is of great importance to gain insights into their combustion and atmospheric chemistry.

Influence of Torsional Anharmonicity on the Reactions of Methyl Butanoate with Hydroperoxyl Radical

An ab initio chemical kinetics study of the reactions of methyl butanoate (MB) with hydroperoxyl radical (HO₂) is presented in this paper. Particular interest is placed on determining the influences of torsional anharmonicity and addition reaction on the rate constants of hydrogen abstraction reactions. Stationary points on the potential energy surface of MB + HO₂ are calculated at the level of QCISD(T)/CBS//B3LYP/6-311++G(d,p). The transition state theory (TST) is used to calculate the high-pressure limit rate constants of the hydrogen abstraction reactions over a board range of temperature (500-2000 K). Anharmonicity of low-frequency torsional modes is considered in the rate calculations by using the one-dimensional hindered rotor approximation and the internal-coordinate multistructural approximation; the latter is used as a higher-level theoretical method to examine the applicability of the former in dealing with strongly coupled torsional modes. The calculated rate constants are compared with the available data from the literature and observed discrepancies are analyzed in detail. An energetically lowest-lying addition reaction with subsequent isomerization and decomposition reactions are identified on the potential energy surface. The multiple-well Master equation analysis shows that these reactions have a secondary influence on the rate constants in the temperature range of interest.

Thermal behaviour of hindered rotor in static electric and laser field

We solve exactly the time independent Schrödinger equation (TISE) for hindered rotor confined in well shaped potential. Afterwards, the confined system is subjected to interact with laser and static electric field. TISE for the dressed confined rotor is solved using standard numerical method to get energy spectrum and eigenfunctions. Dependence of orientation and alignment parameters on static electric field and confining potential is studied. We also compute thermal properties like entropy and heat capacity of the system under consideration using canonical partition within statistical thermodynamic formalism. We have also studied the effect of external field parameters, confinement strength and temperature on these thermal properties.