Let us return to our consideration of radical addition. Earlier, we suggested that the activation energy of this reaction is a total of two effects: deformation and polar interaction. The first can be evaluated by standard deformation energy, E₀^def (see above), and the second by CT energy (E^CT) of the PMO method. To try the possibility of a general scheme of radical activity, all previously obtained results of direct TS calculations were considered within the following equation:
E_a = a₀ + a₁E₀^def + a₂E^CT Eq. (3)

To use the advantages of the N/G method of calculation of E^CT we used the formula (2')

Parameters N and G calculated relatively HOO^• were used for the standard set of monomers' parameters. Parameters of radicals could be easily derived from linear dependencies shown in Figure 5. So, we just needed to obtain parameters a₀, a₁, a₂ of reactions. That was done by the usual optimization procedure. But, it was found that parameters of radicals obtained from π-approximation poorly correspond to the true picture of reactivity (and, really, they have considerable σ-character in TS). So, we decided to adjust parameters of radicals within the same optimization process. Final optimized values are collected in Tables VII and VIII. Figure 6 shows the quality of usage of Eq. (3) for evaluation of activation energies.

The main significance of that correlation is that regulations of radical addition to the C=C bond (how they are seen by semiempirical methods of quantum chemistry) could be explained by the electronic structure of reagents using two indices of reactivity: ability of reaction center to deform and change its hybridization and the energy of interaction of π-MO s of reagents.

It is a justification of our next step: to explain experimental regulations by these same characteristics of reagents and try the mathematical form of Eq. (3) for a correlation analysis of experimental data.

Table VII. Parameters of vinyl monomers; see Eq. (3)

Table VIII. Optimized* parameters of radicals and their reaction series. N, G in eV. Optimized scaling factor a₂ = 40 [see Eq. (3)].

Figure 6. Relationship between directly calculated activation energies and the values evaluated by Eq. (3), kcal/M (β-addition indicated by □, α-addition by +).

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