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 Δ4 vs Δ4/Δ3. 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/γ0, where γ0 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.

Rate constants were measured for the oxidative chlorination reaction of N-phenylbenzenesulfonamide 2 and twelve ortho-, nine meta- and twelve para-substituted derivatives in the aniline moiety, using 1-chloro-3-methyl-2,6-diphenylpiperidin-4-one (1) as chlorinating agent. The kinetics was run in 50% (v/v) aqueous acetic acid acidified with perchloric acid under pseudo-first-order conditions with respect to 1 at five different temperatures between 298 and 318 K. The dependence of rate constants on temperature was analysed in terms of the isokinetic relationship (IKR). The resulting isokinetic temperature was estimated to be 513 K. Using the Linert's theory of the IKR, the experimental isokinetic temperature was interpreted as evidence for the preferential involvement of water molecules in the formation of activated complexes. The dependence of the rate constants on the substituents was analysed using the tetralinear extension of the Yukawa-Tsuno equation for the effects of meta and para substituents. A positively charged transition state was suggested by an experimental value r+ = 0.39 for the resonance demand, which was found to be insensitive to temperature variation. The parameter λ for the para/meta ratio of substituent effects was estimated to be 0.952. The electrostatic modelling of λ values was re-examined in the light of the recent calculations of the energies of interaction between charged and/or dipolar groups by Exner and Böhm. Based on energy ratios, the electrostatic method was shown to remain valid for the purpose of modelling λ values. The experimental λ value for the reaction indicates the formation of an activated complex possessing an electric charge in the vicinity of the nitrogen atom of the substrate. The electrophilic attack on the substrate nitrogen atom by the protonated chlorinating reagent has been proposed as the rate-determining step, with the last step being the fast rearrangement of the intermediate N-chloro-N-phenylbenzenesulfonamidium cation into the products.

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An improved Yukawa-Tsuno equation was obtained by inserting the resonance demand parameter r in the tetralinear extension of the Hammett equation constrained by a hyperbolic relation between meta and para substituent effects. The new equation with five adjustable parameters and other Yukawa-Tsuno models were applied to selected literature data for the ionization equilibria of 21 meta-and 20 para-substituted pyridinium ions in water at 25°C. The data are best described by the new equation using either the sigma-benzoic acid scale with r = 1.35 AE 0.16 or a truncated sigma-plus scale (in which sigma-zero constants are assigned to 4-alkyl substituents) with r = 0.29 AE 0.04. Standard errors were estimated by Monte Carlo simulation. The results for the pyridinium ion demonstrate that the hyperconjugative effect by alkyl groups is inoperative and that through-resonance effects by electron-donating substituents are considerably hindered. The origin of this hindrance is ascribed to the particularities of nitrogen orbitals in heteroaromatic compounds. It is concluded that the pyridine reactivity lies between those of benzoic acid and benzylic cation, being much closer to the former.

Rate constants were measured for the oxidation reaction of benzyl alcohol and twenty-five ortho-, meta-and paramonosubstituted derivatives in the temperature range 293-323 K at intervals of 10 K. The kinetics were followed spectrophotometrically in dry acetonitrile acidified with trichloroacetic acid (TCA) using pyridinium dichromate (PDC) as oxidising agent under pseudo-first-order conditions with respect to PDC. Benzaldehyde is the only oxidation product and no reaction takes place without TCA. From good linear Eyring plots activation enthalpies ∆ ‡ HЊ and entropies ∆ ‡ SЊ are calculated. For ortho-substituted benzyl alcohols high ∆ ‡ HЊ values and small negative ∆ ‡ SЊ values point to an ortho effect on the rate-determining step. Using the tetralinear approach to substituent effects, the average value λ ¯ = 1.09 ± 0.05 for the para/meta ratio of inductive or Electra effects is obtained and negative Hammett reaction constants decreasing in magnitude with increasing temperature are found. A mechanism implicating the prior acid-catalysed formation of neutral benzyl hydrogen dichromate ester followed by intramolecular proton transfer is proposed. Modelling of parameter λ in terms of the electrostatic theory showed its experimental value to be consistent with the ratio of electric potentials generated in the immediate vicinity of the nearest chromium atom by dipolar substituents introduced in the aromatic ring on para and meta positions. At a molecular level the oxidative, rate-determining step is suggested to be triggered by the retraction or shrinkage of electron pairs from sigma bonds in Cr 2 VI species to non-bonding orbitals in unstable Cr IV -O-Cr VI species. In contrast with past interpretations, an electrochemical approach is used to explain negative values for the Hammett reaction constant.