Instability in pyramidal–tetrahedral structure including elements from group 14 induced by pseudo-Jahn–Teller effect

  • Ali Reza IlkhaniEmail author
  • Zhibo Wang
Regular Article


The pseudo-Jahn–Teller effect (PJTE) of the pyramidal–tetrahedral A42− (A = C, Si, Ge, Sn) dianion analogues is investigated by quantum chemical calculations. The adiabatic potential energy surface cross sections obtained from ab initio calculation of the A42− analogues show instability for a degenerate E ground state. Thus, symmetry breaking phenomena induced by the PJTE occur in the series, and the unstable pyramidal–tetrahedral configuration with Td symmetry distorts to the equilibrium geometry structure (lower C2 symmetry) in all considered dianions. Additionally, the (E(1) + A1 + E(2)) ⊗ e problem is formulated for the analogues with the APES cross sections used in order to estimate the coupling constants by fitting the energies acquired from the PJTE equations. To restore the pyramidal–tetrahedral structure with Td symmetry and quenching the PJTE in the series, the PJTE in A42− analogues was suppressed through (1) adding two electrons to the A42− series and (2) either doping the A42− analogues with an atom from group 14 or trapping He2+ and Ne2+ inside the Si42− cage.


PJTE Tetrahedral unstable configuration Pyramidane dianion Restoring Td symmetry 3D distortion 



The corresponding author thanks the Yazd Branch, Islamic Azad University, for their financial support of this research. This work has been enabled in part with support from Westgrid ( and Compute/Calcul Canada (

Compliance with ethical standards

Conflict of interest

The authors declare no conflict of interest in this research.


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Copyright information

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

Authors and Affiliations

  1. 1.Department of Chemistry, Yazd BranchIslamic Azad UniversityYazdIran
  2. 2.Department of ChemistryUniversity of AlbertaEdmontonCanada

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