Real and Ideal Relationships between Selectivity,Reactivity and Equilibrium

Reactivity and selectivity are discussed in terms of quadratic rate—equilibrium relationships for reaction series sharing a common intrinsic barrier, notably Marcus' equation. R.D. Levine's emphasis on such reactions as forming a “Brønsted Series” is suggested as a basis for defining “ideal” reactivity behavior. Ideal relationships between selectivity and reactivity and selectivity and equilibrium are derived based on reaction schemes drawing a formal distinction between reagent and substrate. In a simple Brønsted relationship, the reagent varies and the substrate is held constant. In an extended relationship, in which both substrate and reagent vary, the Brønsted series becomes a selectivity “network” or matrix characterized by direct and cross quadratic coefficients reflecting curvature of a free energy relationship and the dependence of selectivity upon rate or equilibrium respectively. In the ideal case, the quadratic coefficients are equal but, in practice, they generally differ. Inspection of the relevant reaction schemes shows that in evaluating the coefficients, there is greater cancellation of experimental and chemical scatter arising from non-systematic variations in reagent structure for the cross than the direct coefficient; this phenomenon accounts in part for the wider observation of reactivity—selectivity than non-linear free energy relationships. New measurements are reported for reactions of carboxylic acids with enolate and imine substrates. The results are combined with literature data and plotted as reactivity—selectivity and extended Brønsted relationships. The correlations are satisfactorily considered in the context of departures of real from ideal behaviour.