Hammett equation (Hammett relation)

The equation in the form:

$log 10 ( k k 0 ) = ρ σ$

$log 10 ( K K 0 ) = ρ σ$

applied to the influence of meta- or para-substituents X on the reactivity of the functional group Y in the benzene derivative m- or p-XC₆H₄Y. $k$ or $K$ is the rate or equilibrium constant, respectively, for the given reaction of m- or p-XC₆H₄Y; $k 0$ or $K 0$ refers to the reaction of C₆H₅Y, i.e. X = H; is the substituent constant characteristic of m- or p-X: is the reaction constant characteristic of the given reaction of Y. The equation is often encountered in a form with $log 10 k 0$ or $log 10 K 0$ written as a separate term on the right hand side, e.g.

$log 10 k = ρ σ + log 10 k 0$

$log 10 K = ρ σ + log 10 K 0$

It then signifies the intercept corresponding to X = H in a regression of $log 10 k$ or $log 10 K$ on $σ$ .

See also: ρ-value, σ-constant, Taft equation, Yukawa-Tsuno equation

Source:

PAC, 1994, 66, 1077 (Glossary of terms used in physical organic chemistry (IUPAC Recommendations 1994)) on page 1119