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en:reactivity:radical_addition:altpmo

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Alternative Form of the PMO Equation: Effective Electronegativity of Reagent

Eq. (1) can be rewritten as:
, where and (Eq. 1' )

Values EM→R and EM←R can be regarded as the efficient energies of occupied and unoccupied orbital shells of the first reagent M related to the orbitals of the second reagent R. A more convenient notation looks like this:
 , where N = EM→R + EM←R and G = EM←R − EM→R.    (Eq. 2)

Let us call parameter N, by analogy with the Mulliken formula1), the efficient electronegativity (N) of reactive center (which describes acceptor/polar properties) and G the efficient energy gap between interacting orbital shells (which characterizes activity/sensitivity, covalent characters of interaction). As follows from the definition, parameters N and G are not characteristics of a whole reagent but of a certain reactive center. These parameters are useful in discussions concerning reactivity. For example, most simple vinyl monomers have similar values of G so their reactivity can be explained by N only. The dependence of CT energy upon N is of parabolic type with maximum at N = 0. That means that in the case when N of reagents coincide, stabilization via ECT is the lowest. The group of monomers with conjugated double bonds (butadiene, styrene, vinylpyridene, etc.) were found to have close N but strongly differed by energy gap between occupied and unoccupied orbital shells. In such a case, reactivity could be entirely explained by the factor G (see Table V). N is also convenient for discussions of electron donating and related polar effects. For example, N satisfactorily correlates with charge transfer from monomers to the attacking radical.

1)
Electronegativity = ½ (EHOMO + ELUMO)
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