Estimation of Hammett sigma constants Hammett equation

core-electron binding energy (cebe) shifts correlate linearly hammett substituent constants (σ) in substituted benzene derivatives.

consider para-disubstituted benzene p-f-c6h4-z, z substituent such nh2, no2, etc. fluorine atom para respect substituent z in benzene ring. image on right shows 4 distinguished ring carbon atoms, c1(ipso), c2(ortho), c3(meta), c4(para) in p-f-c6h4-z molecule. carbon z defined c1(ipso) , fluorinated carbon c4(para). definition followed z = h. left-hand side of (1) called cebe shift or Δcebe, , defined difference between cebe of fluorinated carbon atom in p-f-c6h4-z , of fluorinated carbon in reference molecule fc6h5.

the right-hand side of eq. 1 product of parameter κ , hammett substituent constant @ para position, σp. parameter κ defined eq. 3:

where ρ , ρ* hammett reaction constants reaction of neutral molecule , core ionized molecule, respectively. Δcebes of ring carbons in p-f-c6h4-z calculated density functional theory see how correlate hammett σ-constants. linear plots obtained when calculated cebe shifts @ ortho, meta , para carbon plotted against hammett σo, σm , σp constants respectively.

κ value calculated ≈ 1.

hence approximate agreement in numerical value , in sign between cebe shifts , corresponding hammett σ constant.