Dunham expansion

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

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.[2] 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. [3]

See also


  1. Dunham, J. L. (1932). "The Energy Levels of a Rotating Vibrator". Phys. Rev. 41: 721–731. Bibcode:1932PhRv...41..721D. doi:10.1103/PhysRev.41.721.
  2. Inostroza, N.; J.R. Letelier; 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.
  3. 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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