Dunham expansion

In quantum chemistry, the Dunham expansion is an expression for the rotational-vibrational energy levels of a diatomic molecule: [1]

${\displaystyle E(v,J,\Omega )=\sum _{k,l}Y_{k,l}(v+1/2)^{k}[J(J+1)-\Omega ^{2}]^{l},}$

where ${\displaystyle v}$ and ${\displaystyle J}$ are the vibrational and rotational quantum numbers, and ${\displaystyle \Omega }$ is the projection of ${\displaystyle J}$ along the internuclear axis in the body-fixed frame. The constant coefficients ${\displaystyle Y_{k,l}}$ are called Dunham parameters with ${\displaystyle Y_{0,0}}$ 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.