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The interaction of M-BZ, M(\(\hbox {H}_{{2}}\hbox {O}\))-BZ, M-2BZ and M(\(\hbox {H}_{{2}}\hbox {O}\))-2BZ (\(\hbox {M} =\hbox {Li}^{+}\), \(\hbox {Na}^{+}\), \(\hbox {K}^{+}\), \(\hbox {Mg}^{2+}\), \(\hbox {Ca}^{2+}\)): EDA and ETS-NOCV approaches


Cation–\(\uppi \) or cation–2\(\uppi \) interactions generally exist between one cation and one or two electron-rich \(\uppi \)-ring, which play an important role in many areas (such as benzene, borazine, aromatic rings, graphene and carbon nanotubes). Here, we report the interaction of M-BZ, M(\(\hbox {H}_{{2}}\hbox {O}\))-BZ, M-2BZ and M(\(\hbox {H}_{{2}}\hbox {O}\))-2BZ (\(\hbox {BZ} = \hbox {borazine}\), \(\hbox {M} =\hbox {Li}^{{+}}\), \(\hbox {Na}^{{+}}\), \(\hbox {K}^{{+}}\), \(\hbox {Mg}^{{2+}}\), \(\hbox {Ca}^{{2+}})\) at the B3LYP-D3/TZ2P levels of theory. We found that the interaction energy decreases as the radii of the cations increase. The total interaction energy was decomposed into the dispersion correction, Pauli repulsion, electrostatic interaction and orbital interaction by using energy decomposition analysis. In addition, the binding energy of M-BZ (2BZ) is similar to that of M-benzene (2benzene), indicating the special importance of M-BZ (2BZ) interaction in biological system. From the extended transition state scheme with the theory of natural orbitals for chemical valence, the first dominant deformation densities plot shown the flow of charge between the fragments, which mean the BZ is \(\uppi \) donation and cation (M(\(\hbox {H}_{{2}}\hbox {O}\))) is \(\upsigma \) or \(\uppi \) acceptor.


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Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: Data is available from the corresponding author on reasonable request.]


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This work was supported by the National Natural Science Foundation of China (Grant Nos. to J.M. 21903057 and 91841301 to H.R.).

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Conceptualization, JM and HR; Data Curation, ZL, BY; Formal Analysis, ZL, RF and JM; Writing—Original Draft Preparation, ZL and BY; Writing—Review and Editing, JM, ZL, YH and HZ.

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Correspondence to Haisheng Ren or Jianyi Ma.

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Li, Z., Yang, B., Fan, R. et al. The interaction of M-BZ, M(\(\hbox {H}_{{2}}\hbox {O}\))-BZ, M-2BZ and M(\(\hbox {H}_{{2}}\hbox {O}\))-2BZ (\(\hbox {M} =\hbox {Li}^{+}\), \(\hbox {Na}^{+}\), \(\hbox {K}^{+}\), \(\hbox {Mg}^{2+}\), \(\hbox {Ca}^{2+}\)): EDA and ETS-NOCV approaches. Eur. Phys. J. D 75, 11 (2021).

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