The Jahn-Teller Effect and Crystalline Stark Splitting for Clusters of the Form XY6

The present article develops the mathematical theory needed in connection with the preceding paper, and with a study of paramagnetic relaxation to appear later. Jahn and Teller have shown that the normal coordinate theory for a molecular cluster such as X·6H2O (X=Ti, V, Cr) is materially different from usual if the X ion is degenerate. Namely, it is impossible to eliminate linear terms in the atomic displacements simultaneously from all substates of the degenerate level. Consequently, stability is achieved only if the degeneracy is lifted, and so the water group distorts itself so that it is not cubically arranged. A calculation is made of the magnitude of the effect, which has an important bearing on magnetic behavior. In order to allow for the disturbing effect of distant atoms, the cluster X·6H2O is not treated as free, but rather as embedded in a trigonal field of force. The Stark splittings in such fields, quite apart from the Jahn-Teller effect, are hence obtained as a corollary.