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In quantum chemistry , the Dunham expansion is an expression for the rotational-vibrational energy levels of a diatomic molecule  :. quantum chemistry. quantum chemistry. diatomic molecule. diatomic molecule. vibrational. Molecular vibration#Quantum mechanics. where v and J are the vibrational and rotational quantum numbers .. vibrational. Molecular vibration#Quantum mechanics. rotational quantum numbers. Rigid rotor#Quantum mechanical linear rigid rotor. The constant coefficients are called Dunham parameters with representing the electronic energy .. The expression derives from a semiclassical treatment of a perturbational approach to deriving the energy levels .. semiclassical. semiclassical physics. perturbational approach. perturbation theory. The Dunham parameters are typically calculated by a least-squares fitting procedure of energy levels with the quantum numbers .. least-squares. least-squares