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 R² equals 0.992, the standard deviation S equals 0.342, the Fischer coefficient F equals 185.088 and the cross-validation coefficient Q²_CV equals 0.992. Those of the second model showing the activity of Staphylococcus aureus are: the regression coefficient R²= 0.987, a standard deviation S=0.193, the Fischer coefficient F=114.955 and the cross-validation coefficient Q²_CV= 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.

This theoretical chemical reactivity study was conducted using the Density Functional Theory (DFT) method, at computational level B3LYP/6-31G (d). It involved a series of six (06) 5-arylidene rhodanines and allowed to predict the chemical reactivity of these compounds. DFT global chemical reactivity descriptors (HOMO and LUMO energies, chemical hardness, softness, electronegativity) were examined to predict the relative stability and reactivity of rhodanin derivatives. Thus, the compound 6 which has an energy gap between the orbitals of ΔEgap = 3.004 eV is the most polarizable, the most reactive, the least stable, the best electron donor and the softest molecule. Calculation of the local indices of reactivity as well as dual descriptors revealed that the sulfur heteroatom of the Rhodanine ring is the privileged site of electrophilic attack in a state of sp3 hybridization and privileged site of nucleophilic attack in a state of sp2 hybridization.

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This QSAR study was conducted by using a series of Azetidinones which belong to Dapsone derivatives. It allowed to obtain two different models according to the molecular descriptors and the antibacterial activities (Bacillus subtilis and Pseudomonas aeruginosa). The molecular descriptors were obtained by applying the methods of quantum chemistry at the B3LYP/6-31G (d) level. The different statistical indicators of the first model which are as a function of the Bacillus subtilis activity are the coefficient of determination R 2 = 0.945, the standard error of the regression S = 0.139, the Statistical significance of regression, Fisher F-test F = 94.315 and the cross-validation correlation coefficient Q 2 cv=0.942. Those of the second model linked to the activity of Pseudomonas aeruginosa are the regression coefficient R 2 = 0.933, the standard deviation S=0.135, the Statistical significance of regression, Fisher F-test F = 46.582 and the cross-validation coefficient Q 2 cv= 0.928. So these models have good statistical performances. The quantum descriptors of electrophilic index (ω), electronic energy (ε 0) and dipole moment (μ) are responsible of the antibacterial activity of the Azetidinones derived from Dapsone. Moreover, the index of electrophilic is the first descriptor in terms of priority for the prediction of the antibacterial activity of the studied compounds. The Eriksson et al. acceptance criteria used for the test set are verified. External validation sets also verified all the Tropsha et al. criteria.