# Symmetry and stability of a molecule (Jahn-Teller Distortion)

I've taught in my class that if a molecule posses high degree of symmetry it's stability will be more,in other words symmetry and stability are directly proportional. Is this statement correct? And if this is correct than why Jahn teller distortion stabilizes a molecule when it's symmetry gets low eventually because of the distortion.

The symmetry and stability are not directly related per se; is benzene more stable that naphthalene for example? Benzene is more 'symmetric' than the naphthalene but both are stable molecules; $D_{6h}$ vs $D_{2h}$ point groups.
Jahn and Teller discovered that in a non-linear molecule in an orbitally degenerate electronic state, say $e_g$ or $t_{2g}$ in an octahedral complex, that there is an interaction between the electronic orbital motion and nuclear vibrational motion, which causes the minimum energy position to differ from the symmetric structure. This motion lifts the orbital degeneracy and lowers the energy. Thus the lower symmetry state has lower energy.
An example might be the lengthening of a pair of axial bonds in a octahedral complex, $\ce{[CoF6]}^{3-}$ for example, however, the J_T theorem does not give any indication of how big the distortion might be, i.e. it does not predict the geometrical nature of the distortion. There is also a restriction which is that if the degenerate structure has a centre of symmetry so does the distorted structure.
• I don't get that how come elongation of the axial bond, say in $Cu^{+2}(d^9)$ configuration, brings in the stability? How does the bond elongation affecting the interaction of ligand (present on $z$-axis) and the $d_{z^2}$ orbital? – Onkar Singh Mar 20 '19 at 10:46