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

  • Fei-peng ZhaiEmail author
  • Hong-en Wei
  • Yi Liu
  • Feng-yun Hu
Original Paper


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 (\( \overline{V_s} \)), variances (\( {\sigma}_{\mathrm{tot}}^2 \), \( {\sigma}_{+}^2 \) and \( {\sigma}_{-}^2 \)), and product of \( {\sigma}_{\mathrm{tot}}^2 \) and electrostatic balance parameter (ν) (\( {\sigma}_{\mathrm{tot}}^2 \)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.

Graphical abstract

Anti-cooperativity effect plays an important role in forming the pharmaceutical incompatibility


Pharmaceutical incompatibility Cooperativity effect Surface electrostatic potential π∙∙∙π RDG 


Compliance with ethical standards

Ethical statement

We allow the journal to review all the data, and confirm the validity of the results. We have none of the financial relationships. This manuscript was not published previously and it is not submitted to more than one journal. This work is not split up into several parts to submit. No data have been fabricated or manipulated.

Supplementary material

894_2019_4060_MOESM1_ESM.doc (543 kb)
ESM 1 (DOC 543 kb)


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Fei-peng Zhai
    • 1
    Email author
  • Hong-en Wei
    • 1
  • Yi Liu
    • 1
  • Feng-yun Hu
    • 1
  1. 1.Department of NeurologyShanxi Provincial People’s HospitalTaiyuanChina

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