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-C6H4-Z), Linderberg et al. 1 demonstrated the validity of an equation similar to: ∆CEBE ≈ κσ, where ∆CEBE is the difference in core-electron binding energies (CEBEs) of the fluorinated carbon in p-F-C6H4-Z and that in FC6H5, 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-C6H4-Z were first calculated using Density Functional Theory (DFT) with the scheme ∆EKS (PW86-PW91)/TZP+Crel//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 σp constants against calculated shifts ∆CEBEs (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 σp constant is proportional to the calculated ∆CEBEs. 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.