Strong Pseudo Jahn—Teller Effect on the Single Hexagonal Unit of Germanene

Abstract

ABSTRACTGermanene, the 2D graphene-like Ge nanosheet, has been recently the subject of many theoretical studies and experimental attempts to synthesize it on Ag(111), Au(111) and Pt(111) surfaces. The experimental and theoretical evidences of germanene show a 2D continuous honeycomb layer with a buckled conformation. Density functional theory (DFT) calculations have predicted a larger buckling for germanene than silicene whose origin is also associated with a pseudo Jahn–Teller (PJT) effect. In this work we show that despite the fact that both, silicene and germanene possess a buckled conformation with a PJT origin, their vibronic coupling have different origins. The analysis is based on the PJT puckering instability of the hexagermabenzene molecule, the single hexagonal unit of germanene. This is done through the linear vibronic coupling model between the ground and the lowest excited states, which leads to a puckering distortion of the more symmetric cluster. We study both, the multilevel superposition vibronic model and possible mixing of excited states of different irreducible representations, which have been used to show the origin of similar structural transitions in hexagonal silicon and gold ring systems respectively. We show that contrary to other cases with one six-member rings, for the hexagermabenzene molecule a mixture of both the multilevel PJT and a ground state coupling with two quasi-degenerate excited states is necessary for a satisfactory explanation of puckering. Our model allows a determination of the coupling constants and predicts simultaneously the Adiabatic Potential Energy Surface (APES) behavior for the ground and excited states around the maximum symmetry point. The analysis is based on a scalar relativistic DFT and time-dependent DFT (TD-DFT) calculations in the Zero Order Regular Approximation (ZORA) using the B3LYP hybrid functional.