Molecular Quantum Similarity Measures from Fermi Hole Densities: Modeling Hammett Sigma Constants

A new approach, based on the use of fragment Quantum Self-Similarity Measures (MQS-SM) as descriptors of electronic substituent effect in aromatic series, was proposed. The novelty of this approach consists of the fact that the corresponding MQS-SM are not derived, as usual, from ordinary density functions (DF) but from the so-called domain averaged Fermi holes. This approach was applied to the study of substituent effects on the acidobasic dissociation constants in 6 series of para-substituted aromatic carboxylic acids. It has been shown that MQS-SM calculated for each particular set of acids correlate with the Hammett substituent constants. As a consequence, the corresponding similarity measures can be used as new efficient descriptors of the substituent effect, which hopefully could replace empirical sigma constants in QSAR models.