An investigation of descriptors based on the critical points in the electron density by building quantitative structure-property relationships for proton chemical shifts

Descriptors used in quantitative structure-activity/property relationships must encode a variety of physical and chemical properties to build reliable models. We have investigated the ability of descriptors based on bond critical points in the electron density according to Bader's quantum theory of atoms in molecules to predict proton nuclear shieldings. This was used as a validation of the bond critical points ability to describe a property related to the local electronic structure around an atom properly. One hundred and seventy distinct proton shieldings in a series of 60 substituted benzene compounds have been computed using ab initio methods. The obtained model with the largest variation in the attached substituents yielded a root mean square error of prediction of 0.1 ppm where the absolute values of the computed proton shielding varied between 22.3 and 26.4 ppm. Even better accuracies were obtained when the model was limited to more homogeneous substituents. While a negative relationship was observed for the value of the electron density at the bond critical point, the Laplacian and ellipticity showed a positive relationship. These effects relate to the degree in which the electrons provide a successful shielding of the proton.