An official website of the United States government
Here’s how you know
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
Secure .gov websites use HTTPS
A lock (
) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.
Contact Transformations and Determinable Parameters in Spectroscopic Fitting Hamiltonians
Published
Author(s)
M A. Mekhtiev, Jon T. Hougen
Abstract
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 (three-Eulerian-angle) asymmetric rotor problem, using J less than or equal} 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 κ of the least-squares matrix, which is a measure of its invertibility in the presence of round-off and other errors. When κ is very large, parameters must be removed from the fit until κ becomes acceptably small, corresponding to procedures which lead to reduced Hamiltonians in molecular spectroscopy. We find that under certain circumstances κ 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.
Mekhtiev, M.
and Hougen, J.
(2000),
Contact Transformations and Determinable Parameters in Spectroscopic Fitting Hamiltonians, Journal of Molecular Spectroscopy
(Accessed February 13, 2025)