The Theory of the Jahn-Teller Effect

Abstract

After a brief historical introduction, the derivation of the so-called Jahn-Teller theorem is discussed. Group-theoretical concepts are introduced and the octahedral group is chosen as an example. The static distortion of a system comprising a T2g electronic state coupled linearly to normal modes of the same type provides an illustration of the calculation of Clebsch-Gordan coefficients for the octahedral group. Annihilation and creation operators are introduced to discuss the vibronic Hamiltonian, and octahedral tensors are brought into play to make the analysis more concise. The differences that occur vhen electron spin is taken into account are pointed out. The advantages and dravbacks of using Glauber (coherent) states in the strong-coupling limit are briefly mentioned. Attention is paid to the Jahn-Teller system in which a T electronic state (such as a p electron) is equally coupled to octahedral t and e modes, these modes possessing equal frequencies and thereby leading to a Hamiltonian vith spherical symmetry. Phase changes associated vith the unequal rotational motion of the T state and the displaced ligands for this system are studied in the strong-coupling limit. The connection vith Berry's phase is discussed.