The three-parameter Nieuwdorp equation is the optimal linear free energy relationship for the prediction of missing data

Abstract

It has been shown that the linear free energy relationship proposed by Nieuwdorp (1979) gives a better fit to available data on substituent effects than the relationships proposed by Taft (1958), Swain (1983), and Yukawa–Tsuno (1980). One reason is that the Nieuwdorp relationship contains three parameters, while the Taft relationship has only two. It is shown here that the Nieuwdorp relationship gives the best prediction of missing data on substituent effects, and that nothing can be gained by adding a fourth p parameter. This is demonstrated with three sets of data: (1) the set of 76 series of data on 17 substituents from which Nieuwdorp derived the values of his σ_I, σ_R, and σ_E variables; (2) a set of 164 series of data on 14 substituents for which the fit by the Nieuwdorp relationship was not satisfactory; and (3) a set of 28 series of data on 14 substituents, selected with the view to provide a large variance that cannot be explained by the Nieuwdorp relationship.