Quantitative structure-property relationship (QSPR) models were firstly established for the hydrophobic substituent constant (πX) using the theoretical descriptors derived solely from electrostatic potentials (EPSs) at the substituent atoms. The descriptors introduced are found to be related to hydrogen-bond basicity, hydrogen-bond acidity, cavity, or dipolarity/polarizability terms in linear solvation energy relationship, which endows the models good interpretability. The predictive capabilities of the models constructed were also verified by rigorous Monte Carlo cross-validation. Then, eight groups of meta- or para- disubstituted benzenes and one group of substituted pyridines were investigated. QSPR models for individual systems were achieved with the ESP-derived descriptors. Additionally, two QSPR models were also established for Rekker's fragment constants (foct), which is a secondary-treatment quantity and reflects average contribution of the fragment to logP. It has been demonstrated that the descriptors derived from ESPs at the fragments, can be well used to quantitatively express the relationship between fragment structures and their hydrophobic properties, regardless of the attached parent structure or the valence state. Finally, the relations of Hammett σ constant and ESP quantities were explored. It implies that σ and π, which are essential in classic QSAR and represent different type of contributions to biological activities, are also complementary in interaction site.