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: Delta CEBE approximate to K sigma, where Delta CEBE is the difference in core-electron binding energies (CEBEs) of the fluorinated carbon in p-F-C,H,-Z and that in FC6H5, the parameter K a function of the type of reaction, and sigma is the Hammett substituent (sigma) constant. In this work, CEBEs of ring carbon atoms for a series of para disubstituted molecules p-F-C,H,-Z were first calculated using Density Functional Theory (DFT) with the scheme Delta 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 up constants against calculated shifts Delta 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 sigma(p) constant is proportional to the calculated Delta CEBES. On the other hand, the slope B of the straight line gives an estimate of the parameter K. Similar statistical correlations were obtained for the carbon atoms ortho and meta to the substituent Z. (c) 2005 Wiley Periodicals, Inc.