Although we have obtained a powerful index of reactivity we remain uncertain of the factors that determine that reactivity. So, let us turn to energy partitioning and divide activation energies into their main parts: energies of former reagents, E^R and E^M, and interaction energies, E^int. Figure 2 shows the results of such partitioning. The whole situation seems to be complicated enough, each of those parts being greater in absolute value than the resulting activation energy, and no clear correlations are visible. Moreover, intermolecular interaction energy values are antibate to activation energies, so they cannot be the main and the only factor of reactivity.

It was mentioned above that the deformation movement of vicinal substituents of the reaction center is the main part of the IRC at the TS point. So, we could expect a possible relationship between energies of a monomer's deformations (E^def) and activation energies.

The energy partitioning procedure gives only the energy of the "reactant molecule" within the supermolecule, the energy comprising not only deformation but also electronic rearrangement. So let's define deformation energy E^def of a molecule as the energy, associated with the change in the its geometry to that one that it has in the TS. Calculation of such values ​​(E^def) shows that they indeed correlate with the activation barriers surprisingly well (see Fig. 3).

Nevertheless, E^def cannot be a true parameter of reactivity – the degree of tortion directly depends on the distance between reagents in TS, which, in turn, depends on the reagents' reactivity itself. We need to adjust deformation to some standard conditions, for example, an average of considered geometries of TSs¹⁾. The values of such «standard» deformation energies (E₀^def) are shown in Table IV.

Figure 3 shows that there exists a close relationship between activation energy of addition and E₀^def of monomers. That means that vinyl monomers endure tortion with ease compared with their reactivity. However, this does not mean that reactivity is but an elastic property of a monomer because neither calculated force constants of valent C=C vibration nor umbrella CH₂ vibration correlate with ΔΔH^≠_f²⁾. Moreover, it was found from other dependencies (other radicals' addition) that polar factors were also present: The monomers with acceptor group (VCl, MA, AN) had extra activity in reactions with CH₃^•; and vice versa, with CF₃^• or CH₃O^• they lacked some activity.

Thus, the complete description of the radical addition reaction requires the simultaneous consideration of these two terms: intra- and intermolecular reforming. Let us choose E₀^def to represent the first factor. And the second, intermolecular term, can be described by means of the PMO theory, especially since our case is a good one for π-approximation.

Figure 2. Partitioning of activation energies of reactions HOO^• + CH₂CHX.

Details of histogram:
(a), E^M, the change of monomer's total energy including E^def, (b); (c), E^R, the change of total energy of HOO; (d), E^int, total energy of interaction; the dashed block (e) shows the value of interaction between reactive centers; (f), resulting value of activation barrier E_a (ΔΔH^≠_f).

Figure 3. Relationship between E_a of HOO β-addition and energies of deformation of vinyl monomers, kcal/M.
1—deformation to geometry of TS, 2 — "standard" deformation E₀^def.

Table IV. Energies of standard deformation (E₀^def) of vinyl monomers (kcal/mol).

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