The structure of Jahn–Teller surfaces

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Abstract
In chemical applications of the Jahn–Teller effect, the shape of the adiabatic potential near the instability point is of primary importance. The present article examines this shape, both in the usual representation in the space of the nuclear configurations and in the less current projective representation in the space of the electronic functions. The general structural aspects of these representations are viewed as the results of a symmetry breaking process, starting at the continuous invariance group of the degenerate coupling limit, and ending with the finite point group of the representation space. The various vibronic coupling mechanisms involved in this process are characterized by irreducible tensor functions of the full orthogonal groups. The leading tensorial rank of the unequal linear coupling mechanism is shown to be four, while the bilinear coupling mechanism also involves an irreducible component of the sixth rank. This tensorial analysis provides a grouptheoretical foundation for the recently formulated epikernel principle, which predicts the location of extremal points on a Jahn–Teller surface.