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en:reactivity:radical_addition:pmo [2026/09/16 17:45] – abcen:reactivity:radical_addition:pmo [2026/09/23 09:50] (current) – abc
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 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: 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:
  
-{{:reactivity:radical_addition:pmo-1.png?direct&300 |}} (**//Eq. 1//**) \\ +{{:reactivity:radical_addition:pmo-1.png?direct&300|}}  
-where the summing is done over a set of spin orbitals and //γ// is the resonance integral on the atomic orbitals (//AOs//) of reactive centers //r// and //s//.+<html><span class="rfloat"><br><b>(eq. 1)</b></span></html> 
 + 
 +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<sup>CT</sup>//) 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).  Using RHF π-orbitals of isolated reagents we calculated CT energies (//E<sup>CT</sup>//) 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<sup>CT</sup>// 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 MOs and their coefficients of the AOs 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.+So, //E<sup>CT</sup>// 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|Footnote]]), it has an obvious advantage: the coefficients and energies of FMO may be used as indices of reactivity. Although //FMO// cannot be approved as a true approximation (see [[#Footnote|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. +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 [[.:altpmo|alternative notation]] of the //PMO// **Eq. (1)**, that gives such effective MOs.+Now, we are going to propose an [[.:altpmo|alternative notation]] of the //PMO// **Eq. (1)**, that gives such effective MO\|s. 
 + 
 +----
  
 **Table V.** //HOO<sup>•</sup>// addition to vinyl monomers. **Table V.** //HOO<sup>•</sup>// addition to vinyl monomers.
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 {{:reactivity:radical_addition:pmo-2.png?direct&300|}} {{:reactivity:radical_addition:pmo-2.png?direct&300|}}
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