====== Comparison of Direct TS Calculations with Indices of Reactivity ====== 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') {{:reactivity:radical_addition:altpmo-5.png?direct&200|}} 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 [[altpmo#figure_5|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)** ^ \\ Мономер ^ β-attack ^^^ α-attack ^^^ ^ ::: ^ //E^def// ^ //N// ^ //G// ^ //E^def// ^ //N// ^ //G// ^ | //Eth// | 6.83 | 1.30 | 14.1 | ||| | //Prop// | 6.51 | 1.15 | 13.7 | 7.45 | 1.46 | 14.2 | | //AN// | 6.57 | −1.74 | 14.1 | 7.19 | 0.28 | 14.8 | | //MA// | 7.01 | −2.19 | 14.4 | 7.65 | 0.73 | 14.8 | | //VA// | 5.64 | 2.01 | 13.3 | 6.10 | 0.74 | 14.4 | | //VCl// | 6.56 | −0.36 | 14.1 | 7.08 | 0.23 | 14.7 | | //VCl2// | 6.07 | −1.63 | 14.0 | 6.96 | −0.46 | 15.1 | | //St// | 4.82 | 1.37 | 13.0 | 7.88 | 1.40 | 14.3 | | //Bu2ene// | 4.786 | 1.39 | 13.1 | ||| | //Hex3ene// | 4.438 | 1.40 | 12.9 | ||| | //ViNaph// | 4.890 | 1.38 | 12.9 | ||| | //2ViPy// | 5.204 | 0.79 | 13.3 | ||| | //4ViPy// | 5.113 | 0.12 | 13.4 | ||| | //4ViPm// | 5.611 | −0.42 | 13.6 | ||| | //2ViPm// | 5.783 | −0.32 | 13.4 | ||| **Table VIII**. Optimized* parameters of radicals and their reaction series. //N, G// in eV. Optimized scaling factor **//a₂// = 40** [see **Eq. (3)**]. ^ \\ Radical ^ \\ //N// ^ \\ //G// ^ β-attack ^^ α-attack ^^ ^ ::: ^ ::: ^ ::: ^ //a₀// ^ //a₁// ^ //a₀// ^ //a₁// ^ | //HOO// | 0 | 0 | 28.0 | 1.46 | 20.8 | 2.85 | | //CH₃// | 1.60 | −1.00 | 21.0 | 0.75 | 23.8 | 0.75 | | //CH₃O// | −0.55 | −0.65 | 26.2 | 0.92 | 14.0 | 3.05 | | //CCl₃// | −1.75 | −1.30 | 28.6 | 0.80 | 24.3 | 2.00 | | //CF₃// | −3.50 | −0.23 | 23.8 | 0.60 | 16.0 | 2.30 | | ^* //HOO// is chosen to be the reper reactant, so relative parameters of other radicals are presented here (//N// < 0 means a more electronegative and //G// < 0 a more "sensitive" radical).||||||| {{:reactivity:radical_addition:comparison-1.png?direct&200 |}} **Figure 6**. Relationship between directly calculated activation energies and the values evaluated by **Eq. (3)**, kcal/M (β-addition indicated by □, α-addition by +). ---- [ [[.:empiric|Next]] ] [ [[.:|Top]] ]