= Solution
{c}
The term $-\alpha\epsilon$ is the leading electronic energy gain from splitting the initially degenerate orbitals and occupying the lower levels. Its negative sign expresses the lowering of the occupied-electron energy for the chosen elongation branch of the <Jahn-Teller effect>. The positive coefficient $\alpha$ is a linear electron-lattice coupling in this reduced model.
The term $\beta\epsilon^2/2$ is the harmonic elastic cost of moving the ligands away from the undistorted reference structure. Mechanical stability requires $\beta>0$. The competition between linear gain and quadratic cost produces a finite equilibrium distortion rather than indefinite elongation.
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