Radical stabilization energy, definition

In this paper the resonance energy Ht of a radical is defined as the increase in stabilization energy of a radical center when an a-methyl group is exchanged for a substituent, e.g. phenyl. For a definition based on methane see Ref. 60... 

A semiempirical procedure based on isodesmic reactions is used to determine unknown heats of formation. The choice of the isodesmic reaction is critical for the validity of the approach. By definition, all the bonds are conserved in number and nature in this type of process. Also, the bond lengths of equivalent bonds in reactants and products should be as similar as possible. The stabilization energies are based on the type of isodesmic reaction which is given for the influence of amino- and cyano-groups in a captodative radical in equation (3). Only radicals appear as reactants and... 

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. 

It is interesting to compare our definition of radical stabilization to previous ones proposed by Szwarc (1948), Benson (1965), and Rodgers et al. (1972). According to Szwarc, the resonance energy of an unsaturated radical is the heat of the following (isodesmic) reaction ... 

The reaction energy for Eq. 5 amounts to -54.7 kj/mol at the ROMP2 level, indicating a substantial captodative stabilization for glycyl radical (9) even with this definition. 

The relatively complicated case of CIO + CIO, where two closely related reactive channels (47a) and (47b) are identified, cannot be paralleled for BrO -I- BrO. No stable OBrO molecule (analogous to OCIO) is definitely known, nor has gaseous BrOO ever been detected as a transient or otherwise. Therefore, the dissociation energy of BrOO, if it exists, must be considerably less than the 29kJmol" suggested for CIOO. In the work of Oyne and Cruse, the number of bromine atoms found from reaction of BrO + BrO approached the number of BrO radicals consumed. This result confirms the correctness of writing this reaction as BrO + BrO -> 2Br + O2 and also confirms a lack of stability for the BrOO radical which, by analogy with CIO -I- QO, is likely to be the initial product, with Br, of reaction (49). In this case, the most probable fate of BrOO... 

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