The correlations in figure 3, figure 4 and figure 5 appear reasonable; for example 21 of the 37 measured activation energies have error bounds that overlap the line of best fit when plotted against the energy decrease due to the charge transfer, Ec (figure 4), also, the standard error of the activation energies estimated by equation 6 (5.3 kJ/mol) is not significantly greater than the mean of the measured standard errors (3.9 kJ/mol). There is however noticeably more scatter for the reactions of ethene. The values of Baldwin et al.[14,16] and of Arsentiev et al.17 for the activation energy for epoxidation of ethene by hydroperoxyl radicals differ by a margin considerably bigger than the measured standard errors. That of Arsentiev is noticeably below the line of best fit for the correlation of activation energy with alkene ionisation energy (figure 1) as well as those of figure 3, figure 4 and figure 5, although this is no reason per se to accept the value of Baldwin et al. over Arsentiev's. Indeed the suggested activation energy for the epoxidation of ethene by t-butylperoxyl radicals also appears to be anomalously low with respect to its other epoxidation reactions (although this value should be viewed with caution as it is based on an assumed A factor: if, for instance, the A factor for epoxidation of ethene by alkylperoxyl radicals was x8 larger than for other alkenes, as is the case with HO2, then the recommended activation energy would be ca. 7kJ/mol higher).
The activation energy for the reaction of hydroperoxyl radicals with ethene is of particular interest, as it has been suggested on the basis of experiments on the O2 + C2H5 system, that the barrier for HO2 + C2H4 must be lower than the heat of formation of O2 + C2H5.[38] More recent experiments on the temperature dependence of the yield of C2H4 from the reaction of O2 + C2H5 gave a small positive activation energy of 4.6±1.0 kJ/mol,[39] implying an activation energy for the addition of HO2 to C2H4 of less than 59.8±1.0 kJ/mol, which is consistent with the value determined by Arsentiev et al. of 56.6±3.4 kJ/mol (dHr (298 K) = 54.3 kJ/mol for O2 + C2H5 -> HO2 + C2H4[40]). The experiments of Arsentiev et al. are also of importance because it has been suggested[41] that side reactions involving oxygen atoms were forming the epoxide in the experiments of Baldwin et al. However, the good correlation between the rate of epoxide formation and the product of the peroxyl radical and alkene concentrations in the experiments of Arsentiev et al. provide direct evidence that epoxidation is by peroxyl radicals.
In the absence of experimental data, values for ionisation energies and electron affinities of the peroxyl radicals have been calculated using Mopac 6.0 with the AM1 Hamiltonian.[34] Jonsson has noted the possible problems of this, pointing out that there is not a good correlation between the measured aqueous phase one electron reduction potentials of peroxyl radicals and their calculated gas phase electron affinities, with in particular the calculated electron affinity for t-C4H9O2 appearing to be too high.[37] However, a lower value for the electron affinity of t-C4H9O2 would give lower values for Ec, Nc and a higher value for (Ialkene-Aperoxyl) for this species, which could actually improve the correlations given in figures 3-5. These correlations should be reinvestigated when experimental data or higher level calculations become available for the properties in question.
For correlations between a number of different peroxyl radicals and different alkenes, there is not a one to one relationship between dNc, dEc or (Ialkene-Aperoxyl). Therefore, in principle, figures 3-5 could be used to determine which of the explanations of reactivity was more appropriate, ie. which has the best correlation. However, considering the uncertainties in the measured and estimated values used in figures 3-5, the correlation coefficients do not differ by significant enough margins to answer this question.