Swain–Lupton equation

[1] A linear least-squares analysis is used to determine the coefficients/constants a, b, and i (Swain and Lupton used a procedure called DOVE: Dual Obligate Vector Evaluation).

[2] Constants were first based on three previous reactions (σm, σp, σp+), which leads to more possible errors since the compiled data is only a minimal combination of a much larger pool.

A zero-scale is used for hydrogen, because it is known to neither readily donate or accept electron density when attached to a carbon atom due to similar electronegativities.

Negatively charged substituents (i.e., CO2− and SO3−) have much lower F values because of their ability to resonate electron density amongst the oxygen atoms and stabilize it through hydrogen-bonding with solvents.

New techniques to solve for Swain–Lupton substituent parameters involve studying chemical shifts through nuclear magnetic resonance spectroscopy.

One can predict the difference in data comparing two substituents using %r: The most dominant effect is clear when looking at the ratio of R to F. For example, a tungsten complex was shown to alkylate allyl carbonates A and B.

This is in agreement with the proposed mechanism (a positive charge forms on the benzylic carbon and is stabilized by resonance; R dominates by a ratio of 0.8/0.2).

[5] Like any other linear free-energy relationship established, the Swain–Lupton equation will too fail when special circumstances arise, i.e. change in the rate determining step of a mechanism or solvation structure.

Fig. 1 Dissociation of substituted benzoic acids.
Fig. 2a F values for common substituents.
Fig. 2b R values for common substituents.
Fig. 3a Allylic alkylation of carbonates.
Fig. 3b Graph of Swain–Lupton parameters.