4. Group-Theoretical Treatment of Pseudo-Jahn-Teller Systems

According to Jahn-Teller (JT) theorem any nonlinear arrangement of atomic nuclei in electron degenerate state (except an accidental and Kramers degeneracy) is unstable. Pseudo-JT systems are treated as an analogy of JT theorem for pseudo-degenerate electron states. Stable nuclear arrangements of lower energy of such systems correspond to the minima of their potential energy surfaces (PES). In large systems the analytical description of their PES is too complicated and a group-theoretical treatment must be used to describe their stable structures. This may be based either on JT active coordinates– as in the epikernel principle– or on the electron states– as in the method of step-by-step descent in symmetry. This review explains the basic terms of group theory (especially of point groups of symmetry) and potential energy surfaces (extremal points and their characteristics) as well as the principles of group-theoretical methods predicting the extremal points of JT systems– the method of epikernel principle (based on JT active coordinates) and the method of step-by-step descent in symmetry (based on a consecutive split of the degenerate electron states). Despite these methods have been elaborated for the case of electron degeneracy, they are applicable to pseudo-degenerate electron states as well. The applications of both methods to pseudo-JT systems are presented on several examples and compared with the published results.