where v and J are the vibrational and rotational quantum numbers. 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. 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. 
- Dunham, J. L. (1932). "The Energy Levels of a Rotating Vibrator". Phys.Rev. 41: 721–731. doi:10.1103/PhysRev.41.721.
- Inostroza, N.; J.R. Letelier and M.L. Senent (2010). "On the numerical determination of Dunham’s coefﬁcients: An application to X1 R + HCl isotopomers". Journal of Molecular Structure: THEOCHEM 947: 40–44. doi:10.1016/j.theochem.2010.01.037.
- Huber, K.P.; Herzberg, G. (1979). Molecular Spectra and Molecular Structure IV. Constants of diatomic molecules. New York: van Nostrand. ISBN 0-442-23394-9.
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