Reactivity parameters and aromatic systems. Part III. Reactivity relationships, and their application to substituent effects in aromatic systems

The principles underlying various reactivity and free-energy relationships are examined. A generalised relationship is derived which incorporates many of those presently accepted, e.g., the Hammett, Yukawa Tsuno, and Taft equations. Three new semi-empirical relationships are derived with differing numbers of constraints. The four factors commonly given independent recognition are represented as, the substituent S, the position of the substituent relative to the position of the reaction P, the reagent–solvent system R, and a factor characteristic of the type of reaction and its corresponding free-energy requirement T. In the first equation the rate or equilibrium of a particular reaction is related to an arbitrary reaction by log k/k0=A+ρ(FX+MY) where F=p(ST), M=r(ST)X=p(P), Y=r(P), ρ=pR=rR, superscripts p and r referring to polar and resonance effects respectively.The second equation log k/k0=A+BFX+CMY corresponds to the first equation with the constraint pR=rR removed, B corresponding to pR and C to rR. In the third equation, log k/k0=A+BpTFX+CrTMY, only the ratio pT to pR can in practice be derived, and then only under the assumption that B=C. Substituent effect data for the naphthalene and fluoranthene systems are considered. For transmission coefficients of delocalisation effects in electrophilic substitution qw values are slightly better than atom–atom polarisabilities. As a measure of the direct field effect of a substituent both 1/d and (cos θ)/d give in most cases equally good results. There is indication that with an improved model separation of the reaction parameter into a type parameter T and a reagent–solvent parameter R may well be viable.