This QSAR study, which involved a series of Azetidinones derived from 4,4'-diaminodiphenylsulfone (dapsone), yielded two models based on molecular descriptors and the antibacterial activities Escherichia coli and Staphylococcus aureus.The molecular descriptors were obtained by applying the methods of quantum chemistry at the B3LYP/6-31G (d) level. The statistical indicators of the first model which is a function of the Escherichia coli activity are: the coefficient of determination R<sup>2</sup> equals 0.992, the standard deviation S equals 0.342, the Fischer coefficient F equals 185.088 and the cross-validation coefficient Q<sup>2</sup><sub>CV</sub> equals 0.992. Those of the second model showing the activity of Staphylococcus aureus are: the regression coefficient R<sup>2</sup>= 0.987, a standard deviation S=0.193, the Fischer coefficient F=114.955 and the cross-validation coefficient Q<sup>2</sup><sub>CV</sub>= 0.987. These models have good statistical performances. The quantum descriptors of dipole moment (μ), global softness (σ) and electronegativity (χ) are responsible of the antibacterial activity of the Azetidinones derived from dapsone. In addition, the dipole moment is the priority descriptor for the prediction of the antibacterial activity of the studied compounds. The Eriksson et al. acceptance criteria used for the test set is verified. The values of the dtheo/dexp ratio of the theoretical and experimental activities for the test set tend towards unity.
The asymmetric unit of the title compound, C17H14N2O, contains two independent molecules each consisting of perimidine and phenol units. The tricyclic perimidine units contain naphthalene ring systems and non-planar C4N2 rings adopting envelope conformations with the C atoms of the NCN groups hinged by 44.11 (7) and 48.50 (6)° with respect to the best planes of the other five atoms. Intramolecular O—H...N hydrogen bonds may help to consolidate the molecular conformations. The two independent molecules are linked through an N—H...O hydrogen bond. The Hirshfeld surface analysis of the crystal structure indicates that the most important contributions for the crystal packing are from H...H (52.9%) and H...C/C...H (39.5%) interactions. Hydrogen bonding and van der Waals interactions are the dominant interactions in the crystal packing. Density functional theory (DFT) optimized structures at the B3LYP/ 6–311 G(d,p) level are compared with the experimentally determined molecular structure in the solid state. The HOMO–LUMO behaviour was elucidated to determine the energy gap.
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