GROUP-THEORETICAL FORMALISM FOR THE LARGE-AMPLITUDE VIBRATION-ROTATION PROBLEM IN $METHYLAMINE-d_{1}$ AND PRELIMINARY ANALYSIS OF THE GROUND-STATE MICROWAVE SPECTRUM
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Date
1990
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Ohio State University
Abstract
A group-theoretical formalism suitable for analyzing high resolution spectra of monodeuterated methyl amine, $CH_{3}NHD$, has been derived. This formalism, which treats simultaneously the methyl-group internal rotaion, the amino-group inversion, and the overall rotation, is obtained using extended-group ideas, and represents a modification of the formalism proviously derived for treating normal methyl amine. The modification is necessary primarily because the H and D atoms in the unsymmetrical amino group are expected to move different distances during the inversion motion. The results of the treatment indicate that elements of the Hamiltonian matrix can be expressed as three separate Fourier series in variables similar to the usual Internal-Axis-Method variable $(2\pi/3)(pK-o)$. One of the Fourier series can be associated with splittings arising from the methyl-group internal rotation tunneling. The other two series can be associated with splittings arising from two symmetrically inequivalent aminogroup inversion tunneling paths. All matrix elements satisfying $\Delta K - 0, \pm 1$ and $\pm 2$ selection rules have been derived in a from appropriate for carrying out a global fit of spectroscopic data. Preliminary fits using a computer program based on this formalism lead to a standard deviation of 0.8 MHz for a fit of 123 microwave transitions with $0 \leq K \leq 3$ and $0 \leq J \leq 15$ and 21 molecular parameters.
Description
Author Institution: Department of Physics. Faculty of Science, Kanazawa University; Department of Physics, Faculty of Science, Toyama University; Molecular Physics Division, National Institute of Standards and Technology