Knowledge Bank

A Theorem, applicable to spinrovibronic states of molecules and crystals, has been derived: No degeneracy based on interchange symmetry is permissible.'' The derivation is based on the Pauli principle (symmetrization postulate) and the application of the theorem is guided by the following mathematical Lemma: The spatial symmetry group can always be written as a direct product of an interchange group and a fixing (non-interchange) group.'' Proofs of both Theorem and Lemma may be outlined (for 0 to 3-dimensional systems). Time reversal symmetry and the resultant (1651) magnetic space groups, as well as flexible (non-rigid) systems, are covered by the Theorem. Double groups are outside the Lemma. Single magnetic (and non-magnetic) space groups obey both Lemma and Theorem. Also derived have been an Electronic-Analog-Jahn-Teller Theorem, a Vibrational-Analog-Jahn-Teller Theorem and a Rotational-Analog-Jahn-Teller Theorem. All are special cases of the general Theorem. The application of all the above theorems will be discussed qualitatively and related to instability, distortions and splittings of spinrovibronic states in molecules and crystals. Net-spinor systems and the Kramers-Wigner degeneracy, as well as the applicability of the Theorem to neat crystals (co-operative-Jahn-Teller-effect'') will be discussed. Birman's extended-Jahn-Teller conjecture for neat crystals is in agreement with our results except for his word almost.''