withdrawing group is going to slow down the reaction by decreasing the electron density in the anti bonding orbital of leaving group in the transition state. Hammett modifications Other equations now exist that refine the original Hammett equation: the Swain–Lupton equation, the Taft equation, the Grunwald–Winstein equation, and the Yukawa–Tsuno equation. An equation that addresses stereochemistry in aliphatic systems has also been developed. Estimation of Hammett sigma constants Core-electron binding energy (CEBE) shifts correlate linearly with the Hammett substituent constants (σ) in substituted benzene derivatives. Consider para-disubstituted benzene p-F-C6H4-Z, where Z is a substituent such as NH2, NO2, etc. The fluorine atom is para with respect to the substituent Z in the benzene ring. The image on the right shows four distinguished ring carbon atoms, C1(ipso), C2(ortho), C3(meta), C4(para) in p-F-C6H4-Z molecule. The carbon with Z is defined as C1(ipso) and fluorinated carbon as C4(para). This definition is followed even for Z = H. The left-hand side of () is called CEBE shift or ΔCEBE, and is defined as the difference between the CEBE of the fluorinated carbon atom in p-F-C6H4-Z and that of the fluorinated carbon in the reference molecule FC6H5. The right-hand side of Eq. is a product of a parameter κ and a Hammett substituent constant at the para position, σp. The parameter is defined by eq. : where and are the Hammett reaction constants for the reaction of the neutral molecule and core ionized molecule, respectively. ΔCEBEs of ring carbons in p-F-C6H4-Z were calculated with density functional theory to see how they correlate with Hammett σ-constants. Linear plots were obtained when the calculated CEBE shifts at the ortho, meta and para carbon were plotted against Hammett σo, σm and σp constants respectively. value calculated ≈ 1. Hence the approximate agreement in numerical value and in sign between the CEBE shifts and their corresponding Hammett σ constant. See also Bell–Evans–Polanyi principle Craig plot Free-energy relationship pKa Quantitative structure–activity relationship References Further reading General Thomas H. Lowry & Kathleen Schueller Richardson, 1987, Mechanism and Theory in Organic Chemistry, 3rd Edn., New York, NY, US: Harper & Row, , see , accessed 20 June 2015. Francis A. Carey & Richard J. Sundberg, 2006, "Title Advanced Organic Chemistry: Part A: Structure and Mechanisms," 4th Edn., New York, NY, US: Springer Science & Business Media, , see , accessed 19 June 2015. Michael B. Smith & Jerry March, 2007, "March's Advanced