Interdependence of the Hammett and isokinetic relationships: a numerical simulation approach

Many homologous reaction series present linear correlations between the enthalpy ( Δ H_,i^o ) and entropy ( Δ S_,i^ o ) of activation (kinetic compensation effect), the slope being the isokinetic temperature of the series ( T iso ), so that at T = T iso , all the reactions of the family share the same value of the rate constant. However, the random errors committed in the laboratory in the determination of Δ H_,i^o and Δ S_,i^ o are interrelated, and so tend to produce false isokinetic relationships. As a result, the existence of physically meaningful isokinetic relationships is a topic of lasting controversy. Here, it is shown that both the LFER (linear free energy relationships)-type and isokinetic linear correlations are direct consequences of two other correlations, those of Δ H_,i^o vs. σ _i and Δ S_,i^ o vs. σ _i , where the abscissa is the Hammett (or Taft) substituent parameter. A mathematical model has been developed, according to which T iso can be interpreted as the temperature at which the reaction constant obtained as the slope of the LFER-type straight line takes a zero value ( ρ = 0). Moreover, the numerical simulations performed indicated that the logk_ T vs. σ _i and Δ H_,i^o vs. Δ S_,i^ o linear plots can be visualized as two faces of the same coin, since, if the kinetic data obey the first with a correlation coefficient high enough, the probability of fulfillment of the second will be very high. Finally, it has been found that values of T iso and T δ (the slope of the linear correlation between the enthalpy–entropy deviations) very close to the mean working temperature, as well as correlation coefficients of the Δ H_,i^o vs. Δ S_,i^ o linear plots much higher than those corresponding to the Δ H_,i^o vs. σ _i and Δ S_,i^ o vs. σ _i plots, are all indicative of false isokinetic relationships, highly contaminated by the statistical correlation between the enthalpy and entropy experimental errors. Graphic abstract