DETERMINING DIATOM DISSOCIATION LIMITS AND LONG-RANGE POTENTIAL COEFFICIENTS FROM DIRECT FITS TO VIBRATIONAL ENERGIES AND ROTATIONAL CONSTANTS.
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Date
1989
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Ohio State University
Abstract
The usual method of analysing spectroscopic data for levels lying near dissociation in order to determine the dissociation energy and obtain estimates of the characteristic inverse-power long-range potential coefficients, involves first the determination of turning points for those levels, followed by least-squares fits of the outer turning points to the usual long-range potential form: $V(R) = D - \Sigma C_{m}/R^{m}.^{1}$ However, such fits are very highly correlated, leading to large statistical uncertainties in the resulting parameters, and more seriously, this approach offers no way of properly estimating the effect on these results of uncertainties in the experimental data. This paper describes an alternate approach to this problem, in which the the semiclassical expressions for the vibrational energies and rotational constants are fitted directly to the experimental data. This allows the effect of the experimental uncertainties to be directly reflected in the fitted parameter values and their uncertainties. Moreover, the effects of interparameter correlation are considerably reduced when one fits to the experimental quantities themselves, rather than to turning points derived from them.2 Applications to both a model problem and to experimental data for real systems will be presented.
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$^{1}$ See, e.g., S. Gerstenkorn and P. Luc, J. Physique 48, 1685 (1987). $^{2}$ RJ. Le Roy, J. Chem. Phys. 73, 6003 (1980).
Author Institution: Guelph-Waterloo Centre for Graduate Work in Chemistry, University of Waterloo
Author Institution: Guelph-Waterloo Centre for Graduate Work in Chemistry, University of Waterloo