02732 IUPAC Gold Book - Hammett equation 10.1351/goldbook.H02732 H02732 current mentioned: rho-sigma equation synonyms: Hammett relation, ρσ-equation 1 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 $\ce{X}$ on the reactivity of the functional group $\ce{Y}$ in the benzene derivative m- or $\ce{p-XC6H4Y}$. \(k\) or \(K\) is the rate or equilibrium constant, respectively, for the given reaction of m- or $\ce{p-XC6H4Y}$; \(k_{0}\) or \(K_{0}\) refers to the reaction of $\ce{C6H5Y}$, i.e. $\ce{X} = \ce{H}$; is the substituent constant characteristic of m- or $\ce{p-X}$: is the reaction constant characteristic of the given reaction of $\ce{Y}$. 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 $\ce{X} = \ce{H}$ in a regression of \(\log _{10}k\) or \(\log _{10}K\) on \(\sigma \). ρ-value https://goldbook.iupac.org/terms/view/V05019 Taft equation https://goldbook.iupac.org/terms/view/T06247 Yukawa–Tsuno equation https://goldbook.iupac.org/terms/view/Y06734 equilibrium constant https://goldbook.iupac.org/terms/view/E02177 functional group https://goldbook.iupac.org/terms/view/F02555 σ-constant https://goldbook.iupac.org/terms/view/C05438 PAC, 1994, 66, 1077. 'Glossary of terms used in physical organic chemistry (IUPAC Recommendations 1994)' on page 1119 (https://doi.org/10.1351/pac199466051077) https://goldbook.iupac.org/terms/view/H02732/html https://goldbook.iupac.org/terms/view/H02732/json https://goldbook.iupac.org/terms/view/H02732/plain Citation: 'Hammett equation' in IUPAC Compendium of Chemical Terminology, 5th ed. International Union of Pure and Applied Chemistry; 2025. Online version 5.0.0, 2025. 10.1351/goldbook.H02732 The IUPAC Gold Book is licensed under Creative Commons Attribution-ShareAlike CC BY-SA 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/) for individual terms. If you are interested in licensing the Gold Book for commercial use, please contact the IUPAC Executive Director at executivedirector@iupac.org . The International Union of Pure and Applied Chemistry (IUPAC) is continuously reviewing and, where needed, updating terms in the Compendium of Chemical Terminology (the IUPAC Gold Book). Users of these terms are encouraged to include the version of a term with its use and to check regularly for updates to term definitions that you are using. 2026-05-10T20:42:00+00:00