ρ-value (rho-value)

https://doi.org/10.1351/goldbook.V05019
A measure of the susceptibility to the influence of @[email protected] groups on the @[email protected] or @[email protected] of a particular organic reaction involving a family of related @[email protected] Defined by Hammett for the effect of ring substituents in meta- and para-positions of aromatic side-chain reactions by the empirical '$$\rho \sigma$$-equation' of the general form: $\log _{10}(\frac{k_{\text{X}}}{k_{\text{H}}}) = \rho \ \sigma _{\text{X}}$ in which $$\sigma _{\text{X}}$$ is a constant characteristic of the substituent X and of its position in the reactant molecule. More generally (and not only for aromatic series), $$\rho$$-values (modified with appropriate subscripts and superscripts) are used to designate the susceptibility of reaction series for families of various organic compounds to any substituent effects, as given by the modified set of $$\sigma$$-constants in an empirical $$\rho \sigma$$-correlation. Reactions with a positive $$\rho$$-value are accelerated (or the equilibrium constants of analogous equilibria are increased) by substituents with positive $$\sigma$$-constants. Since the sign of $$\sigma$$ was defined so that substituents with a positive $$\sigma$$ increase the @[email protected] of benzoic acid, such substituents are generally described as attracting electrons away from the aromatic ring. It follows that reactions with a positive $$\rho$$-value are considered to involve a @[email protected] (or reaction product) so that the difference in energy between this state and the reactants is decreased by a reduction in @[email protected] at the reactive site of the substrate.