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MIRZA A. MEKHTIEV AND JON T. HOUGEN, Optical Technology Division, National Institute of Standards and Technology, Gaithersburg, MD 20899.
In recent least-squares fits of torsion-rotation spectra of acetaldehyde and methanol it was found possible to adjust more fourth-order parameters than would be expected from traditional contact-transformation considerations. To investigate this discrepancy between theory and practice we have carried out numerical fitting experiments on the simpler three-dimensional asymmetric rotor problem, using J\leq 20 energy levels generated artificially from a full orthorhombic Hamiltonian with quadratic through octic operators in the angular momentum components. Results are analyzed using the condition number \kappa of the least-squares matrix, which is a measure of its invertibility in the presence of round-off and other errors. When \kappa is very large, parameters must be removed from the fit until \kappa becomes acceptably small, corresponding to procedures which lead to reduced Hamiltonians in molecular spectroscopy. We find that under certain circumstances \kappa can be decreased to an acceptable level for Hamiltonians which are only partially reduced when compared to Watson A and S reductions. Some insight into this behavior is obtained from classical mechanics and from the concept of delayed contact transformations. Our attempts to transfer this understanding to the four-dimensional methyl-top internal rotor problem are complicated by the fact that both order-of-magnitude considerations and commutation relations are somewhat different.