Theoretical explanation for the pharmaceutical incompatibility through the cooperativity effect of the drug–drug intermolecular interactions in the phenobarbital∙∙∙paracetamol∙∙∙H2O complex

In order to reveal the essence of the pharmaceutical incompatibility, the cooperativity effects of the drug–drug intermolecular π∙∙∙π and H∙∙∙O H-bonding interactions involving hydration were evaluated in the phenobarbital∙∙∙paracetamol∙∙∙H2O complex at the M06-2X/6–311++G** and MP2/6–311++G** levels. The thermodynamic cooperativity effects were also investigated by the statistical thermodynamic method. The results show that the π∙∙∙π stacking ternary complexes with the moderate anti-cooperativity effects are dominant in controling the aggregation process of phenobarbital, paracetamol, and H2O, as is confirmed by the atoms-in-molecules (AIM) and reduced density gradient (RDG) analyses. Therefore, it can be inferred that the anti-cooperativity effect plays an important role in forming the pharmaceutical incompatibility, and thus a deduction on the formation process of the pharmaceutical incompatibility between phenobarbital and paracetamol, with the hydration effect, is given. Several valuable models that relate the features of molecular surface electrostatic potentials or their statistical parameters, such as the surface areas, average values (Vs¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \overline{V_s} $$\end{document}), variances (σtot2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\sigma}_{\mathrm{tot}}^2 $$\end{document}, σ+2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\sigma}_{+}^2 $$\end{document} and σ−2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\sigma}_{-}^2 $$\end{document}), and product of σtot2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\sigma}_{\mathrm{tot}}^2 $$\end{document} and electrostatic balance parameter (ν) (σtot2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\sigma}_{\mathrm{tot}}^2 $$\end{document}ν), to the values of the cooperativity effects were predicted. The formation of the pharmaceutical incompatibility is a thermodynamic cooperativity process driven by the enthalpy change.