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.

A structure activity relationship for ring closure reactions in unsaturated alkylperoxy radicals

Terpenoids are an important class of multi-unsaturated volatile organic compounds emitted to the atmosphere. During their oxidation in the troposphere, unsaturated peroxy radicals are formed, which may undergo ring closure reactions by an addition of the radical oxygen atom on either of the carbons in the C[double bond, length as m-dash]C double bond. This study describes a quantum chemical and theoretical kinetic study of the rate of ring closure, finding that the reactions are comparatively fast with rates often exceeding 1 s-1 at room temperature, making these reactions competitive in low-NOx environments and allowing for continued autoxidation by ring closure. A structure-activity relationship (SAR) is presented for 5- to 8-membered ring closure in unsaturated RO2 radicals with aliphatic substituents, with some analysis of the impact of oxygenated substituents. H-migration in the cycloperoxide peroxy radicals formed after the ring closure was found to be comparatively slow for unsubstituted RO2 radicals. In the related cycloperoxide alkoxy radicals, migration of H-atoms implanted on the ring was similarly found to be slower than for non-cyclic alkoxy radicals and is typically not competitive against decomposition reactions that lead to cycloperoxide ring breaking. Ring closure reactions may constitute an important reaction channel in the atmospheric oxidation of terpenoids and could promote continued autoxidation, though the impact is likely to be strongly dependent on the specific molecular backbone.

Large Anharmonic Effects on Tunneling and Kinetics: Reaction of Propane with Muonium

Calculations of kinetic isotope effects (KIEs) provide challenging tests of quantal mass effects on reaction rates, and muonium KIEs are the most challenging. Here, we show that it can be very important to include reaction-coordinate-dependent vibrational anharmonicity along the whole reaction path to calculate tunneling probabilities and KIEs. For the reaction of propane with Mu, this decreases both the height and width of the vibrationally adiabatic potential barrier, with both effects increasing the rate constants. Our results agree well with the experimental observations.

Multistructural Anharmonicity Controls the Radical Generation Process in Biofuel Combustion

The OH radical plays an important role in combustion, and isopentanol (3-methylbutan-1-ol) is a promising sustainable fuel additive and second-generation biofuel. The abstractions of H atoms from fuel molecules are key initiation steps for chain branching in combustion chemistry. In comparison with the more frequently studied ethanol, isopentanol has a longer carbon chain that allows a greater number of products, and experimental work is unavailable for the branching fractions to the various products. However, the site-dependent kinetics of isopentanol with OH radicals are usually experimentally unavailable. Alcohol oxidation by OH is also important in the atmosphere, and in the present study we calculate the rate constants and branching fractions of the hydrogen abstraction reaction of isopentanol by OH radical in a broad temperature range of 298-2400 K, covering temperatures important for atmospheric chemistry and those important for combustion. The calculations are done by multipath variational transition state theory (MP-VTST). With a combination of electronic structure calculations, we determine previously missing thermochemical data. With MP-VTST, a multidimensional tunneling approximation, multiple-structure anharmonicity, and torsional potential anharmonicity, we carried out more realistic rate constant calculations than can be computed by conventional single-structure harmonic transition state theory or by the empirical relations that are currently used in atmospheric and combustion modeling. The roles of various factors in determining the rates are elucidated, and we show that recrossing, tunneling, and multiple structures are all essential for accurate work. We conclude that the multiple structure anharmonicity is the most important correction to conventional transition state theory for this reaction, although recrossing effects and tunneling are by no means insignificant and the tunneling depends significantly on the path. The thermodynamic and kinetics data determined in this work are indispensable for the gas-phase degradation of alcohols in the atmosphere and for the detailed understanding and prediction of ignition mechanisms of biofuels in combustion.

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

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

Variational transition state theory: theoretical framework and recent developments

This article reviews the fundamentals of variational transition state theory (VTST), its recent theoretical development, and some modern applications.

Kinetics of Hydrogen Radical Reactions with Toluene Including Chemical Activation Theory Employing System-Specific Quantum RRK Theory Calibrated by Variational Transition State Theory

Pressure-dependent reactions are ubiquitous in combustion and atmospheric chemistry. We employ a new calibration procedure for quantum Rice-Ramsperger-Kassel (QRRK) unimolecular rate theory within a chemical activation mechanism to calculate the pressure-falloff effect of a radical association with an aromatic ring. The new theoretical framework is applied to the reaction of H with toluene, which is a prototypical reaction in the combustion chemistry of aromatic hydrocarbons present in most fuels. Both the hydrogen abstraction reactions and the hydrogen addition reactions are calculated. Our system-specific (SS) QRRK approach is adjusted with SS parameters to agree with multistructural canonical variational transition state theory with multidimensional tunneling (MS-CVT/SCT) at the high-pressure limit. The new method avoids the need for the usual empirical estimations of the QRRK parameters, and it eliminates the need for variational transition state theory calculations as a function of energy, although in this first application we do validate the falloff curves by comparing SS-QRRK results without tunneling to multistructural microcanonical variational transition state theory (MS-μVT) rate constants without tunneling. At low temperatures, the two approaches agree well with each other, but at high temperatures, SS-QRRK tends to overestimate falloff slightly. We also show that the variational effect is important in computing the energy-resolved rate constants. Multiple-structure anharmonicity, torsional-potential anharmonicity, and high-frequency-mode vibrational anharmonicity are all included in the rate computations, and torsional anharmonicity effects on the density of states are investigated. Branching fractions, which are both temperature- and pressure-dependent (and for which only limited data is available from experiment), are predicted as a function of pressure.

Hydroxyalkoxy radicals: importance of intramolecular hydrogen bonding on chain branching reactions in the combustion and atmospheric decomposition of hydrocarbons

During both the atmospheric oxidation and combustion of volatile organic compounds, sequential addition of oxygen can lead to compounds that contain multiple hydrogen-bonding sites. The presence of two or more of these sites on a hydrocarbon introduces the possibility of intramolecular H-bonding, which can have a stabilizing effect on the reactants, products, and transition states of subsequent reactions. The present work compares the absolute energies of two sets of conformations, those that contain intramolecular H-bonds and those that lack intramolecular H-bonds, for each reactant, product, and transition state species in the 1,2 through 1,7 H-migrations and Cα-Cβ, Cα-H, and Cα-OH-bond scission reactions in the n-hydroxyeth-1-oxy through n-hydroxyhex-1-oxy radicals, for n ranging from 1 to 6. The difference in energy between the two conformations represents the balance between the stabilizing effects of H-bonds and the steric cost of bringing the two H-bonding sites together. The effect of intramolecular H-bonding and the OH group is assessed by comparing the net intramolecular H-bond stabilization energies, the reaction enthalpies, and barrier heights of the n-hydroxyalkoxy radical reactions with the corresponding alkoxy radicals values. The results suggest that there is a complex dependence on the location of the two H-bonding groups, the location of the abstraction or bond scission, and the shape of the transition state that dictates the extent to which intramolecular H-bonding effects the relative importance of H-migration and bond scission reactions for each n-hydroxyalkoxy radical. These findings have important implications for future studies on hydrocarbons with multiple H-bonding sites.

Quantum instanton calculation of rate constant for CH4 + OH → CH3 + H2O reaction: torsional anharmonicity and kinetic isotope effect

Thermal rate constants for the title reaction are calculated by using the quantum instanton approximation within the full dimensional Cartesian coordinates. The results reveal that the quantum effect is remarkable for the reaction at both low and high temperatures, and the obtained rates are in good agreement with experimental measurements at high temperatures. Compared to the harmonic approximation, the torsional anharmonic effect of the internal rotation has a little influence on the rates at low temperatures, however, it enhances the rate by about 20% at 1000 K. In addition, the free energy barriers for the isotopic reactions and the temperature dependence of kinetic isotope effects are also investigated. Generally speaking, for the title reaction, the replacement of OH with OD will reduce the free energy barrier, while substituting D for H (connected to C) will increase the free energy barrier.

Ab initio kinetics for the decomposition of hydroxybutyl and butoxy radicals of n-butanol

The decomposition kinetics of the hydroxybutyl and butoxy radicals (C4H9O) arising via H abstraction from n-butanol were studied theoretically with ab initio transition-state-theory-based master equation analyses. Stationary points on the C4H9O potential energy surface were calculated at either the RQCISD(T)/CBS//B3LYP/6-311++G(d,p) level or the RQCISD(T)/CBS//CASPT2/aug-cc-pVDZ level. Unimolecular pressure- and temperature-dependent rate coefficients were calculated over broad ranges of temperature (300-2500 K) and pressure (1.3 × 10(-3) to 10(2) atm) by solving the time-dependent multiple-well master equation. The "well merging" phenomenon was observed and analyzed for its influence on the branching ratios and rate coefficients. The theoretical predictions were compared with the available experimental and theoretical data and any discrepancies were analyzed. The predicted rate coefficients are represented with forms that may readily be used in combustion modeling of n-butanol.

Multistructural variational transition state theory: kinetics of the hydrogen abstraction from carbon-2 of 2-methyl-1-propanol by hydroperoxyl radical including all structures and torsional anharmonicity

We calculated the forward and reverse rate constants of the hydrogen abstraction reaction from carbon-2 of 2-methyl-1-propanol by hydroperoxyl radical over the temperature range 250-2400 K by using multistructural canonical variational transition state theory (MS-CVT) including both multiple-structure and torsional potential anharmonicity effects by the multistructural torsional anharmonicity (MS-T) method. In these calculations, multidimensional tunneling (MT) probabilities used to compute the tunneling transmission coefficients were evaluated by the small-curvature tunneling (SCT) approximation. Comparison with the rate constants obtained by the single-structural harmonic oscillator (SS-HO) approximation shows that multistructural anharmonicity increases the forward rate constants for all temperatures, but the reverse rate constants are reduced for temperatures lower than 430 K and increased for higher temperatures. The neglect of multistructural torsional anharmonicity would lead to errors of factors of 1.5, 8.8, and 13 at 300, 1000, and 2400 K, respectively, for the forward reaction, and would lead to errors of factors of 0.76, 3.0, and 6.0, respectively, at these temperatures for the reverse reaction.