Definition of Hammett equation (or Hammett relation)

The equation in the form

lg(k/ko) = [rho] [sigma]

lg(K/Ko) = [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; ko or Ko refers to the reaction of C6H5Y, i.e. X = H; [sigma] is the substituent constant characteristic of m- or p-X; [rho] is the reaction constant characteristic of the given reaction of Y. The equation is often encountered in a form with lg ko or lg Ko written as a separate term on the right hand side, e.g.

lg k = [rho] [sigma] + lg ko

lg K = [rho] [sigma] + lg Ko

It then signifies the intercept corresponding to X = H in a regression of lg k or lg K on [sigma] . HAMMETT (1940, 1970). See also [rho] -value, [sigma] -constant, Taft equation, Yukawa-Tsuno equation.