Pseudo-Jahn–Teller effects in two-dimensional silicene, germanene and stanene: a crystal orbital vibronic coupling density analysis

The presence of the pseudo-Jahn–Teller (PJT) effect has been investigated in the heavier analogues of graphene, namely silicene, germanene and stanene, by applying the orbital vibronic coupling density theory. In order to do so, we have made a vis-a-vis analogy with their respective planar, honeycomb molecular cluster models, namely hexasilabenzene $({\text{Si}}_6{\text{H}}_6$), hexagermabenzene $({\text{Ge}}_6{\text{H}}_6$) and hexastannabenzene $\left({\text{Sn}}_6{\text{H}}_6\right)$. One-to-one mapping of the occupied crystal orbitals and unoccupied crystal orbitals in two-dimensional (2D) Si, Ge and Sn systems to the occupied molecular orbitals and unoccupied molecular orbitals of the corresponding molecular units are used to identify PJT-active bands and compute the crystal orbital vibronic coupling density (c-OVCD) and crystal orbital vibronic coupling constants (c-OVCCs). c-OVCD and c-OVCC show the local picture of the PJT coupling in these 2D systems. This article exemplifies the fruitfulness of deciphering the structural aspects in materials based on orbitals of their corresponding simple molecular units—a reductionist quantum chemical approach to materials.