The Stability of Carbon-Centered Radicals

Carbon-centered radicals play an important role in organic synthesis, biological chemistry, and polymer chemistry. The radical chemistry observed in these areas can, to a good part, be rationalized by the thermodynamic stability of the open shell species involved. Challenges associated with the experimental determination of homolytic bond dissociation energies (BDEs) have lead to the widespread use of theoretically calculated values. These can be presented either directly as the enthalpy for the C-H bond dissociation reaction described in Equation 5.1, the gas-phase thermodynamic values at the standard state of 298.15K and 1 bar pressure being the most commonly reported values. 

Carbon-Centered Free Radicals and Radical Cations, Edited by Malcolm D. E. Forbes Copyright 2010 John Wiley Sons, Inc. 

Alternatively, the BDE values may be reported relative to the C-H bond dissociation energy in methane (3) as the reference. This is quantitatively described in Equation 5.3 as a formal hydrogen transfer process between methane (3) and a substituted carbon-centered radical 2. The reaction enthalpy for this process is often interpreted as the stabilizing influence of substituents Rj, R2, and R3 on the radical center and thus referred to as the radical stabihzation energy (RSE). When defined as in Equation 5.3, positive values imply a stabilizing influence of the substituents on the radical center. The RSE energies are connected to the BDE values in Equations 5.land 5.2 as described in Equation 5.4. 

It has been pointed out by Zavitsas that RSE values calculated according to Equation 5.3 reflect the influence of substituents Ri, R2, and R3 on both the radical and its parent hydrocarbon. This latter effect will be particularly large for all bond dissociation processes, in which the cleaved bond has substantial polar character, and Equation 5.5 has therefore been suggested as an alternative approach for the determination of RSE values. 

The RSE is calculated here as the difference between the homolytic C-C bond dissociation energy in ethane (5) and a symmetric hydrocarbon 6 resulting from dimerization of the substituted radical 2. By definition the C-C bonds cleaved in this process are unpolarized and, baring some strongly repulsive steric effects in symmetric dimer 6, the complications in the interpretation of substituent effects are thus avoided. Since two substituted radicals are formed in the process, the reaction enthalpy for the process shown in Equation 5.5 contains the substituent effect on radical stability twice. The actual RSE value is therefore only half of the reaction enthalpy for reaction 5.5 as expressed in Equation 5.6. 

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The stabilization of carbon-centered radicals through alkyl groups is due to a closely similar orbital interaction as that shown for n systems (Scheme 2). 

Due to their importance aaoss a wide range of chemical and biological processes, the effects of primary substituents on the stability of carbon-centered radicals have been widely... 

Coote ML, Lin C-Y, Zipse H. The stability of carbon-centered radicals. In Forbes MDE, ed. Carbon-Centered Free Radicals and Radical Cations Structure, Reactivity and Dynamics. New Jersey John Wiley Sons, Inc 2010 83—104. 

A quantity called the radical stabilization energy (RSE) may be defined to relate the stabilities of substituted carbon radicals to the methyl radical. The effects of adjacent X , Z, and C substituents on the RSEs of carbon-centered radicals has been widely investigated [142,143]. The expectations based on simple orbital interaction theory as espoused above are widely supported by the experimental findings, except that when the the n donor or n acceptor ability of the group is weak and the inductive electron-withdrawing power is large, as in F3C and (Me N+CHj, the net effect is to destabilize the radical relative to the methyl radical [143]. The BDE of a C—H bond of a compound R—H is another measure of stability of the product radical, R. It is related to the RSE by... 

The chemical dynamics, reactivity, and stability of carbon-centered radicals play an important role in understanding the formation of polycyclic aromatic hydrocarbons (PAHs), their hydrogen-dehcient precursor molecules, and carbonaceous nanostructures from the bottom up in extreme environments. These range from high-temperature combustion flames (up to a few 1000 K) and chemical vapor deposition of diamonds to more exotic, extraterrestrial settings such as low-temperature (30-200 K), hydrocarbon-rich atmospheres of planets and their moons such as Jupiter, Saturn, Uranus, Neptune, Pluto, and Titan, as well as cold molecular clouds holding temperatures as low as 10... 

One of the most important manifestations of Si-C hyperconjugation is the well-established P stabilization of carbon-centered radicals and carbon-ium ions by silyl groups. 

Treatment of a-iodo ketone and aldehyde with an equimolar amount of Et3B yielded the Reformatsky type adduct in the absence of PhaSnH (Scheme 21), unlike ot-bromo ketone as shown in Scheme 15 [22], Ethyl radical abstracts iodine to pro-duee carbonylmethyl radical, which would be trapped by EtsB to give the corresponding boron enolate and regenerate an ethyl radical. The boron enolate reacts with aldehyde to afford the adduct. The three-component coupling reaction of tert-butyl iodide, methyl vinyl ketone and benzaldehyde proceeded to give the corresponding adduct 38, with contamination by the ethyl radical addition product 39. The order of stability of carbon-centered radical is carbonylmethyl radical > Bu > Pr > Ef > Me . 

Most radicals are transient species. They (e.%. 1-10) decay by self-reaction with rates at or close to the diffusion-controlled limit (Section 1.4). This situation also pertains in conventional radical polymerization. Certain radicals, however, have thermodynamic stability, kinetic stability (persistence) or both that is conferred by appropriate substitution. Some well-known examples of stable radicals are diphenylpicrylhydrazyl (DPPH), nitroxides such as 2,2,6,6-tetramethylpiperidin-A -oxyl (TEMPO), triphenylniethyl radical (13) and galvinoxyl (14). Some examples of carbon-centered radicals which are persistent but which do not have intrinsic thermodynamic stability are shown in Section 1.4.3.2. These radicals (DPPH, TEMPO, 13, 14) are comparatively stable in isolation as solids or in solution and either do not react or react very slowly with compounds usually thought of as substrates for radical reactions. They may, nonetheless, react with less stable radicals at close to diffusion controlled rates. In polymer synthesis these species find use as inhibitors (to stabilize monomers against polymerization or to quench radical reactions - Section 5,3.1) and as reversible termination agents (in living radical polymerization - Section 9.3). 

The reaction enthalpy and thus the RSE will be negative for all radicals, which are more stable than the methyl radical. Equation 1 describes nothing else but the difference in the bond dissociation energies (BDE) of CH3 - H and R - H, but avoids most of the technical complications involved in the determination of absolute BDEs. It can thus be expected that even moderately accurate theoretical methods give reasonable RSE values, while this is not so for the prediction of absolute BDEs. In principle, the isodesmic reaction described in Eq. 1 lends itself to all types of carbon-centered radicals. However, the error compensation responsible for the success of isodesmic equations becomes less effective with increasingly different electronic characteristics of the C - H bond in methane and the R - H bond. As a consequence the stability of a-radicals located at sp2 hybridized carbon atoms may best be described relative to the vinyl radical 3 and ethylene 4 ... 

Radical stabilization energies for a wide variety of carbon-centered radicals have been calculated at G3(MP2)-RAD or better level. While the interpretation of these values as the result of substituent effects on radical stability is not without problems, the use of these values in rationalizing radical reactions is straight forward. This is not only true for reactions involving hydrogen atom transfer steps but also for other reactions involving typical elementary reactions such as the addition to alkene double bonds and thiocarbonyl compounds. 

Generalized to any type of carbon-centered radical, this approach has led to use of C—H bond dissociation energies for estimating the unpaired electron delocalization energies of these species. As shown in Tables XXXIII, XXXIV, and XXXV, bond dissociation energies which, except for a constant, are equal to heats of reaction do not provide satisfactory resonance (or stabilization) energies of free radicals. Indeed, as stated before, a heat of reaction can never be used for determining any property of one of the species involved in that reaction. 

The species [H2BCH2] and [H2BSIH2] were included in a study of the effect of substituents on the stabilization of carbon- and silicon-centered radicals. The process [H2BXH2] + XH4- H2BXH3 + [XHa] (X = C or Si) is endotherm. Delocalization of the odd electron into the vacant p orbital on boron is responsible for stabilizing [H2BCH2] by 9.7 kcal/mol and [H2BSiH2] by 11.3 kcal/mol [14]. 

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