Taft equation

[6] The hydrolysis of esters can occur through either acid and base catalyzed mechanisms, both of which proceed through a tetrahedral intermediate.

Due to the similar tetrahedral intermediates, Taft proposed that under identical conditions any steric factors should be nearly the same for the two mechanisms and therefore would not influence the ratio of the rates.

Due to this, the steric substituent constant Es was determined from solely the acid catalyzed reaction, as this would not include polar effects.

However, because context will have an effect on steric interactions[7] some Es values can be larger or smaller than expected.

[9][10] Using molecular mechanics, Meyers has defined Va values that are derived from the volume of the portion of the substituent that is within 0.3 nm of the reaction center.

Similar to the Hammett ρ value: Similar to the polar sensitivity factor, the steric sensitivity factor δ for a new reaction series will describe to what magnitude the reaction rate is influenced by steric effects.

When a reaction series is not significantly influenced by polar effects, the Taft equation reduces to: A plot of the ratio of the rates versus the Es value for the substituent will give a straight line with a slope equal to δ.

Similarly to the Hammett ρ value, the magnitude of δ will reflect to what extent a reaction is influenced by steric effects: Since Es values are large and negative for bulkier substituents, it follows that: When both steric and polar effects influence the reaction rate the Taft equation can be solved for both ρ* and δ through the use of standard least squares methods for determining a bivariant regression plane.

In a recent example, Sandri and co-workers[13] have used Taft plots in studies of polar effects in the aminolysis of β-lactams.

They have looked at the binding of β-lactams to a poly(ethyleneimine) polymer, which functions as a simple mimic for human serum albumin (HSA).

As a part of their mechanistic studies Sandri and co-workers plotted the rate of aminolysis versus calculated σ* values for 6 penicillins and found no correlation, suggesting that the rate is influenced by other effects in addition to polar and steric effects.