The Jahn-Teller theorem (1937): any non-linear molecule with a degenerate electronic state will distort to break the symmetry and lift the degeneracy. In an octahedral complex (Oh → D4h), the Q₃ (elongation/compression) mode couples to e_g orbitals. Energy: E±(Q) = ½KQ² ± λQ, giving a double-well with minima at Q₀ = ±λ/K and energy gain E_JT = λ²/2K. Mn³⁺ in perovskites is the textbook case — drives colossal magnetoresistance.