An improved procedure for the description of substituent effects on equilibrium and rate constants, based on factor analysis of the whole body of appropriate data

Abstract

By comparing the two most widely used descriptions of substituent effects by Hammett type substituent constants, viz., the Taft equation and the Yukawa–Tsuno relation, it is shown that a general descriptive equation should be of the type: log (K_X/K_H)= [graphic omitted]ρ_iσ_i. In this equation, the left hand side is the substituent effect, ρ is a reaction constant, and σ is a substituent constant. With the aim of finding optimal values of ρ and σ which can be used in this general equation, a large number (570) of log (K_X/K_H) values for chemical reactions and equilibria was selected from the literature. These data were taken for 76 reactions or equilibria, and 17 substituents. A special statistical procedure, which included factor analysis, was designed and applied to extract optimal ρ and σ values from the data. The results of the procedure show that only three substituent constants, σ_I, σ_R, and σ_E, are required to describe log (K_X/K_H) values for all reaction types mentioned by Ehrenson, Brownlee, and Taft, viz.σ_I, σ_R⁰, σ_R(BA), σ_R⁺, and σ_R^– reaction types. So, the general regression equation is log (K_X/K_H)=ρ_Iσ_I+ρ_Rσ_R+ρ_Eσ_E. The constants σ_I and σ_R are comparable to Taft's σ_I and σ_R⁰. The magnitude of the ρ_Eσ_E term is indicative of the reaction type : ρ_E is zero for σ_R⁰ reactions, negative for para-substituted σ_R^– reactions, and positive for σ_R⁺ reactions (the substituent effects were defined in such a way that ρ_I and ρ_R are positive for all reactions). Optimal values of σ_I, σ_R, and σ_E are given for the 17 substituents. As an illustration of their applicability, regression analysis of phase equilibrium data on σ_I, σ_R, and σ_E is performed, and the results are compared with those of regression analysis on the Taft σ parameters.