Physical factors determining the activation energy of alkyl radical addition to unsaturated compounds

A parabolic model of the transition state is used for the analysis of experimental data (rate constants and activation energies) for reactions of addition of alkyl and phenyl radicals to multiple bonds of unsaturated compounds. The parameters describing the activation energy as a function of the enthalpy of the reactions were calculated from the experimental data. The activation energy depends also on the strength of the forming C−C bond, the presence of π-bonds in the α-position near the attacked C=C bond and the presence of polar groups in the monomer and radical. The empirical dependence of the activation energy of a thermoneutral addition reactionE _e0 on the dissociation energyD _e of the forming C−C bond was obtained:E _e0=(5.95±0.06)·10⁻⁴ D _e ² kJ mol⁻¹, indicating the important role of triplet repulsion in the formation of the transition state of radical addition. The contribution of the polar interaction to the activation energy of addition of polar radicals to polar monomers was calculated. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 445–450, March, 1999.     

Ab initio study on alkyl radical decomposition and alkyl radical addition to olefins

The β bond dissociation of alkyl radicals and their reverse reactions, the addition of alkyl radicals to olefins were studied by G3MP2 level of theory to obtain a consistent kinetic data set. Both reaction families can be classified depending on the type of radical formed by β bond scission, namely the CH₃, primary, secondary tertiary radical formed. The kinetics of the reaction classes were described by only a limited number of Arrhenius parameters. The unified A factor of 10^13.7 s⁻¹ was found for all β bond dissociations. The Arrhenius activation energies are 125, 121, 113 and 103 kJ mol⁻¹, for methyl, primary, secondary, and tertiary radicals, respectively. The activation energies of 32, 25 and 18 kJ mol⁻¹ are calculated for the terminal addition of primary (including methyl), secondary, and tertiary radicals to olefins, respectively. The biologically important nonterminal radical additions to olefins have higher barriers of 37, 31 and 35 kJ mol⁻¹, respectively. At room temperature both strongly exothermic additions can compete with H-atom abstraction. New groups for Benson’s group additivity rules were defined to describe activation parameters for the β bond dissociation reactions. The group values were calculated by using the ab initio heats of formation of transition state structures.     

Kinetic parameters and geometry of the transition state of acyl radical decarbonylation

Experimental data on acyl radical decomposition reactions (RC^·O → R^· + CO, where R = alkyl or aryl) are analyzed in terms of the intersecting parabolas method. Kinetic parameters characterizing these reactions are calculated. The transition state of methyl radical addition to CO at the C atoms is calculated using the DFT method. A semiempirical algorithm is constructed for calculating the transition state geometry for the decomposition of acyl radicals and for the reverse reactions of R^· addition to CO. Kinetic parameters (activation energy and rate constant) and geometry (interatomic distances in the transition state) are calculated for 18 decomposition reactions of structurally different acyl radicals. A linear correlation between the interatomic distance r ^#(C…C) (or r ^#(C…O)) in the transition state the enthalpy of the reaction (δH _e) is established for acyl decomposition reactions (at br _e = const). A comparative analysis of the enthalpies, activation energies, and interatomic distances in the transition state is carried out for the decomposition and formation of acyl, carboxyl, and formyl radicals.     

The reactivity of phenoxyl radicals of bioantioxidants in the abstraction reactions

The enthalpies, activation energies, and rate constants for the reactions of 15 phenoxyl radicals derived from natural bioantioxidants with hydroperoxides, C-H bonds of linoleic acid, SH-groups of l-cysteine, and O-H bonds of α-tocopherol (60 reactions) were calculated. The activation energies were calculated using the model of intersecting parabolas. The interatomic distances in the reaction sites of the transition states of the studied reactions were calculated. The factors affecting the reactivity of these radicals are discussed. The activation energy of the reaction of oxygen with the O-H bond of the 1,2-dihydroxybenezene semiquinone radical was estimated.     

Polar and solvation effects in reactions of oxygen atoms and hydroxyl and alkoxyl radicals with oxygen-containing compounds

Experimental data on the activation energies of reactions of H-abstraction from oxygencontaining compounds by oxygen atoms and hydroxyl and alkoxyl radicals in the gas and liquid phases have been analyzed by means of the parabolic model of the transition state. The contribution of polar interaction to the activation energies of the reactions has been calculated. The contribution of solvation to the activation energy has been calculated by comparison of the reaction parameters of the respective reaction in the liquid and gas phases.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 38–42, January, 1994.     

Kinetics of the interaction of ketyl and semiquinone radicals with dioxygen. Concerted electron and proton transfer involving ketyl and semiquinone radicals

Kinetics of the interaction of ketyl and neutral semiquinone radicals with dioxygen was studied by the flash photolysis technique. The reactivity of neutral semiquinone radicals in the transfer of a hydrogen atom to O₂ is lower than that of ketyl radicals and increases as the reduction ability of the radicals increases, which give evidence for the charge transfer from the radicals to O₂ in the transition state of the reaction. The deuterium kinetic isotope effect of the reaction (up to 2.6) suggests considerable weakening of the O−H bond of the seminquinone radical in the transition state. A cyclic structure of the transition state similar to that in the reactions of ketyl radicals with hydrogen atom acceptors is proposed. In aprotic volvents, solvation has essentially no effect on the reactivity of neutral anthrasemiquinone radicals up to solvent nucleophilicityB≈240. In solvents with higher nucleophilicity and in protic solvents, their reactivity drops sharply. Hydrogen atom transfer reactions involving ketyl and neutral semiquinone radicals are shown to involve concerted electron and proton transfers, and to have transition states in which the partial transfer of an electron and a proton from the ketyl or semiquinone radical to an acceptor occurs. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 6, pp. 1131–1137, June, 1997.     

Reactivity of quinones as alkyl radical acceptors

The enthalpies of the addition of 11 alkyl radicals to ortho-and para-benzoquinones and substituted para-benzoquinones and the enthalpies of formation of various alkoxyphenoxyl radicals have been calculated. Experimental data for the addition of alkyl radicals to quinones are analyzed in terms of the intersection of two parabolic potential curves, and parameters characterizing this class of reactions are calculated. The classical potential barrier of the thermally neutral reaction of alkyl radical addition to benzoquinone is E _e,0 = 82.1 kJ/mol. This class of reactions is compared to other classes of free-radical addition reactions. The interaction between the electrons of the reaction center and the π electrons of the aromatic ring is a significant factor in the activation energy. Activation energies, rate constants, and the geometric parameters of the transition state have been calculated for 40 reactions of alkyl radical addition to quinones. Strong polar interaction has been revealed in the addition of polar macroradicals to quinones, and its contribution to the activation energy has been estimated. Kinetic parameters, activation energies, and rate constants have been calculated for the reverse reactions of alkoxyphenoxyl radical decomposition to quinone and alkyl. The competition between chain termination and propagation reactions in alkoxyphenol-inhibited hydrocarbon oxidation is discussed.     

Cyclopropane ring opening in the reaction of methylenecyclopropane with silyl radicals stabilized on an activated Aerosil surface

Alkyl type radicals stable at room temperature and incorporating a double bond not conjugated with the free valence, ≡Si−C(=CH₂)−CH₂−CH₂, are formed in the reaction of methylenecyclopropane with silyl radicals (≡SiO)₃Si on an activated Aerosil surface. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 5, pp. 1065–1066, May, 1997.     

The reactivity of ketyl and alkyl radicals in reactions with carbonyl compounds

A parabolic model of bimolecular radical reactions was used for analysis of the hydrogen transfer reactions of ketyl radicals: >C·OH+R¹COR²→>C=O+R¹R²C·OH. The parameters describing the reactivity of the reagents were calculated from the experimental data. The parameters that characterize the reactions of ketyl and alkyl radicals as hydrogen donors with olefins and with carbonyl compounds were obtained: >C·OH+R¹CH=CH₂→>C=O+R¹C·HCH₃; >R¹CH=CH₂+R²C·HCH₂R³→R²C·HCH₃+R²CH=CHR³. These parameters were used to calculate the activation energies of these transformations. The kinetic parameters of reactions of hydrogen abstraction by free radicals and molecules (adelhydes, ketones, and quinones) from the C−H and O−H bonds were compared. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 11, pp. 2178–2184, November, 1998.     

Relations Between Structure and Reactivity in Free-Radical Chemistry

An analysis of the relations between structure and reactivity in free-radical chemistry has shown that the usual interpretation of reactivities by means of the stability of the radicals involved is greatly simplified and often incorrect. The C? X bond energies of the alkanes and simple alkyl derivatives can be explained qualitatively by strain effects in the ground state on the basis of the VSEPR theory and nonbonding interactions. To be able to explain reactivities in free-radical chemistry, it is necessary to deduce information about the geometry of the transition states during free-radical formation from experimental measurements. The relations between structure and reactivity in free-radical chemistry are interpreted in terms of bond dissociation energies, as well as polar and steric effects.     

Activation and reaction volumes of the reactions of <Emphasis Type="Italic">o</Emphasis>-and <Emphasis Type="Italic">p</Emphasis>-nitrophenylsulfenyl chlorides with styrene and cyclohexene in some solvents

The effect of hydrostatic pressure below 1000 kg cm⁻² on the rate of reactions of o-and p-nitrophenylsulfenyl chlorides with styrene and cyclohexene was studied. The activation and reaction volumes (cm³ mol⁻¹) for the reactions of o-nitrophenylsulfenyl chloride with styrene in acetonitrile (−23.1 and −23.6), 1,2-dichloroethane (−29.2 and −24.7), chlorobenzene (no, −20.2), and anisole (−25.1 and −21.2) and for the reaction of p-nitrophenylsulfenyl chloride with styrene in carbon tetrachloride (−39.5±1.5 and −22.0) were determined. In carbon tetrachloride the activation volumes for the reactions of cyclohexene with o-and p-nitrophenylsulfenyl chlorides (−37.7±2.0 and −40.9±1.2 cm³ mol⁻¹, respectively) are almost the same and coincide with the data for the reactions with styrene. The considerable decrease in the volume of the transition state in the nonpolar solvent is considered as a consequence of the enhanced electrostriction of carbon tetrachloride in the solvate sphere of the transition state of the reaction, which excludes the nonpolar transition state of the sulfuran type. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 477–480, March, 2007.     

The Impact of Resonance Stabilization on the Intramolecular Hydrogen‐Atom Shift Reactions of Hydrocarbon Radicals

A series of intramolecular H‐atom shift reactions of both alkenyl and allylic radicals were investigated by using CBS‐QB3 electronic structure calculations. In the first set of reactions, an alkyl radical site was converted into an allylic radical site. In the second set, an allylic radical was converted into another allylic radical. The results are discussed in the context of a Benson‐type model to examine the impact of the transition‐state partial resonance stabilization on both the activation energies and the pre‐exponential factors. In most cases, the differences in the activation energies relative to those for the analogous alkyl radicals are primarily due to the barriers of the bimolecular reaction component of the activation energy. For the first set of reactions, there is additional entropy loss relative to the alkyl radical analogues. This additional loss of entropy may be smaller than some previous estimates. The pre‐exponential factors for the second set of reactions are generally similar to those of the analogous alkyl radical reactions (once the double bond in the transition state is accounted for).     

Geometry of the transition state of radical abstraction reactions involving Si-H, Ge-H, and Sn-H Bonds

Transition-state interatomic distances in the reactions C˙H₃+SiH₄, Si˙H₃+SiH₄, C˙H₃+GeH₄, and C˙H₃+SnH₄ are calculated by the B3LYP density functional and intersecting parabolas methods. A semiempirical algorithm is developed for the calculation of the Y...H and C...H distances in the transition state of the radical abstraction reactions R˙+YH involving silanes, germanes, and stannanes and the reverse reactions of silyl, germanyl, and stannyl radicals with hydrocarbons. This algorithm is used to calculate interatomic distances in these reactions. An analysis of the calculated data shows that the Y...H and C...H distances in these reactions depend on the following factors: the enthalpy of reaction, the radius of the Y atom (Y = C, Si, Ge, Sn), and four-electron repulsion during the attack of a radical on the C-H bond adjacent to the double bond. Empirical equations relating the interatomic distances to the enthalpy of reaction and to the Y-R bond length are set up.     

Silylboranes as new sources of silyl radicals for chain-transfer reactions

Various silylboranes, which were outfitted with a catecholborane moiety at one end and a (Me(3)Si)(3)Si moiety at the other end of a carbon chain, were prepared through the hydroboration of the corresponding unsaturated silanes. The C-centered radical species generated from these silylboranes efficiently cyclized to provide, through a 5-exo intramolecular homolytic substitution at the silicon center, the corresponding silacycle and a Me(3)Si radical that was subsequently trapped by sulfonyl acceptors. These cyclizations proceeded at unprecedented rates, due, in part, to a strong gem-dialkyl effect that was attributable to the presence of bulky substituents on a quaternary center located on the chain. In parallel, we designed arylsilylboranes that produced silyl radicals through a 1,5-hydrogen transfer. Such silyl radicals may be valuable radical chain carriers, for instance, in oximation reactions of alkyl halides. Finally, computational studies allowed calculation of activation barriers of the homolytic substitution step and additionally illustrated that the overall reaction mechanism involved a transition state in which the attacking carbon center, the central silicon atom, and the Me(3)Si leaving group were collinear.     

Competition between mono-and bimolecular reactions of artemisinin alkoxyl radicals

The competition between intramolecular and bimolecular reactions of alkoxyl radicals formed from artemisinin was theoretically analyzed. The enthalpies of these reactions were calculated. The activation energies and rate constants of reactions of intramolecular hydrogen atom transfer, decyclization, and decomposition of alkoxyl radicals of artemisinin and several its derivatives, as well as the activation energies and rate constants of reactions of these radicals with the C-H, S-H, and O-H bonds in biological substrates and their analogs were calculated by the intersecting parabolas method The fastest reactions of artemisinin alkoxyl radicals were identified. The full kinetic scheme of transformation of these radicals was proposed. Artemisinin radicals with the free valence on the carbon atom are predominantly formed due to the transformation of the artemisininoxyl radicals. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1502–1510, September, 2006.     

Kinetics and thermodynamics of the exchange reactions of peroxy radicals with hydroperoxides

The enthalpies and equilibrium constants of the exchange reactions of peroxy radicals with hydroperoxides of various structures are calculated. The experimental data on the reactions of hydrogen atom abstraction by the peroxy radicals from the hydroperoxides are analyzed, and the kinetic parameters characterizing these reactions are calculated using the intersecting parabolas method. The activation energies and rate constants for nine reactions of H atom abstraction by a peroxy radical from the OOH group of a peroxide are calculated using the above parameters. The geometric parameters of the transition states for the reactions are calculated. The low triplet repulsion plays an important role in the fast occurrence of the reactions. The polar interaction in the transition state is manifested in the reactions of the peroxy radicals with hydroperoxides containing a polar group.     

First-principles prediction and interpretation of propagation and transfer rate coefficients

Propagation and transfer rate coefficients in free-radical polymerizations are calculated from first principles, using quantum calculations (both ab initio and semi-empirical) to determine geometries, frequencies, torsional potentials and energies of reactants and transition state, after which transition state theory yields the Arrhenius parameters. While activation energies can only be calculated for small species and with large computational resources, acceptable frequency factors (A) are obtained with relative ease provided that lower frequencies corresponding to torsions are treated as hindered rotors, not harmonic oscillators; this entails finding the torsional potential and exact evaluation of the corresponding partition function. Simple theory can be used to find A because this involves a ratio of partition functions of reactant and transition state, and because torsions (which are dominated by geometrical considerations) dominate A. A is determined by three modes in the transition state: rotation of the monomer about the forming bond, rotation of a “propylene”-group about the terminal C–C bond in the radical, and simultaneous bending of the two angles associated with the forming bond. Calculations on ethylene and acrolein give agreement with experiment. These studies explain some experimental observations. (i) Changing the penultimate unit gives a small but significant change in the torsion of two of the three modes dominating A, leading to a penultimate-unit effect of ca. a factor of 1–10. (ii) Deuteration affects the moments of inertia of the torsions, leading to changes in A in accord with experiment. (iii) A, but not the activation energy, changes predictably along a homologous series (e.g., methyl, butyl methacrylate). (iv) For a given monomer, A's for transfer to monomer and propagation are similar.     

Role of Radical Elimination Reactions with Concerted Fragmentation in the Chain Decomposition of Alkyl Nitrates

The reactions X? + HCR₂ONO₂ → XH + R₂C=O + ?NO₂ are very exothermic due to the cleavage of the weak N?O bond and the formation of the energy-intensive C=O bond. The quantum chemical calculation of the transition state of these reactions for X? = Et? and EtO? used as examples showed that they actually proceed in one elementary act as eliminations with concerted fragmentation. The kinetic parameters were estimated within the framework of the intersecting parabolas model; the parameters allow the calculation of the activation energy and rate constant from the enthalpy of the above reaction. For a series of reactions involving the Et?, EtO?, RO?₂, and ?NO₂ radicals, on the one hand, and a number of alkyl nitrates, on the other, their enthalpies, activation energies, and rate constants were calculated. Based on the data obtained, new kinetic schemes of the chain decomposition of alkyl nitrates involving eliminations with fragmentation were proposed.     

Parametric method three (PM3) study of the tautomerization of 2- pyridone systems

The parametric method three (PM3) has been used to predict the optimized geometries of the transition state involved in the tautomerization process of 2-pyridone, its 6-chloro derivative and carbostyril. The estimated activation energies for the hydrogen shift of the three compounds are 41.2, 41.3 and 44.9 kcal mol⁻¹, respectively. The effect of polar solvents on the tautomerization process has been discussed by consideration of the calculated dipole moments for the reactant, the transition state and the product. Examination of OH and NH bond orders reveals a point of inflection in each case in the vicinity of the transition state.     

A theoretical investigation of (−)-deprenyl (selegiline) as a radical scavenger

The chemical reactions between (−)-deprenyl and ·OH or ·OOH were studied using molecular orbital theory, with N,N-dimethylpropargylamine as a model. (−)-Deprenyl was confirmed to be a good radical scavenger. The active site was the acetylenic part and ·OH- or ·OOH was trapped on either acetylenic carbon. The activation energies were about 10–20 kcal/mol. The resulting ·OH- or ·OOH-adducts, still radicals, trapped further radicals on the remaining carbon of the acetylenic part. The final double trapping products were at extraordinarily lower energy levels than the original reactants by 50–70 kcal/mol. The secondary transition states were not detected, suggesting that the reactions occurred at once or in a cascade. Some results with the model system were verified by the results with the real (−)-deprenyl system. Received: 6 October 1999 / Accepted: 5 March 2000 / Published online: 21 June 2000