Separation of polar and enthalpic effects on radical addition reactions using principal component analysis

Abstract

Principal component analysis (PCA) was performed on rate constants of radical addition reactions involving various carbon centred radicals and vinyl type alkenes. Reactivity data for reactions of nine radicals with eight alkenes (data set A) and of five radicals with 15 alkenes (data set B) were analysed. In addition, a mixed case (data set C) was also considered with 13 variables of seven alkenes (reactivities of nine radicals toward the alkenes and four thermodynamic properties of the alkenes). It was found that in all cases two principal components account for more than 90% of the total variance in the data. With data sets (A) and (B) the plots of component loadings and component scores showed significant groupings of radicals and alkenes, respectively, according to similarity in reactivity and character. The component scores were found to be significantly correlated with certain thermodynamic properties of the alkenes. The correlations were in agreement with the Frontier Molecular Orbital model, the first principal component being correlated with the electron affinity and the second one with the ionization potential of the alkenes. Thus, PCA was able to decompose the individual reactivities into nucleophilic and electrophilic components. The first principal component also correlates with exothermicity (–ΔrH) suggesting that the radical addition reactions investigated are partly controlled by Hammond's postulate. With data set (C) a plot of component loadings showed that the rate constants for the less nucleophilic radicals correlate with exothermicity, whereas those for the more nucleophilic radicals correlate with electron affinity. Consequently, the reactivities of the less nucleophilic radicals appear to be well described by Hammond's postulate and those of the more nucleophilic radicals by the FMO model.