Previous work, particularly on the hydroperoxyl and acetylperoxyl radicals, has established that the rate of addition of peroxyl radicals to alkenes is correlated to the ionisation energy of the alkene (figure 1 and figure 2), indicating a degree of charge transfer from the radical and to the alkene at the transition state for the initial addition forming the peroxyalkyl adduct, reaction 1.[6] It would also be of practical use to be able to relate the rate of epoxidation to a physical property of the attacking radical as this would allow the estimation of rates of epoxidation for reactions that have not yet been examined experimentally.

One possible rationalisation for the reactivity of electrophilic addition of radicals to alkenes is that during the reaction of two species to form an adduct, electron density flows between the two until an energy minimum is obtained.[29-31] The degree of charge transfer (dN_c) in forming the adduct and the corresponding energy decrease (dE_c) can be estimated from the absolute electronegativity (chi) and absolute hardness (eta) of the two species (a and b) forming the adduct, which are in turn are related to their ionisation energy (I) and electron affinity (A):[29]

         dNc =   (chia - chib)/2(etaa + etab)        (1)

         dEc =   -(chia - chib)2/4(etaa + etab)      (2)

         chi = (I + A)/2                            (3)

         eta = (I - A)/2                            (4)

An alternative explanation for electrophilic addition reactions is that the rate will be faster, the smaller the energy gap between the highest occupied molecular orbital (HOMO) of the alkene and the lowest unoccupied molecular orbital (LUMO) of the radical, which can be approximated by the difference between the ionisation energy of the alkene and the electron affinity of the radical (I_alkene-A_peroxyl).[32]

Typically, correlations have only been examined for an individual species attacking a number of substrates [eg. 30] However, the assumption is tested here that for peroxyl radical addition to alkenes in the gas phase, all 36 reactions that have been investigated between 17 alkenes and 5 peroxyl species share a common behaviour, and correlations are examined between the activation energies of the reactions (E) and the charge transfer in forming the adduct, Nc (figure 3), the energy decrease due to the charge transfer, Ec (figure 4), and the difference between the alkene ionisation energy and the peroxyl radical electron affinity, (Ialkene-Aperoxyl) (figure 5). Calculations of Nc, Ec and (Ialkene-Aperoxyl) are given in table 1, using values of I, A, and given in table 2. Linear regressions of figures 3, 4 and 5 are given by equations 5, 6 and 7 (r is the correlation coefficient, and deltaE is the standard error of the estimated activation energies, as calculated by equations 5-7).

E (kJ/mol) =  109  kJ/mol - (456±31 kJ/mol) Nc          (r=0.93, deltaE=6.2 kJ/mol)    (5)

E (kJ/mol) =  83.0 kJ/mol - (1.82±0.10) Ec (kJ/mol)       (r=0.95, deltaE=5.3 kJ/mol)   (6)
  
E (kJ/mol) = -61.0 kJ/mol + (14.0±1.2)(Ialkene - Aperoxyl) (eV)  (r=0.89, deltaE=7.4 kJ/mol)  (7)