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The splitting, into two, of the potential function along the bending coordinate in degenerate electronic states of linear triatomic or polyatomic molecules. Most of the areas and methods of molecular physics and spectroscopy assume the validity of the Born-Oppenheimer approximation. The nuclei generally move much more slowly than the electrons, the frequencies associated with electronic transitions are much higher than vibrational frequencies, and one can consider separately the three types of molecular motion: electronic, vibrational, and rotational. These statements are no longer necessarily valid for electronic states which are degenerate or at least close to degeneracy, and the Born-Oppenheimer approximation breaks down.
Degenerate electronic states usually occur in molecules having a high degree of symmetry. The symmetric equilibrium geometry which causes the electronic degeneracy is, in general, lowered in the course of molecular vibrations, and this may lead to splitting of the potential. The molecular potential is usually expressed in terms of a polynomial expansion in displacements r, and, in nonlinear molecules, the linear terms may lead to coupling of the electronic and vibrational degrees of freedom. The resulting breakdown of the Born-Oppenheimer approximation is in this case known as the Jahn-Teller effect. In linear molecules the symmetry is lowered during bending vibrations. In the bending potential the linear (and other odd) terms are zero by symmetry. The first nonvanishing terms which can couple the degenerate electronic states are quadratic in the bending coordinate. The results of this coupling in linear molecules are referred to as the Renner-Teller effect, or simply the Renner effect. See Jahn-Teller effect, Molecular structure and spectra