Group-Theoretical Analysis of Jahn-Teller Systems

The problem of searching the stable structures obtained by the symmetry descent of high-symmetric non-linear parent systems in a degenerate electronic state (except an accidental and Kramers degeneracy) due to Jahn-Teller effect is solved by a group-theoretical treatment. The basic terms of group theory (especially of point groups of symmetry) and potential energy surfaces are explained. The methods of epikernel principle (based on Jahn-Teller active coordinates obtained by the first order perturbation theory) and step-by-step descent in symmetry (based on a consecutive split of the degenerate electronic state due to a symmetry descent) are explained. Both methods are illustrated by several examples and their results are compared with the structures obtained by high-level quantum-chemical calculations. The method of step-by-step descent in symmetry seems to be more complete.