Hammett Equation - Dominating Inductive Effects

Dominating Inductive Effects

3 kinds of ground state or static electrical influences predominate:

• Resonance (mesomeric) effect
• Inductive effect: electrical influence of a group which is transmitted primarily by polarization of the bonding electrons from one atom to the next
• Direct electrostatic (field) effect: electrical influence of a polar or dipolar substituent which is transmitted primarily to the reactive group through space (including solvent, if any) according to the laws of classical electrostatics

The latter two influences are often treated together as a composite effect, but are treated here separately. Westheimer demonstrated that the electrical effects of π-substituted dipolar groups on the acidities of benzoic and phenylacetic acids can be quantitatively correlated, by assuming only direct electrostatic action of the substituent on the ionizable proton of the carboxyl group. Westheimer’s treatment worked well except for those acids with substituents that have unshared electron pairs such as –OH and –OCH3, as these substituents interact strongly with the benzene ring.

Roberts and Moreland studied the reactivities of 4-substituted bicyclooctane-1-carboxylic acids and esters. In such a molecule, transmission of electrical effects of substituents through the ring by resonance is not possible. Hence, this hints on the role of the π-electrons in the transmission of substituent effects through aromatic systems.

Reactivity of 4-substituted bicyclooctane-1-carboxylic acids and esters were measured in 3 different processes, each of which had been previously used with the benzoic acid derivatives. A plot of log(k) against log(K_A) showed a linear relationship. Such linear relationships correspond to linear free energy relationships, which strongly imply that the effect of the substituents are exerted through changes of potential energy and that the steric and entropy terms remain almost constant through the series. The linear relationship fit well in the Hammett Equation. For the 4-substituted bicyclooctane-1-carboxylic acid derivatives, the substituent and reaction constants are designated σ’ and ρ’.