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   <subfield code="a">Hydrogen binding effect on charged P2 n ( n</subfield>
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   <subfield code="a">An all-electron (AE) calculation of the hydrogen binding effect on charged phosphorus clusters has been performed under the framework of density functional theory (DFT). Compared with the $\mbox{P}_{2n}^\pm $ (n = 1-7) clusters, the $\mbox{HP}_{2n}^\pm $ (n = 1-7), cluster has shorter average P-P bond length, larger binding energy and HOMO-LUMO gap (HLG), higher chemical hardness and frequency of P-P mode. After binding with one hydrogen atom, the electronic structure is changed from open electronic shell to closed electronic shell. Geometrical stability, chemical stability and electronic stability are strengthened. These stability enhancements may be simply understood considering the electron pairing effect. Graphical Abstract The influence of hydrogen binding effect on the even-numbered charged phosphorus clusters has been investigated under the framework of DFT. The stability enhancement can be observed clearly and may be understood by considering the electron pairing effect.</subfield>
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