Deformation of $$\hbox {E}_{4}\,(\hbox {E} = \hbox {P}, \hbox {As}, \hbox {Sb})$$ tetrahedron structures via doping two atoms with elements from group 13: a study of the pseudo-Jahn–Teller effect

Abstract

White phosphorus and yellow arsenic are the most famous inorganic four-membered tetrahedral molecules in nature. Due to the recent application of the tetrahedron-based system as a carrier in drug delivery, the manipulation of the $$\hbox {E}_{4}\,(\hbox {E} = \hbox {P}, \hbox {As}, \hbox {Sb})$$ tetrahedron structure by replacing two of the E atoms by elements from group 13 $$(\hbox {D} = \hbox {Al}, \hbox {Ga}, \hbox {In})$$ has been computationally explored. The symmetry-breaking phenomenon induced by the pseudo-Jahn–Teller effect was reported in the $$\hbox {E}_{2}\hbox {D}_{2}$$ tetrahedral structure. State averaging of the four low-lying electronic states along the $$a_{2}$$ deformation normal coordinate for the series in CASSCF(4,4)/cc–pVTZ–(PP) was carried out to formulate the $$(1\hbox {A}_{1} + 2\hbox {A}_{1 }+ 1\hbox {A}_{2}) \otimes a_{2}$$ PJTE problem and their corresponding coupling constants estimated by fitting the obtained state energies. Moreover, the deformed $$\hbox {C}_{\mathrm{2v}}$$ tetrahedral configuration of $$\hbox {E}_{2}\hbox {D}_{2 }$$ can be restored by i) the protonation of the D atoms or ii) trapping a noble gas dication in the center cavity cage of the systems. Furthermore, the calculated thermodynamic properties of the $$\hbox {E}_{2}\hbox {D}_{2}$$ show that the protonation reaction acts as a spontaneous process fulfilling the $${\Delta \hbox {G}}< 0$$ conditions and the considered series obeys the Bronsted–Lowry base behaviors. The adiabatic potential energy surface calculation of white phosphorus tetrahedron structure via doping two atoms with elements from group 13 demonstrates that the $$(\hbox {1A}_{{1}} + 2\hbox {A}_{1 }+ 1\hbox {A}_{2}) \otimes a_{2}$$ pseudo-Jahn–Teller problem is the reason for the origin of the symmetry breaking phenomena in the series.