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Additional resources for Molecular Spectroscopy: Modern Research
The best way to remove indeterminacies is to choose the transformation e to bring H' to some special form, which is then called a reduced Hamil tonian // . Examples of possible reductions are to choose S so that par ticular terms or matrix elements vanish. The remaining coefficients are then functions of the determinable combinations of the original coefficients. The results of a fit can be presented in terms of either the coefficients in the reduced Hamiltonian or the determinable combinations of the original coefficients.
When these are transformed to the basis that diagonalizes H , then the resulting off-diagonal matrix elements are responsible for the principal rotational resonances, such as / doubling and / resonance. The higher anharmonic terms H also contain contributions that are off-diagonal in the H basis, and these produce vibrational resonances. The nomenclature for these various resonances in axially symmetric molecules is discussed by Amat and Nielsen (1967). ΐα ί & a h t 02 2 2n 2 1 m0 2l A near-degeneracy that does not result from symmetry is called an acci dental degeneracy, and the off-diagonal matrix elements produce accidental resonances.
W A T S O N quartic (four linear, one quadratic) and sextic (four linear, three quadratic) determinable combinations. B. V I B R A T I O N A L D E P E N D E N C E OF R O T A T I O N A L HAMILTONIAN The operators H , H , / / , . . contain the terms describing the de pendence of the rotational and centrifugal constants on the vibrational quantum numbers. In addition, in the case of degenerate or near-degenerate vibrational states, these terms provide resonances that can be either essential (for symmetric or spherical tops) or accidental (for all types of molecule).