Hammett equation: a standalone construct

Louis P. Hammett introduced this relationship in 1937, in the Journal of the American Chemical Society paper "The effect of structure upon the reactions of organic compounds. Benzene derivatives", to quantify how a chemical group attached to a benzene ring changes the rate or the equilibrium of a reaction taking place elsewhere on that ring. It states that log(k/k0) equals the product of two numbers: a substituent constant sigma, assigned once to each attached group to capture how strongly it pulls or pushes electron density, and a reaction constant rho, which measures how sensitive a given reaction is to that electronic effect. Because sigma is fixed from a single reference reaction, the ionisation of substituted benzoic acids, and then reused unchanged across many other reactions, one scale of substituent numbers predicts behaviour it was never fitted to, which is why chemists call it a linear free-energy relationship: a straight-line link between the free energy of one process and that of another. Corwin Hansch, Albert Leo, and Robert W. Taft compiled and extended the substituent scales in a 1991 survey that remains the standard reference table. The relationship reaches from physical organic chemistry and reaction-mechanism analysis into quantitative structure-activity work in medicinal chemistry, where the same sigma values feed models that relate molecular structure to biological potency.[1][2]

Unit

A linear free-energy relationship, log(k/k0) = rho times sigma, linking a substituent constant to a reaction's rate or equilibrium constant

Recovery means

Not applicable

Measured by

Quantified by plotting log(k/k0) for a series of substituents against their tabulated sigma values; the slope gives rho and the linearity of the fit gauges how well the relationship holds