Reassessment of Hammett σ as an effective parameter representing intermolecular interaction energy-links between traditional and modern QSAR approaches

The Hammett σ constant has for a long time been known to be one of most important linear free-energy related parameters that correlate with biological activity. It is a conventionally used electronic parameter in studies of enzymatic quantitative structure-activity relationships (QSAR). However, it is not necessarily obvious why σ represents variations in the free-energy change associated with the complex formation between a congeneric series of ligands with their target protein. So far, several powerful molecular calculations, such as the ab initio fragment molecular orbital (FMO) one, that are directly applicable to ligand-protein complexes have emerged. In this study, we comprehensively reevaluate experimentally derived parameter σ confirming it represents intermolecular interaction energy terms, by applying molecular orbital (MO) calculations to a simple ligand-protein complex model. The current results provide a rational and quantitative basis for bridging the gap between the traditional QSAR approach and 'the modern QSAR one', which involves the molecular calculations to evaluate the overall free-energy change for complex formation.