Accurate thermochemistry of hydrocarbon radicals via an extended generalized bond separation reaction scheme

Detailed knowledge of hydrocarbon radical thermochemistry is critical for understanding diverse chemical phenomena, ranging from combustion processes to organic reaction mechanisms. Unfortunately, experimental thermochemical data for many radical species tend to have large errors or are lacking entirely. Here we develop procedures for deriving high-quality thermochemical data for hydrocarbon radicals by extending Wheeler et al.'s "generalized bond separation reaction" (GBSR) scheme (J. Am. Chem. Soc., 2009, 131, 2547). Moreover, we show that the existing definition of hyperhomodesmotic reactions is flawed. This is because transformation reactions, in which one molecule each from the predefined sets of products and reactants can be converted to a different product and reactant molecule, are currently allowed. This problem is corrected via a refined definition of hyperhomodesmotic reactions in which there are equal numbers of carbon-carbon bond types inclusive of carbon hybridization and number of hydrogens attached. Ab initio and density functional theory (DFT) computations using the expanded GBSRs are applied to a newly derived test set of 27 hydrocarbon radicals (HCR27). Greatly reduced errors in computed reaction enthalpies are seen for hyperhomodesmotic and other highly balanced reactions classes, which benefit from increased matching of hybridization and bonding requirements. The best performing DFT methods for hyperhomodesmotic reactions, M06-2X and B97-dDsC, give average deviations from benchmark computations of only 0.31 and 0.44 (±0.90 and ±1.56 at the 95% confidence level) kcal/mol, respectively, over the test set. By exploiting the high degree of error cancellation provided by hyperhomodesmotic reactions, accurate thermochemical data for hydrocarbon radicals (e.g., enthalpies of formation) can be computed using relatively inexpensive computational methods.     

Enthalpies of formation, bond dissociation energies, and molecular structures of the n-aldehydes (acetaldehyde, propanal, butanal, pentanal, hexanal, and heptanal) and their radicals

Aldehydes are important intermediates and products in a variety of combustion and gas-phase oxidation processes, such as in low-temperature combustion, in the atmosphere, and in interstellar media. Despite their importance, the enthalpies of formation and bond dissociation energies (BDEs) for the aldehydes are not accurately known. We have determined enthalpies of formation for acetaldehyde, propanal, and butanal from thermodynamic cycles, using experimentally measured reaction and formation enthalpies. All enthalpy values used for reference molecules and reactions were first verified to be accurate to within around 1 kcal mol-1 using high-level ab initio calculations. Enthalpies of formation were found to be -39.72 +/- 0.16 kcal mol-1 for acetaldehyde, -45.18 +/- 1.1 kcal mol-1 for propanal, and -49.27 +/- 0.16 kcal mol-1 for butanal. Enthalpies of formation for these three aldehydes, as well as for pentanal, hexanal, and heptanal, were calculated using the G3, G3B3, and CBS-APNO theoretical methods, in conjunction with bond-isodesmic work reactions. On the basis of the results of our thermodynamic cycles, theoretical calculations using isodesmic work reactions, and existing experimental measurements, we suggest that the best available formation enthalpies for the aldehydes acetaldehyde, propanal, butanal, pentanal, hexanal, and heptanal are -39.72, -45.18, -50.0, -54.61, -59.37, and -64.2 kcal mol-1, respectively. Our calculations also identify that the literature enthalpy of formation of crotonaldehyde is in error by as much as 1 kcal mol-1, and we suggest a value of -25.1 kcal mol-1, which we calculate using isodesmic work reactions. Bond energies for each of the bonds in the aldehydes up to pentanal were calculated at the CBS-APNO level. Analysis of the BDEs reveals the R-CH(2)CH=O to be the weakest bond in all aldehydes larger than acetaldehyde, due to formation of the resonantly stabilized vinoxy radical (vinyloxy radical/formyl methyl radical). It is proposed that the vinoxy radical as well as the more commonly considered formyl and acetyl radicals are important products of aldehyde combustion and oxidation, and the reaction pathways of the vinoxy, formyl, and acetyl radicals are discussed. Group additivity values for the carbon-oxygen-hydrogen groups common to the aldehydes are also determined. Internal rotor profiles and electrostatic potential surfaces are used to study the dipole induced dipole-dipole interaction in the synperiplanar conformation of propanal. It is proposed that the loss of this dipole-dipole interaction in RC(.-)HCH(2)CH=O radicals causes a ca. 1-2 kcal mol-1 decrease in the aldehyde C-H and C-C bond energies corresponding to RC(.-)HCH(2)CH=O radical formation.     

Thermochemistry of 2-methylbenzoxazole and 2,5-dimethylbenzoxazole: an experimental and computational study

The standard (p° = 0.1 MPa) molar energies of combustion of 2-methylbenzoxazole and 2,5-dimethylbenzoxazole were measured by static-bomb combustion calorimetry. The standard molar enthalpies of vapourization, at T = 298.15 K, were obtained from high-temperature Calvet microcalorimetry. The experimental results enable the calculation of the standard molar enthalpies of formation in the gaseous state, at T = 298.15 K, for both compounds, being the results discussed in terms of structural and energetic contributions. The theoretically estimated gas-phase enthalpies of formation were calculated from high-level ab initio molecular orbital calculations at the G3(MP2)//B3LYP level of theory. The computed values compare very well with the experimental results obtained in this work and show that the 2,5-dimethylbenzoxazole is enthalpically the most stable compound. Furthermore, this composite approach was also used to obtain information about the gas-phase basicities, proton and electron affinities and adiabatic ionization enthalpies.     

A mechanistic and kinetic study on the decomposition of morpholine

The combustion chemistry of morpholine (C(4)H(8)ONH) has been experimentally investigated recently as a representative model compound for O- and N-containing structural entities in biomass. Detailed profiles of species indicate the self-breakdown reactions prevailing over oxidative decomposition reactions. In this study, we derive thermodynamic and kinetic properties pertinent to all plausible reactions involved in the self-decomposition of morpholine and its derived morphyl radicals as a crucial task in the development of comprehensive combustion mechanism. Potential energy surfaces have been mapped out for the decomposition of morpholine and the three morphyl radicals. RRKM-based calculations predict the self-decomposition of morpholine to be dominated by 1,3-intramolecular hydrogen shift into the NH group at all temperatures and pressures. Self-decomposition of morpholine is shown to provide pathways for the formation of the experimentally detected products such as ethenol and ethenamine. Energetic requirements of all self-decomposition of morphyl radicals are predicted to be of modest values (i.e., 20-40 kcal/mol) which in turn support the occurrence of breaking-down reactions into two-heavy-atom species and the generation of doubly unsaturated four-heavy-atom segments. Calculated thermochemical parameters (in terms of standard enthalpies of formation, standard entropies, and heat capacities) and kinetic parameters (in terms of reaction rate constants at a high pressure limit) should be instrumental in building a robust kinetic model for the oxidation of morpholine.     

Methyl-and tert-butyl-substituted hydroquinones and semiquinone radicals: Bond strength estimates, enthalpy of formation, and the rate constants of their reactions with peroxy radicals

The strength of the O-H bonds (D) in hydroquinone (HQH) and its alkyl derivatives has been estimated by the intersecting parabolas method using rate constants known for the reactions of these compounds with the styrene peroxy radical. For unsubstituted HQH, D = 352.6 kJ/mol; for substituted HQH derivatives, D = 349.9 (Me), 346.9 (2,5-Me₂), 343.0 (Me₃), 347.6 (CMe₃), and 340.2 (2,5-(CMe₃)₂) kJ/mol. The enthalpies of formation of these HQH derivatives have been calculated. The O-H bond strengths in the semiquinone radicals (HQ^.) resulting from the above HQH derivatives have been calculated using a thermochemical equation to be $D_{HQ^. } $ = 236.7, 237.4, 239.8, 244.7, 240.1, and 247.5 kJ/mol, respectively. Rate constants have been determined for the reactions of the hydroquinones with tertiary and secondary peroxy radicals and HOO^. at 323 K. The rate constants of the reactions between HOO^. and benzoquinones and the relative reactivities of the HQ^. radicals in their reactions with ROO^. have been estimated.     

Competition of monomolecular and bimolecular reactions of the alkyl radicals of artemisinin

The competition between monomolecular and bimolecular reactions of alkyl radicals of artemisinin is considered theoretically. The enthalpies of these reactions are calculated. The activation energies and rate constants of intramolecular hydrogen atom transfer, of the decyclization of the alkyl radicals of artemisinin, and of the bimolecular reactions of these radicals with C-H, S-H, and O-H bonds of biological substrates and their analogues are calculated in the framework of the parabolic model. The intramolecular hydrogen transfer reactions proceed at the highest rate. The bimolecular reactions occur somewhat less rapidly. The fastest of them are the reactions of the alkyl radicals with the thio groups of cysteine. The decyclization reactions of all artemisinin alkyl radicals are very slow.     

Enthalpies of formation and bond dissociation energies of lower alkyl hydroperoxides and related hydroperoxy and alkoxy radicals

The enthalpies of formation and bond dissociation energies, D(ROO-H), D(RO-OH), D(RO-O), D(R-O 2) and D(R-OOH) of alkyl hydroperoxides, ROOH, alkyl peroxy, RO, and alkoxide radicals, RO, have been computed at CBS-QB3 and APNO levels of theory via isodesmic and atomization procedures for R = methyl, ethyl, n-propyl and isopropyl and n-butyl, tert-butyl, isobutyl and sec-butyl. We show that D(ROO-H) approximately 357, D(RO-OH) approximately 190 and D(RO-O) approximately 263 kJ mol (-1) for all R, whereas both D(R-OO) and D(R-OOH) strengthen with increasing methyl substitution at the alpha-carbon but remain constant with increasing carbon chain length. We recommend a new set of group additivity contributions for the estimation of enthalpies of formation and bond energies.     

Combined experimental and computational study of the thermochemistry of the fluoroaniline isomers

The standard (p degrees = 0.1 MPa) molar enthalpies of formation in the condensed phase of all the fluoroanilines, with the exception of the 2,3,5-trifluoroaniline compound, were derived from the standard molar energies of combustion in oxygen at T = 298.15 K, measured by rotating bomb combustion calorimetry. Calvet high-temperature vacuum sublimation experiments were performed to measure their enthalpies of vaporization or sublimation. These experiments allowed the determination of the standard molar enthalpies of formation in the gaseous phase and at T = 298.15 K. These values are also compared with estimates based on G3MP2B3 and BP86/6-31+G(d) computations, which have been extended also to the fluoroaniline that was not studied experimentally. The results are in close agreement with a mean deviation of approximately 3 kJ.mol-1. The largest difference between experimental and G3MP2B3 values is found for the pentafluoroaniline (-7.0 kJ.mol-1). For the three monofluoroanilines, the composite approach has been used also to compute gas-phase acidities, electron and proton affinities, ionization enthalpies and N-H bond dissociation enthalpies. The computed values compare well with available experimental results supporting the new computed data.     

The enthalpies of formation and reorganization of aromatic radicals

The enthalpies of formation of some biphenyl derivatives were determined. A "double difference" method for calculating the enthalpies of formation of aromatic radicals and the bond dissociation energies was proposed. The enthalpies of formation of the radicals biphenyl, diphenyl oxide, and phenyl oxide were determined. The energies of reorganization of these radicals as well as phenyl and 4-, 3-, and 2-pyridyls were calculated. The sums of the energies of the chemical bonds in the molecular moieties transformed into radicals upon the decomposition of chemical compounds were found to be constant for different compounds. The energies of the chemical bonds in arenes were determined.     

Intramolecular reactions of free radicals formed from artemisinin

Two cyclic alkoxyl radicals are formed as a result of peroxide bridge scission in artemisinin. Intramolecular reactions of these radicals induce the cascade of reactions of isomerization, decyclization, and decomposition of formed free radicals. It includes 14 reactions of intramolecular free radical hydrogen transfer, 17 reactions of decyclization of alkoxyl and alkyl radicals, and 4 reactions of decomposition of alkoxyl, acyl, and carboxyl radicals. The enthalpies of these 35 reactions are calculated. Using intersection parabolas method, activation energies and rate constants of all these reactions are calculated. The most rapid reactions are selected for every intermediate free radical. © 2005 Wiley Periodicals, Inc. Int J Chem Kinet 37: 554–565, 2005     

Standard Enthalpies of Formation of 2,6-Di-tert-butyl4-methylphenol and 3,5-Di-tert-butylphenol and Their Phenoxy Radicals

The standard (p^o = 0.1 MPa) enthalpies of formation of 2,6-di-tert-butyl-4-methylphenol and 3,5-di-tert-butylphenol in the gaseous phase, –315.5 ± 4.4 kJ mol^–1 and –312.7 ± 4.6 kJ mol^–1, respectively, were derived from the standard enthalpies of combustion, in oxygen, at 298.15 K, measured by static bomb combustion calorimetry, and from the standard enthalpies of sublimation, at 298.15 K, measured by Calvet microcalorimetry. The O—H bond dissociation enthalpies in those compounds were determined in benzene by photoacoustic calorimetry, leading to the standard enthalpies of formation of the gaseous phenoxy radicals: –189 ± 8 kJ mol^–1 and –154 ± 6 kJ mol^–1, respectively. These results were used to calculate enthalpies of substituent redistribution reactions, which are proposed as a method to estimate new data for substituted phenols.     

A DFT‐Based Investigation of Hydrogen Abstraction Reactions from Methylated Polycyclic Aromatic Hydrocarbons

The growth of polycyclic aromatic hydrocarbons (PAHs) is in many areas of combustion and pyrolysis of hydrocarbons an inconvenient side effect that warrants an extensive investigation of the underlying reaction mechanism, which is known to be a cascade of radical reactions. Herein, the focus lies on one of the key reaction classes within the coke formation process: hydrogen abstraction reactions induced by a methyl radical from methylated benzenoid species. It has been shown previously that hydrogen abstractions determine the global PAH formation rate. In particular, the influence of the polyaromatic environment on the thermodynamic and kinetic properties is the subject of a thorough exploration. Reaction enthalpies at 298 K, reaction barriers at 0 K, rate constants, and kinetic parameters (within the temperature interval 700–1100 K) are calculated by using B3LYP/6‐31+G(d,p) geometries and BMK/6‐311+G(3df,2p) single‐point energies. This level of theory has been validated with available experimental data for the abstraction at toluene. The enhanced stability of the product benzylic radicals and its influence on the reaction enthalpies is highlighted. Corrections for tunneling effects and hindered (or free) rotations of the methyl group are taken into account. The largest spreading in thermochemical and kinetic data is observed in the series of linear acenes, and a normal reactivity–enthalpy relationship is obtained. The abstraction of a methyl hydrogen atom at one of the center rings of large methylated acenes is largely preferred. Geometrical and electronic aspects lie at the basis of this striking feature. Comparison with hydrogen abstractions leading to arylic radicals is also made.     

Thermal,photochemical and mass spectral reactions of 2-ethyl-5-methyl-1-pyrroline

Pyrolysis of 2-ethyl-5-methylpyrroline ( 1 ) results in formation of 2,5-dimethylpyrrole, 2-ethyl-5-methylpyrrole, 2-ethylpyrrole and other minor products. Loss of a hydrogen atom or methyl radicals is suggested as the first step in these reactions. Support for the former comes from hydrogen atom abstraction by photo-excited benzophenone. The mass spectral reactions of 1 are briefly considered.     

Correlations between F NMR chemical shifts and bond dissociation energies, enthalpies of formation and group electronegativities

Correlations between ¹⁹F NMR chemical shifts (Φ) in fluorohalohydrocarbons and enthalpies of formation, bond dissociation energies, group contribution to enthalpies of formation and enthalpies of formation of free radicals are presented. A good correlation between these properties has been found with the square root of Φ. A relationship between fluorine chemical shifts and group electronegativities is also discussed.     

DFT evidence for a stepwise mechanism in the O-neophyl rearrangement of 1,1-diarylalkoxyl radicals

Hybrid DFT calculations of the potential energy surface (PES) relative to the O-neophyl rearrangement of a series of ring-substituted 1,1-diarylalkoxyl radicals have been carried out at the UB3LYP/6-31G(d) level of theory. On the basis of the computational data, the rearrangement can be described as a consecutive reaction of the type a <--/--> b --> c (see above graphic), and the steady-state approximation could be applied in all cases to the intermediate b. The first-order rearrangement rate constants [kobs = k1k2/(k-1 + k2)] were thus obtained from the computed activation free-energies and were compared with the experimental rate constants measured previously in MeCN solution by laser flash photolysis. An excellent agreement is observed along the two series, which strongly supports the hypothesis that the O-neophyl rearrangement of 1,1-diarylalkoxyl radicals proceeds through the formation of the reactive 1-oxaspiro [2,5]octadienyl radical intermediate. This is in contrast to previous hypotheses that involve either a long-lived intermediate or the absence of this intermediate along the reaction path. The calculated rearrangement free-energies decrease upon going from the methoxy-substituted radical (Delta G degrees = -16.4 kcal x mol-1) to the nitro-substituted one (Delta G degrees = -21.8 kcal x mol-1), which follows a trend that is similar to the one observed for the CAr-O bond dissociation enthalpies (BDEs) of ring-substituted anisoles. This evidence indicates that in the O-neophyl rearrangement the effect of ring substituents on the strength of the newly formed CAr-O bond plays an important role.     

Direct dynamics studies on hydrogen abstraction reactions of CH3CHFCH3 and CH3CH2CH2F with OH radicals

The hydrogen abstraction reactions of CH3CHFCH3 and CH3CH2CH2F with the OH radicals have been studied theoretically by a dual-level direct dynamics method. The geometries and frequencies of all the stationary points are optimized by means of the DFT calculation. There are complexes at the reactant side or exit route, indicating these reactions may proceed via indirect mechanisms. To improve the reaction enthalpy and potential barrier of each reaction channel, the single point energy calculation is performed by the MC-QCISD/3 method. The rate constants are evaluated by canonical variational transition state theory (CVT) with the small-curvature tunneling correction method (SCT) over a wide temperature range 200-2000 K. The canculated CVT/SCT rate constants are consistent with available experimental data. The results show that both the variation effect and the SCT contribution play an important role in the calculation of the rate constants. For reactions CH3CHFCH3 and CH3CH2CH2F with OH radicals, the channels of H-abstraction from -CHF- and -CH2- groups are the major reaction channels, respectively, at lower temperature. Furthermore, to further reveal the thermodynamics properties, the enthalpies of formation of reactants CH3CHFCH3, CH3CH2CH2F, and the product radicals CH3CFCH3, CH3CHFCH2, CH3CH2CHF, CH3CHCH2F, and CH2CH2CH2F are studied using isodesmic reactions.     

Thermochemistry of biphenylcarboxylic and dicarboxylic acids. A combined experimental and theoretical study

The standard molar enthalpies of combustion and sublimation of 2- and 4-biphenylcarboxylic acid, 2,2'- and 4,4'-biphenyldicarboxylic acid were measured and the gas-phase enthalpies of formation, at T= 298.15 K, were determined. Ab initio calculations were performed and a theoretical study on molecular structure of all the biphenyl acid isomers has been carried out. Calculated enthalpies of formation using appropriate isodesmic reactions are compared with experimental values, and a good agreement is observed. Estimates of enthalpies of formation for the isomers, which were not studied experimentally, are presented. All the acids containing at least one ortho COOH are comparatively less stable than their isomers having just meta or para COOH group(s).     

Toluene combustion: reaction paths, thermochemical properties, and kinetic analysis for the methylphenyl radical + O2 reaction

Aromatic compounds such as toluene and xylene are major components of many fuels. Accurate kinetic mechanisms for the combustion of toluene are, however, incomplete, as they do not accurately model experimental results such as strain rates and ignition times and consistently underpredict conversion. Current kinetic mechanisms for toluene combustion neglect the reactions of the methylphenyl radicals, and we believe that this is responsible, in part, for the shortcomings of these models. We also demonstrate how methylphenyl radical formation is important in the combustion and pyrolysis of other alkyl-substituted aromatic compounds such as xylene and trimethylbenzene. We have studied the oxidation reactions of the methylphenyl radicals with O2 using computational ab initio and density functional theory methods. A detailed reaction submechanism is presented for the 2-methylphenyl radical + O2 system, with 16 intermediates and products. For each species, enthalpies of formation are calculated using the computational methods G3 and G3B3, with isodesmic work reactions used to minimize computational errors. Transition states are calculated at the G3B3 level, yielding high-pressure limit elementary rate constants as a function of temperature. For the barrierless methylphenyl + O2 and methylphenoxy + O association reactions, rate constants are determined from variational transition state theory. Multichannel, multifrequency quantum Rice-Ramsperger-Kassel (qRRK) theory, with master equation analysis for falloff, provides rate constants as a function of temperature and pressure from 800 to 2400 K and 1 x 10(-4) to 1 x 10(3) atm. Analysis of our results shows that the dominant pathways for reaction of the three isomeric methylphenyl radicals is formation of methyloxepinoxy radicals and subsequent ring opening to methyl-dioxo-hexadienyl radicals. The next most important reaction pathway involves formation of methylphenoxy radicals + O in a chain branching process. At lower temperatures, the formation of stabilized methylphenylperoxy radicals becomes significant. A further important reaction channel is available only to the 2-methylphenyl isomer, where 6-methylene-2,4-cyclohexadiene-1-one (ortho-quinone methide, o-QM) is produced via an intramolecular hydrogen transfer from the methyl group to the peroxy radical in 2-methylphenylperoxy, with subsequent loss of OH. The decomposition of o-QM to benzene + CO reveals a potentially important new pathway for the conversion of toluene to benzene during combustion. A number of the important products of toluene combustion proposed in this study are known to be precursors of polyaromatic hydrocarbons that are involved in soot formation. Reactions leading to the important unsaturated oxygenated intermediates identified in this study, and the further reactions of these intermediates, are not included in current aromatic oxidation mechanisms.     

A determination of antioxidant efficiencies using ESR and computational methods

Using Transition-State Theory, experimental rate constants, determined over a range of temperatures, for reactions of Vitamin E type antioxidants are analysed in terms of their enthalpies and entropies of activation. It is further shown that computational methods may be employed to calculate enthalpies and entropies, and hence Gibbs free energies, for the overall reactions. Within the linear free energy relationship (LFER) assumption, that the Gibbs free energy of activation is proportional to the overall Gibbs free energy change for the reaction, it is possible to rationalise, and even to predict, the relative contributions of enthalpy and entropy for reactions of interest, involving potential antioxidants. A method is devised, involving a competitive reaction between *CH3 radicals and both the spin-trap PBN and the antioxidant, which enables the relatively rapid determination of a relative ordering of activities for a series of potential antioxidant compounds, and also of their rate constants for scavenging *CH3 radicals (relative to the rate constant for addition of *CH3 to PBN).     

Local and global uncertainty analyses of a methane flame model

Local and global uncertainty analyses of a flat, premixed, stationary, laminar methane flame model were carried out using the Leeds methane oxidation mechanism at lean (phi = 0.70), stoichiometric (phi = 1.00), and rich (phi = 1.20) equivalence ratios. Uncertainties of laminar flame velocity, maximal flame temperature, and maximal concentrations of radicals H, O, OH, CH, and CH(2) were investigated. Global uncertainty analysis methods included the Morris method, the Monte Carlo analysis with Latin hypercube sampling, and an improved version of the Sobol' method. Assumed probability density functions (pdf's) were assigned to the rate coefficients of all the 175 reactions and to the enthalpies of formation of the 37 species. The analyses provided the following answers: approximate pdf's and standard deviations of the model results, minimum and maximum values of the results at any physically realistic parameter combination, and the contribution of the uncertainty of each parameter to the uncertainty of the model result. The uncertainty of a few rate parameters and a few enthalpies of formation causes most of the uncertainty of the model results. Most uncertainty comes from the inappropriate knowledge of kinetic data, but the uncertainty caused by thermodynamic data is also significant.