Dunham-type formula

The algebraic approach begins with the notion of a zeroth-order description based on a dynamical symmetry, a concept which is a generalization of the usual definition of the symmetry group of the Hamiltonian. What a dynamical symmetry means in practice is that one constructs a zeroth-order Hamiltonian for which there is a full set of quantum numbers for labeling the eigenstates and that the energy is an analytical function of these quantum numbers. In the infrared or Raman spectroscopy of polyatomic molecules (1) one knows that to zeroth order it is practical to represent the spectrum by a Dunham-type formula... 

According to apphcation of Dunham s formalism to analysis of molecular spectra, as for GaH and H2, these radial coefficients of seven types represent many Dunham coefficients Ym and their auxiliary coefficients Zki of various types that collectively allow wave numbers of observed transitions to be reproduced almost within their uncertainty of measurement through formula 54. Mostly because of inconsistency between reported values of frequencies of pure rotational transitions [118,119], the reduced standard deviation of the fit reported in table 3 is 1.25, slightly greater than unity that would be applicable with consistent data for which uncertainty of each measurement were carefully assigned. 

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