Core-electron binding energy (CEBE) shifts correlate linearly with the Hammett substituent constants (σ) in substituted benzene derivatives.
Consider para-disubstituted benzene p-F-CH-Z, where Z is a substituent such as NH, NO, 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-CH-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-CH-Z and that of the fluorinated carbon in the reference molecule FCH.
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-CH-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 σ, σ and σ 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.