Dunham expansion

In quantum chemistry, the Dunham expansion is an expression for the rotational-vibrational energy levels of a diatomic molecule:

E(v,J,\Omega) = \sum_{k,l} Y_{k,l} (v+1/2)^k [J(J+1) - \Omega^2]^l, $$ where $$v$$ and $$J$$ are the vibrational and rotational quantum numbers, and $$\Omega$$ is the projection of $$J$$ along the internuclear axis in the body-fixed frame. The constant coefficients $$Y_{k,l}$$ are called Dunham parameters with $$Y_{0,0}$$ representing the electronic energy. The expression derives from a semiclassical treatment of a perturbational approach to deriving the energy levels. The Dunham parameters are typically calculated by a least-squares fitting procedure of energy levels with the quantum numbers.

Relation to conventional band spectrum constants
This table adapts the sign conventions from the book of Huber and Herzberg.