The PMO theory remains the best tool to discuss the reactivity of various chemical reactions. Our reaction is a suitable case for its application and, moreover, in π-approximation. The interaction energy of the PMO theory, also called "charge transfer" (CT) energy, has a well-known form:

(eq. 1)

where the summing is done over a set of spin orbitals and γ is the resonance integral on the atomic orbitals (AO) of reactive centers r and s.

Using RHF π-orbitals of isolated reagents we calculated CT energies (E^CT) of all series in consideration (see, e.g., Tables V and VI). Figure 4 shows that there is some symbasis between them and the activation barriers of corresponding reactions. Addition to a substituted position (α-addition) gives less satisfactory correlations, that are obviously caused by a greater steric effect (deformation of reaction center).

So, E^CT could also be taken for another factor of reactivity. But, there is one inconvenience with it: it is not an ordinary index of reactivity; it is the whole set of energies of MO s and their coefficients of the AO s of the reaction center. It is no wonder that when using the PMO theory researchers frequently truncate orbital sets to HOMO and LUMO to avoid the summing in Eq. (1); this method is known as the frontier molecular orbitals (FMO) approach.

Although FMO cannot be approved as a true approximation (see Footnote), it has an obvious advantage: the coefficients and energies of FMO may be used as indices of reactivity.

The use of localized molecular orbitals can serve as another approach. For example, using a projective procedure we managed to build a pair of localized MOs of a monomer that combined ≈95% of π-density both of occupied and unoccupied shells. It is a pity that even 5% is too great an error for such sums as Eq. (1). So, a desire arises to "correct" the energies (or coefficients) of such localized orbitals in such a way that they would give exact values of the sums in Eq. (1). As a result, we would get some fictitious but effective orbitals.

Now, we are going to propose an alternative notation of the PMO Eq. (1), that gives such effective MO s.

Table V. HOO^• addition to vinyl monomers. E_a, kcal/mol; E^CT, (γ²/eV); N и G, eV.

Table VI. CH₃^• addition to vinyl monomers.

Figure 4. Relationships between activation energies and CT energy of the PMO method, HOO addition. •, β-attack; ○, α-attack. 1, Eth; 2, Prop; 3, St; 4, AN; 5, MA; 6, VA; 7, VCl; 8, VCl2.

In our case the FMO approach failed entirely, for example, styrene having the most reactive C=C bond (both experimental and calculational data) appears to be completely inert from the point of view of the FMO approach. Obviously, this is due to truncation of many π-orbitals in this case, not to the different electronic structure of styrene.

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