Geometry, solvent, and polar effects on the relationship between calculated core-electron binding energy shifts (ΔCEBE) and Hammett substituent (σ) constants

According to Lindberg et al. there exists an equation ΔCEBE=κσ for substituted benzene derivatives. Core-electron binding energy shift (ΔCEBE) is the difference between the CEBE of a specific carbon in monosubstituted benzene derivatives (C6H5-Z) and in benzene (C6H5-H); κ is related to a reaction constant and σ is the experimental Hammett substituent constant. The object of the present work is to investigate geometry, solvent, and polar effects on Lindberg's equation using theoretically calculated ΔCEBE. The CEBEs were calculated using DFT within the scheme ΔEKS (PW86x-PW91c/TZP+Crel). The geometry has only little effect on the CEBE values. A regression relation between ΔCEBE and σ takes the form ΔCEBE=κσ−C with κ≅1.17 and C≅0.17. We estimated 69 σ constants in water that have not been presented in the literature. Theoretical resonance (σR) and inductive (σI) effects were calculated using Taft equations. ΔCEBE (R) and ΔCEBE (I) effects on ΔCEBE were also calculated using Taft-like equations. The quality of the correlation to the resonance is better than that to the inductive effect, in water. The regression quality in aqueous organic solvent is poorer than in water in both Lindberg and Taft equations. The solvent effect is greater on the resonance than on the inductive effect.