Is the Hammett’s Constant Free of Steric Effects? Luis Rincó n* and Rafael Almeida Departamento de Química, Facultad de Ciencias, Universidad de Los Andes, La Hechicera, Merida-5101, Venezuela ABSTRACT: In this work, we have explored the validity of the hypotheses on which rest the Hammett's approach to quantify the substituent effect on a reaction center, by applying two DFT energy decomposition schemes. This is performed by studying the change in the total electronic energy, ΔΔE, associated with a proton transfer isodesmic equilibrium. For this reaction, two sets of substituted benzoic acids and their corresponding benzoate anions have been considered. One of these sets contains para- and meta-substitutions, whereas the other one includes ortho-substituted benzoic acids. For each case, the gas phase change in the total electronic energy has been calculated, and two DFT energy decomposition schemes have been applied. The experimental σ X was found to be nearly proportional to the computed ΔΔE. The results for the para- and meta-substituted benzoic acids lead to the conclusion that it is possible to treat separately and, in an additive manner, the electrostatic and steric contributions; and also that the Hammett constant depends mainly on the electronic contributions to the free energy, while the steric contribution is negligible. However, the results for the ortho-substituted cases lead to the conclusion, as was assumed by Hammett, that there are significant qualitative differences between the effects on a reaction site of substituents in the meta- and para-positions and those in the ortho-position. 1. INTRODUCTION The problem of how to quantify the substituent effects on a reaction center, connected to those substituents by a molecular skeletal structure, was addressed by Louis P. Hammett 1−3 in seminal works that have become, even today, some of the most influential contributions in physical organic chemistry. He proposed that the ionization reaction of meta- and para- substituted benzoic acids could be used as a reference to quantify the substituent electronic effects on similar reactions. In his work, for a given substituent X, Hammett defined the constant σ X (that now has his name) through the equation σ = ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ K K log X X H (1) Here, K H is the ionization constant of benzoic acid, and K X is the ionization constant of a meta- or para-substituted benzoic acid, both measured in water (or in a polar solvent) at 25 °C. According to the Hammett interpretation, the σ X values embody the sum of the total electronic effects (resonance plus inductive/field effects); positive values are associated with electron-withdrawing substituents, while negative values correspond to electron-donating groups. By using the set of σ X values, the quantification of electronic effects in similar reactions to benzoic acid ionization can be accomplished by means of the Hammett equation ρσ = ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ K K log X H X (2) Here, ρ is a constant that measures the sensitivity of the studied reaction to electronic effects, compared to the reference reaction, due to the presence of a substituent on the molecular substrate. Reactions with a positive ρ are promoted by electron- withdrawing substituents and vice versa. Employing the well- known relationship between the equilibrium constant and the corresponding change in Gibbs free energy, ΔG, the Hammett equation can be rewritten as a linear relationship between ΔG and σ X . Hence, the σ X value becomes also a free energy change measure for the reference reaction. The Hammett equation can also be rewritten in terms of rate constants, instead of equilibrium constants. Thus, by using the Arrhenius equation, a similar linear relationship between the activation free energy and σ X can be obtained. On the basis of these facts, the Hammett type equations are generally referred to as linear free- energy relationships in the literature. 1−5 Even though the Hammett equation still remains as one of the most general means for estimating the substituent electronic effects on a reaction site, some failures in the predictive capabilities of the original approach have been reported. This has prompted proposals of several kinds of substituent constants, and the attempt to separate the σ X values into their resonance and inductive/field contributions. 4,5 Also, in this line and maintaining the basic ideas behind Hammett’s approach, Taff 6 and Hanch 7 have extended it to quantify the substituent steric and hydrophobic effects. It is interesting to emphasize that, for all the existing versions, the Hammett constant values implicitly take into account the effects of the medium where they are measured, which constitutes a formidable task to accomplish relying on approaches based only on first principles theoretical arguments. Received: January 5, 2012 Revised: May 30, 2012 Article pubs.acs.org/JPCA © XXXX American Chemical Society A dx.doi.org/10.1021/jp300160g | J. Phys. Chem. A XXXX, XXX, XXX−XXX