Definition of dual substituent-parameter equation

In a general sense, this is any equation which expresses substituent effects in terms of two parameters. However, in practice the term is used more specifically for an equation for summarizing the effects of meta- or para-substituents (i = m or p) X on chemical reactivity, spectroscopic properties, etc. of a probe site Y in benzene or other aromatic system.

Pi = [rho] Ii [sigma] I + [rho] Ri [sigma] R

P is the magnitude of the property Y for substituent X, expressed relative to the property for X=H; [sigma] I and [sigma] R are inductive or polar and resonance substituent constants, respectively, there being various scales for [sigma] R; [rho] I and [rho] R are the corresponding regression coefficients. EHRENSON, BROWNLEE, and TAFT (1973); TAFT and TOPSOM (1987). See also extended Hammett equation.