Hammett equation (Hammett relation)

https://doi.org/10.1351/goldbook.H02732
The equation in the form: \[\log _{10}(\frac{k}{k_{0}}) = \rho \ \sigma \] or \[\log _{10}(\frac{K}{K_{0}}) = \rho \ \sigma \] 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. \[\log _{10}k = \rho \ \sigma +\log _{10}k_{0}\] or \[\log _{10}K = \rho \ \sigma +\log _{10}K_{0}\] It then signifies the intercept corresponding to X = H in a regression of \(\log _{10}k\) or \(\log _{10}K\) on \(\sigma \).
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 (https://doi.org/10.1351/pac199466051077)