The lifetimes of gas phase CO2˙− and N2O˙− calculated from the transition probability of the autodetachment process A− → A + e−

A procedure to calculate the quantum mechanical transition probability of a unimolecular primary chemical process, A^? → A + e^? is investigated for the circumstance where A^? and A have different numbers of vibrational and rotational degrees of freedom (one is linear, the other not). A procedure is introduced to deal with the coupling between the vibrational and rotational motions. The proposed method was applied to calculating the lifetimes of CO₂^˙? and N₂O^˙? in the gas phase. The geometry optimizations and frequency calculations for CO₂, CO₂^˙?, N₂O, and N₂O^˙? are performed at HF, MP2, and QCISD(T) levels with 6-31G* or 6–31+G* basis sets, in order to obtain reliable geometric and spectroscopic information on these systems. Lifetimes are calculated for several of the lower vibrational–rotational states of the anions, as well as for the Boltzmann distribution of states at 298 K. The lifetime of the lowest vibrational–rotational state of CO₂^˙?, is 1.03 × 10^?4 s, and of the lowest vibrational state with rotational levels weighted by Boltzmann distribution at 298 K, 1.50 × 10^?4 s. These values are in good agreement with the experimental number, 9.0 ± 2.0 × 10^?5 s, and support the experimental evidence that CO₂^˙? was formed in its ground vibrational level by the techniques used. The lifetime of CO₂^˙? calculated with Boltzmann distribution over its vibrational and rotational levels at 298 K, is 1.51 × 10^?5 s. There are no direct measurements of the lifetime of N₂O^˙?, but it was estimated to be greater than 10^?4 s from experimental evidence. The predicted lifetimes of N₂O^˙?, at its lowest vibrational–rotational state (0 K) and lowest vibrational state with rotational levels weighted by the Boltzmann distribution at 298 K, are 238 and 19.1 s, respectively. The lifetime of N₂O^˙? at thermal equilibrium at 298 K is 6.66 × 10^?2 s, indicating that electron loss from the excited vibrational states of N₂O^˙? is significant. This study represents the first theoretical investigation of CO₂^˙? and N₂O^˙? lifetimes. © 1994 John Wiley & Sons, Inc.     

Solvent effects on the rate of reaction of Cl2˙− and SO4˙− radicals with unsaturated alcohols

Rate constants have been measured in several aqueous/organic solvent mixtures for the addition reaction of Cl₂^˙? radicals with 2-propen-1-o1 and 2-buten-1-o1 as a function of temperature and with 2, 3-dimethyl-2-butene at room temperature. The rate constants were in the range of 10⁶–10⁹ L mol^?1 s^?1, the activation energies were relatively low (1–10 kJ mol^?1), and the pre-exponential factors varied over the range log A = 7.9 to 9.4. The rate constants (k) decreased (by up to a factor of 30) upon increasing the fraction of organic solvent and log k correlated linearly with the dielectric constant for a given water/organic solvent system, but the lines for the different solvent systems had different slopes. A better correlation of log k was found with a combination of the solvatochromic factor, E_T(30), and the hydrogen-bond donor acidity factor, α. This suggests that the rate of reaction is influenced by the solvent polarity and also by specific solvation of the ionic reactant and product. Solvent effect on the reaction of SO₄^˙? with 2-propen-1-o1 was studied for comparison. © 1993 John Wiley & Sons, Inc.     

Structure and formation of gaseous [C4H6O]+˙ ions: 1—The enolic ions [CH2C(OH)?CHCH2]+˙ and [CH2CH?CHCH(OH)]+˙ and their relationship with their keto counterparts

The [C₄H₆O]^+˙ ion of structure [CH₂?CHCH?CHOH]^+˙ (a) is generated by loss of C₄H₈ from ionized 6,6-dimethyl-2-cyclohexen-1-ol. The heat of formation ΔH_f of [CH₂?CHCH?CHOH]^+˙ was estimated to be 736 kJ mol^?1. The isomeric ion [CH₂?C(OH)CH?CH₂]^+˙ (b) was shown to have ΔH_f, ? 761 kJ mol^?1, 54 kJ mol^?1 less than that of its keto analogue [CH₃COCH?CH₂]^+˙. Ion [CH₂?C(OH)CH?CH₂]^+˙ may be generated by loss of C₂H₄ from ionized hex-1-en-3-one or by loss of C₄H₈ from ionized 4,4-dimethyl-2-cyclohexen-1-ol. The [C₄H₆O]^+˙ ion generated by loss of C₂H₄ from ionized 2-cyclohexen-1-ol was shown to consist of a mixture of the above enol ions by comparing the metastable ion and collisional activation mass spectra of [CH₂?CHCH?CHOH]^+˙ and [CH₂?C(OH)CH?CH₂]^+˙ ions with that of the above daughter ion. It is further concluded that prior to their major fragmentations by loss of CH₃˙ and CO, [CH₂?CHCH?CHOH]⁺˙ and [CH₂?C(OH)CH?CH₂]^+˙ do not rearrange to their keto counterparts. The metastable ion and collisional activation characteristics of the isomeric allenic [C₄H₆O]^+˙ ion [CH₂?C?CHCH₂OH]^+˙ are also reported.     

Variation of the ℏω with the particle number and the appearance of “kinks” for atomic clusters

The dependence of the harmonic oscillator (HO) energy level spacing ?ω on the particle number N is studied analytically for atomic (metal) clusters on the basis of their electronic densities, parametrizing Ekardt's results (for sodium clusters) by means of a Fermi distribution. An interesting feature of such an approach is that it leads, under the assumptions made, to “kinks,” that is, to “marked discontinuities in the slope” of ?ω at the closed shells. These discontinuities diminish as N increases. For large N, ?ω becomes simply: ?ω?c₁N^?1/3+c₂N^?1. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Rate constants for reactions of SO4˙− radicals in acetonitrile

Rate constants have been measured for the reactions of the sulfate radical, SO₄^˙?, with alkanes, alkenes, alcohols, ethers, and amines in 95% acetonitrile solution. The rate constants were in the range of 10⁶ L mol^?1 s^?1 for the abstraction reactions and 10⁷?10⁹ L mol^?1 s^?1 for the addition and electron transfer reactions. These values are 20 to 80 times lower than those measured in aqueous solutions. Furthermore, the rate constants for the reactions of SO₄^˙? with the primary alcohols increase with the number of carbon atoms and then level off, in contrast to the behavior observed in aqueous solution, where the rate constant increases more sharply for the larger alcohols. © 1993 John Wiley & Sons, Inc.     

The methylamine radical cation [CH3NH2]+˙ and its stable isomer the methylenammonium radical cation [CH2NH3]+˙

The potential energy surface for the [CH₅N]^+˙ system has been investigated using ab initio molecular orbital calculations with large, polarization basis sets and incorporating valence-electron correlation. Two [CH₅N]^+˙ isomers can be distinguished: the well known methylamine radical cation, [CH₃NH₂]^+˙, and the less familiar methylenammonium radical cation, [CH₂NH₃]^+˙. The latter is calculated to lie 8 kJ mol^?1 lower in energy. A substantial barrier (176 kJ mol^?1) is predicted for rearrangement of [CH₂NH₃]^+˙ to [CH₃NH₂]^+˙. In addition, a large barrier (202 kJ mol^?1) is found for loss of a hydrogen radical from [CH₂NH₃]^+˙ via direct N—H bond cleavage to give the aminomethyl cation [CH₂NH₂]⁺. These results are consistent with the existence of the methylenammonium ion [CH₂NH₃]^+˙ as a stable observable species. The barrier to loss of a hydrogen radical from [CH₃NH₂]^+˙ is calculated to be 140 kJ mol^?1.     

Dissociation of the diphenylnitrile imine radical cation into benzonitrile and [phenylnitrene]+˙

The collision induced dissociation/mass analysed ion kinetic energy mass spectra of 2,5-diphenyltetrazole demonstrate the decay sequence [diphenyltetrazole]^+˙→ [diphenylnitrile imine]^+˙→ m/z 91. The m/z 91 ion was shown to be identical to the ion formed by loss of N₂ from the phenyl azide radical cation, thus suggesting the phenylnitrene structure for the m/z 91 ion.     

Elementary reaction analysis of the radical polymerization of α‐ethyl β‐N‐(α′‐methylbenzyl)itaconamates carrying (RS)‐ and (S)‐α‐methylbenzylaminocarbonyl groups

The polymerizations of α‐ethyl β‐N‐(α′‐methylbenzyl)itaconamates carrying (RS)‐ and (S)‐α‐methylbenzylaminocarbonyl groups (RS‐EMBI and S‐EMBI) with dimethyl 2,2′‐azobisisobutyrate (MAIB) were studied in methanol (MeOH) and in benzene kinetically and with electron spin resonance (ESR) spectroscopy. The initial polymerization rate (R_p) at 60 °C was given by R_p = k[MAIB]^{0.58 ± 0.05}[RS‐EMBI]^{2.4 ± 0.l} and R_p = k[MAIB]^{0.61 ± 0.05}[S‐EMBI]^{2.3 ± 0.l} in MeOH and R_p = k[MAIB]^{0.54 ± 0.05}[RS‐EMBI]^{1.7 ± 0.l} in benzene. The rate constants of initiation (k_df), propagation (k_p), and termination (k_t) as elementary reactions were estimated by ESR, where k_d is the rate constant of MAIB decomposition and f is the initiator efficiency. The k_p values of RS‐EMBI (0.50–1.27 L/mol s) and S‐EMBI (0.42–1.32 L/mol s) in MeOH increased with increasing monomer concentrations, whereas the k_t values (0.20?7.78 × 10⁵ L/mol s for RS‐EMBI and 0.18?6.27 × 10⁵ L/mol s for S‐EMBI) decreased with increasing monomer concentrations. Such relations of R_p with k_p and k_t were responsible for the unusually high dependence of R_p on the monomer concentration. The activation energies of the elementary reactions were also determined from the values of k_df, k_p, and k_t at different temperatures. R_p and k_p of RS‐EMBI and S‐EMBI in benzene were considerably higher than those in MeOH. R_p of RS‐EMBI was somewhat higher than that of S‐EMBI in both MeOH and benzene. Such effects of the kinds of solvents and monomers on R_p were explicable in terms of the different monomer associations, as analyzed by ¹H NMR. The copolymerization of RS‐EMBI with styrene was examined at 60 °C in benzene. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 1819–1830, 2003     

The potential energy surface for the [C2H2O]+˙ system: The ketene radical cation [CH2CO]+˙ and its isomers

Ab initio molecular orbital calculations with large, polarization basis sets and incorporating valence electron correlation have been employed to examine the [C₂H₂O]^+˙ potential energy surface. Four [C₂H₂O]^+˙ isomers have been identified as potentially stable, observable ions. These are the experimentally well-known ketene radical cation, [CH₂?C?O]^+˙ (a), and the presently unknown ethynol radical cation, [CH₂?C? OH]^+˙ (b), the oxirene radical cation (c) and an ion resembling a complex of CO with [CH₂]^+˙, (d). The calculated energies of b, c and d relative to a are 189, 257 and 259 kJ mol^?1, respectively. Dissociation of ions a and d is found to occur without reverse activation energy.     

Mass spectra of aliphatic dicarboxylic acids and their dimethyl esters: Cyclic structures for the [M − H2O]+˙ ions from the diacids and [M − MeOH]+˙ ions from the dimethyl esters

Methyl 2-oxocycIoalkane carboxylate structures are proposed lor the [M ? MeOH]^+˙ ions from dimethyl adipate, pimelate, suberate and azelate. This proposal is based on a comparison of the metastable ion mass spectra and the kinetic energy releases for the major fragmentation reaction of these species with the same data for the molecular ions of authentic cyclic β-keto esters. The mass spectra of α,α,α′,α′-d₄-pimelic acid and its dimethyl ester indicate that the α-hydrogens are involved only to a minor extent in the formation of [M ? ROH]^+˙ and [M ? 2ROH]^+˙ ions, while these α-hydrogens are involved almost exclusively in the loss of ROH from the [M ? RO˙]⁺ ions (R = H or CH₃). The molecules XCO(CH₂)₇COOMe (X = OH, Cl) form abundant ions in their mass spectra with the same structure as the [M ? 2MeOH]^+˙ ions from dimethyl azelate.     

Four isomers of [C3H8O]+˙ distinguished by collisional activation

Collisional activation of the molecular ions of 1-propanol, 2-propanol and methyl ethyl ether, and of the m/z 60 ion from 1,2-dimethoxyethane provides evidence for four distinct forms of [C₃H₈O]^+˙. Collision induced decompositions may be explained either by simple cleavages, by cyclic processes involving adjacent substituents, or by bicyclic processes of adjacent substituents. Evidence for a form of [C₃H₈O]^+˙ in which charge and radical site are separate is assembled from the spectra.     

Correlation of substituted aromatic β‐diketones' characteristic protons chemical shifts with Hammett substituent constants

Influence of dibenzoylmethane's substituents in meta and para positions on chemical shift values of tautomers' characteristic protons was investigated in four solvents with ¹H NMR spectroscopy: acetone‐d₆, benzene‐d₆, CDCl₃ and deuterated dimethyl sulfoxide (DMSO‐d₆). It was proved that the influence of substituents on chemical shifts strongly depends on the kind of the solvent; the greatest changes were observed in benzene‐d₆ and the smallest in CDCl₃. In acetone‐d₆ and DMSO‐d₆, the influence of substituents on chemical shifts is similar and the most regular. It allowed a fair correlation of chemical shifts of para‐substituted dibenzoylmethane derivatives' characteristic protons with Hammett substituent constants in these solvents. In CDCl₃, characteristic protons' chemical shifts were near ¹H NMR spectroscopy measurement error limits, and, therefore, correlation with Hammett substituent constants in this solvent was unsatisfactory. In benzene, although the changes of chemical shifts are the most evident, the changes are also the most irregular, and, therefore, correlation in this solvent failed completely. Results of meta‐substituted derivatives were much more irregular, and their correlation with Hammett substituent constants was poor in all investigated solvents. Copyright © 2013 John Wiley & Sons, Ltd.     

Rate constants for the elementary reactions between CN radicals and CH4, C2H6, C2H4, C3H6, and C2H2 in the range: 295 ⩽ T/K ⩽ 700

Pulsed laser photolysis, time-resolved laser-induced fluorescence experiments have been carried out on the reactions of CN radicals with CH₄, C₂H₆, C₂H₄, C₃H₆, and C₂H₂. They have yielded rate constants for these five reactions at temperatures between 295 and 700 K. The data for the reactions with methane and ethane have been combined with other recent results and fitted to modified Arrhenius expressions, k(T) = A′(298) (T/298)ⁿ exp(?θ/T), yielding: for CH₄, A′(298) = 7.0 × 10^?13 cm³ molecule^?1 s^?1, n = 2.3, and θ = ?16 K; and for C₂H₆, A′(298) = 5.6 × 10^?12 cm³ molecule^?1 s^?1, n = 1.8, and θ = ?500 K. The rate constants for the reactions with C₂H₄, C₃H₆, and C₂H₂ all decrease monotonically with temperature and have been fitted to expressions of the form, k(T) = k(298) (T/298)ⁿ with k(298) = 2.5 × 10^?10 cm³ molecule^?1 s^?1, n = ?0.24 for CN + C₂H₄; k(298) = 3.4 × 10^?10 cm³ molecule^?1 s^?1, n = ?0.19 for CN + C₃H₆; and k(298) = 2.9 × 10^?10 cm³ molecule^?1 s^?1, n = ?0.53 for CN + C₂H₂. These reactions almost certainly proceed via addition-elimination yielding an unsaturated cyanide and an H-atom. Our kinetic results for reactions of CN are compared with those for reactions of the same hydrocarbons with other simple free radical species. © John Wiley & Sons, Inc.     

[M + 11]+˙ and [M + 11]−˙ ions in the nitrogen positive and negative ion chemical ionization mass spectra of aromatic amines

The N₂ negative ion chemical ionization (NICI) mass spectra of aniline, aminonaphthalenes, aminobiphenyls and aminoanthracenes show an unexpected addition appearing at [M + 11]^?˙. This addition is also observed in the N₂ positive chemical ionization (PCI) mass spectra. An ion at [M – 15]^? is found in the NICI spectra of aminoaromatics such as aniline, 1- and 2-aminonaphthalene and 1- and 2-aminoanthracene. Ion formation was studied using labeled reagents, variation of ion source pressure and temperature and examination of ion chromatograms. These experiments indicate that the [M + 11]^?˙, [M – 15]^?˙ and [M + 11]^+˙ ions result from the ionization of analytes altered by surface-assisted reactions. Experiments with ¹⁵N₂, [¹⁵N] aniline, [2,3,4,5,6-²H₅] aniline and [¹³C₆] aniline show that the [M + 11]^?˙ ion corresponds to [M + N – 3H]^?˙. The added nitrogen originates from the N₂ buffer gas and the addition occurs with loss of one ring and two amino group hydrogens. Fragmentation patterns in the N₂ PCI mass spectrum of aniline suggest that the neutral product of the surface-assisted reaction is 1,4-dicyanobuta-1,3-diene. Experiments with diamino-substituted aromatics show analogous reactions resulting in the formation of [M – 4H]^?˙ ions for aromatics with ortho-amino groups. Experiments with methylsubstituted aminoaromatics indicate that unsubstituted sites ortho to the amino group facilitate nitrogen addition, and that methyl groups provide additional sites for nitrogen addition.     

Complex Topology of Uranyl Polyphosphate Frameworks: Crystal Structures of α‐, β‐K[(UO2)(P3O9)] and K[(UO2)2(P3O10)]

Three new uranyl polyphosphates, α‐K[(UO₂)(P₃O₉)] ( 1 ), β‐K[(UO₂)(P₃O₉)] ( 2 ), and K[(UO₂)₂(P₃O₁₀)] ( 3 ), were prepared by high‐temperature solid‐state reactions. The crystal structures of the compounds have been solved by direct methods: 1 – monoclinic, P2₁/m, a = 8.497(1), b = 15.1150(1), c = 14.7890(1) Å, β = 91.911(5)°, V = 1898.3(3) ų, Z = 4, R₁ = 0.0734 for 4181 unique reflections with |F₀| ≥ 4σ_F; 2 – monoclinic, P2₁/n, a = 8.607(1), b = 14.842(2), c = 14.951(1) Å, β = 95.829(5)°, V = 1900.0(4) ų, Z = 4, R₁ = 0.0787 for 3185 unique reflections with |F₀| ≥ 4σ_F; 3 – Pbcn, a = 10.632(1), b = 10.325(1), c = 11.209(1) Å, V = 1230.5(2) ų, Z = 4, R₁ = 0.0364 for 1338 unique reflections with |F₀| ≥ 4σ_F. In the structures of 1 and 2 , phosphate tetrahedra share corners to form infinite [PO₃]^? chains, whereas, in the structure of 3 , tetrahedra form linear [P₃O₁₀]^5? trimers. The structures are based upon 3‐D frameworks of U and P polyhedra linked by sharing common O corners. The infinite [PO₃]^? chains in the structures of 1 and 2 are parallel to [100] and [–101], respectively. The uranyl polyphosphate frameworks are occupied by host K⁺ cations.     

A field ionization and collisionally activated dissociation/charge stripping study of some [C9H10]+˙ ions

The extent of isomerization of [C₉H₁₀]^+˙ ions, with lifetimes of approximately 10^?11 and 10^?6 s has been investigated using field ionization, collisionally activated dissociation and charge stripping techniques. The [C₉H₁₀]^+˙ ions which were investigated included the molecular ions of α-methylstyrene, β-methylstyrene, o-methylstyrene, m-methylstyrene, p-methylstyrene, indan, cyclopropylbenzene, allylbenzene and the product of water loss from 3-phenylpropanol. The field ionization spectra of all the C₉H₁₀ hydrocarbons were different indicating that isomerization to a common ion structure had not occurred to a measurable extent for ions with lifetimes of approximately 10^?11 s. Collisionally activated dissociation and charge stripping results indicated that most of the [C₉H₁₀]^+˙ ions continued to maintain unique ion structures (or mixtures of structures) at ion lifetimes of 10^?6 s. Possible exceptions are the [C₉H₁₀]^+˙ ions from allylbenzene and cyclopropylbenzene which gave indistinguishable collisionally activated dissociation and charge stripping spectra.     

Loss of methyl from [H2CC(OH)?CH3]+˙ ions prepared by electron impact ionization of unstable 2-hydroxypropene

Unstable 2-hydroxpropene was prepared by retro-Diels-Alder decomposition of 5-exo-methyl-5-norbornenol at 800°C/2 × 10^?6 Torr. The ionization energy of 2-hydroxypropene was measured as 8.67±0.05 eV. Formation of [C₂H₃O]⁺ and [CH₃]⁺ ions originating from different parts of the parent ion was examined by means of ¹³C and deuterium labelling. Threshold-energy [H₂C?C(OH)? CH₃]^+˙ ions decompose to CH₃CO⁺+CH₃^˙ with appearance energy AE(CH₃CO⁺) = 11.03 ± 0.03 eV. Higher energy ions also form CH₂?C?OH⁺ + CH₃ with appearance energy AE(CH₂?C?OH⁺) = 12.2–12.3 eV. The fragmentation competes with hydrogen migration between C(1) and C(3) in the parent ion. [C₂H₃O]⁺ ions containing the original methyl group and [CH₃]⁺ ions incorporating the former methylene and the hydroxyl hydrogen atom are formed preferentially, compared with their corresponding counterparts. This behaviour is due to rate-determining isomerization [H₂C?C(OH)? CH₃]^+˙ →[CH₃COCH₃]^+˙, followed by asymmetrical fragmentation of the latter ions. Effects of internal energy and isotope substitution are discussed.     

Calculation of the H2+ rovibrational energies and spectroscopic constants in the 2pπ, 3dσ, 4dσ, 4fπ, 4fσ, 5gσ, and 6iσ electronic states

Starting with the Hamilton‐Jacobi equation, Campos et al. have applied Hylleraas' method along with the series obtained by Wind‐Jaffe to several molecular ions, among which the H₂⁺ system, to determine their electronic energies in different states. In this work, we have fitted the potential energy curves for the 2pπ, 3dσ, 4dσ, 4fπ, 4fσ, 5gσ, and 6iσ electronic states of the H₂⁺ ion employing the Rydberg generalized function. From these fittings, the spectroscopic constants and the rovibrational energies have been determined by two distinct methods: Dunham's and the discrete variable representation. The theoretically obtained results are in a satisfactory agreement and are expected to provide a comparison source to future works in the experimental field. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Structure and reactivity of α,β-unsaturated ethers. V. Cationic copolymerizations of ring-substituted phenyl vinyl ethers

Phenyl vinyl ether (M₁) has been copolymerized with its various ring-substituted derivatives (M₂) in toluene at ?78°C with stannic tetrachloride as catalyst. The substituents investigated include p-CH₃O, m-CH₃O, p-CH₃, m-CH₃, p-Cl, and m-Cl. The course of copolymerization was followed by gas chromatographic determinations of residual monomers, and the monomer reactivity ratios were evaluated by use of the integral form of the Mayo-Lewis copolymerization equation. Except for the unusual case of the m-CH₃O derivative, the observed values of log (1/r₁) were found to be linearly correlated with Hammett's σ constants, the reaction constant being ρ = ?1.76 with the correlation coefficient r = 0.990. Comparisons of these results with the existing data for the styrene copolymerizations have enlightened the behavior of the oxygen atom in transmitting the electronic effects of ring substituents onto the reaction center.     

“Complex” versus “free radical” mechanism for the catalytic decomposition of H2O2 by ferric ions

Kinetic and spectrophotometric measurements made during the Fe³⁺ ion catalyzed decomposition of H₂O₂ have been analyzed using the computer simulation method. Improved values of the rate constants of the “complex scheme” and of the molar absorptivities ofthe intermediates were obtained: k₃/K_M = 4.94 M^?1 min^?1, k₄ = 193 M^?1 min^?1, ε_I/K_M = 52.3 M^?2 cm^?1, ε_II = 25.7 M^?1 cm^?1. The simulation revealed details of the reaction which were unavailable by other means and which explained several features of its kinetics. The total amount of O₂ evolved in the reaction using [H₂O₂] ～ 10^?2 M has been calculated and found to be nearly stoichiometric. O₂ evolution experiments in this region cannot, thus, distinguish between the “complex mechanism” predicting nearly stoichiometric evolution of O₂ and the “free radical mechanism” predicting exactly stoichiometricamounts of O₂. There are discrepancies within the “free radical scheme” with regard to the correct values of the rate constants to fit the reactions of H₂O₂ both with Fe²⁺ and Fe³⁺ ions, as well as other reactions assumed to proceed via free radicals.