The relevance of third-derivative cross-interaction coefficients in Hammett-type treatments of nucleophilic substitution reactions

Abstract

Six nucleophilic substitution reactions of (Y)-phenylalkyl or (Y)-phenacyl (Z)-arenesulfonates with (X)-anilines or (X)-benzylamines are analysed in terms of a modified Hammett equation incorporating both second- and third-derivative cross-interaction coefficients. For five of the six reported analyses, the standard errors associated with the third-derivative value (ρ_XYZ) are large and the probabilities that the contribution to the overall analysis is statistically insignificant are very high (0.53–0.92). Although we confirm a previous report that the sixth system appears to have a marginally acceptable ρ_XYZ value, minor adjustments of six of the 48 rate coefficients (so as better to accommodate trends within the matrix of values) leads to improved correlations, an appreciably reduced ρ_XYZ(or ρ_XYZⁱⁿ) value, and a 0.45 probability that the term involving ρ_XYZ is not statistically significant. Extremely fast methanolyses of the more reactive 1-phenylethyl arenesulfonates are predicted and previously reported studies, by conventional techniques, of their reactions with anilines, in methanol as the solvent, need to be reevaluated.