Plurilinear improvement of the Hammett equation

Abstract The original Hammett equation, Δ = ρσ, is transformed in a constrained tetralinear relationship where each straight line with variable intercept term correlates one of the following four groups or subsets of dipolar substituents: normal and special substituents (depending on the absence or the presence of a lone electron pair in their atom next to the aromatic ring) and, in each of these classes, separating meta and para derivatives. There are a total of four fitting parameters in the resulting plurilinear Hammettian transformation (PHT) from which the statistically corrected parameters λ and γ are derived; λ and γ are the asymptotic values in a hyperbolic model for the representation of Δ 4 vs Δ 4 /Δ 3 . This meta – para interrelationship is assumed to hold in the absence of through‐resonance effects which, in turn, are allowed for by the use of alternative sigma scales of substituent constants. By applying the PHT to a large number of selected literature data, parameters λ and γ are determined for the ionization equilibria of 3‐ and 4‐monosubstituted benzoic acids, anilinium ions, phenols and pyridinium ions. In these reactions series, parameter λ, which measures the para / meta ratio of field/inductive effects, is lower than unity and shows a marked dependence on the basic molecular framework. It is best modelled in terms of a through‐space field effect approach. The ratio γ/γ 0 , where γ 0 is referred to the unified sigma‐zero scale, is shown to correspond to the original Hammett's reaction constant ρ. It is concluded that the PHT constitutes an improved Hammett equation for the analysis of substituent effects in benzene derivatives taking into account statistical errors and making allowance for different transmission coefficients for the field/inductive effect from meta and para positions in different reaction series.