Tetrahedral doublet distortion-sign ambiguity ($E(Q)=K{Q}^2/2-g|Q|$)

For a linearly split orbital doublet occupied by one electron or one hole, the lower adiabatic branch has a cusp $-g|Q|$. A harmonic elastic cost produces equal minima at $Q=\pm g/K$. Orbital degeneracy therefore establishes instability of the regular geometry, but cannot alone distinguish opposite tetragonal distortions. A symmetry-allowed cubic elastic invariant in the two-component distortion can select one sign.