In quantum chemistry, the Dunham expansion is an expression for the rotational-vibrational energy levels of a diatomic molecule: [1]
where and are the vibrational and rotational quantum numbers, and is the projection of along the internuclear axis in the body-fixed frame. 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.[2] The Dunham parameters are typically calculated by a least-squares fitting procedure of energy levels with the quantum numbers.
This table adapts the sign conventions from the book of Huber and Herzberg. [3]