Estimation of Hammett sigma constants of substituted benzenes through accurate density‐functional calculation of core‐electron binding energy shifts

For substituted benzenes such as (p‐F‐C 6 H 4 ‐Z), Linderberg et al. 1 demonstrated the validity of an equation similar to: ΔCEBE ≈ κσ, where ΔCEBE is the difference in core‐electron binding energies (CEBEs) of the fluorinated carbon in p‐F‐C 6 H 4 ‐Z and that in FC 6 H 5 , the parameter κ is a function of the type of reaction, and σ is the Hammett substituent (σ) constant. In this work, CEBEs of ring carbon atoms for a series of para disubstituted molecules p‐F‐C 6 H 4 ‐Z were first calculated using Density Functional Theory (DFT) with the scheme Δ E KS (PW86‐PW91)/TZP+C rel //HF/6‐31G*. An average absolute deviation of 0.13 eV from experiment was obtained for the CEBEs. Then we performed a linear regression analysis in the form of Y = A+B*X for a plot of Hammett σ p constants against calculated shifts ΔCEBEs (in eV) for the fluorinated carbon. The results were: A = –0.08 and B = 1.01, with correlation coefficient R = 0.973, standard deviation = 0.12, and P < 0.0001. The intercept A of the fitted line, close to zero, shows that the Hammett σ p constant is proportional to the calculated ΔCEBEs. On the other hand, the slope B of the straight line gives an estimate of the parameter κ. Similar statistical correlations were obtained for the carbon atoms ortho and meta to the substituent Z. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005