Vibronic (In)stability of mono- and di-Periodic Systems

Abstract

According to the classical Jahn-Teller theorem nonlinear molecules are vibronically unstable if an electronic state is orbitally degenerate. In order to reestablish stability, symmetry braeking occures, i. e. the configuration of the molecule changes so that, considering the new symmetry of the molecule, the electronic degeneracy is removed. The symmetries of molecules are described by finite point groups: in the proof of the Jahn-Teller theorem , dynamical representations of the orbits and irreducible representations of these groups are analysed. In the quasi-1D case (i. e. polymers) direct generalisation of the original proof of the Jahn-Teller theorem is not possible: dynamical representation is infinite and instead of the standard group projector technique, its nontrivial modification is unavoidable. Using modified group projector technique the proof of the Jahn-leller theorem for polymers is straightforward. As for diperiodic systems described by infinite discrete diperiodic groups the Jahn-Teller theorem breaks down. The counter example is the diperiodic group Dg61 with three types (out of 14) of its orbits and four irreducible representations (degenerate electronic states). It is interesting that both the considered group and the considered orbits are related to the CuO2 layers in high-temperature superconductors.