Molecular electrostatic potential as a general and versatile indicator for electronic substituent effects: statistical analysis and applications

It is necessary to quantitatively determine substituent effects to accurately elucidate reaction mechanisms in the field of organic chemistry. This paper reports that the molecular electrostatic potential (MESP) can be used as a general and versatile measure for the substituent effects in various chemical reactions by performing extensive density functional theory (DFT) calculations for more than 400 molecules, followed by statistical analyses. We observed a robust and linear correlation between the electrostatic potential and the substituent parameters for various cases of reactive systems, regardless of the DFT functionals, basis sets, and solvation models used. In addition, we statistically analysed the normality of the residuals from the linear regression to demonstrate that strong linear relationships hold universally, which indicates that the electrostatic potential can serve as a physically meaningful quantity for the predictive estimation of substituent effects. In contrast, conventionally used methods based on the charge deviation in the aromatic carbons, as computed using various charge analysis methods, (e.g., Hirshfeld charge analysis) do not demonstrate the statistical normality. Furthermore, we illustrate that MESP can be extensively adopted to strengthen the validity of the linear free energy relationships (LFERs) under various chemical conditions. The results revealed that the MESP shift derived by a functional group on a mono-substituted benzene ring is a strong predictor for the substituent effects on the electronic behaviours in chemical reactions; thus, it can serve as an alternative to other empirical parameters such as the Hammett or Swain-Lupton parameters, or the charge shift.