In the paper Stability if Polyatomic Molecules in Degenerate Electronic States II - Spin Degeneracy the author wrote:

Thus a twofold degeneracy cannot produce instability for a molecule containing an odd number of electrons with spin.

It is really disturbing for me as I'm looking to the Jahn-Teller effect being strong on the $e_g$ orbitals when there is a odd number of electrons on it.

  • $\begingroup$ I haven't got a chance to delve in this paper in detail, but it seems to be referring to the specific case of twofold spin degeneracy (for example an single electron being spin up or down produces two degenerate states). $e_g$ describes the spatial symmetry and it can still produce a Jahn-Teller distortion. @Tom $\endgroup$ – Tyberius Mar 3 '19 at 22:28

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