INTENSITY RELATIONS IN $C_{av}$ MOLECULES
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Date
1957
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Ohio State University
Abstract
“The electric moment, $E_{A}$ of a $C_{av}$ type of molecule has been transformed by a contact transformation $TE_{A}T^{-1}=E^{1}_{A}$$^{1}$ T is so chosen that $TH_{0}T^{-1}=H^{\prime}_{0}=H_{0}$ $TH_{1}T^{-1}=H^{1}_{1}=0$, II being the Hamiltonian for the molecule. The latter is tantamount to stipulating that the wave functions of $H_{0}+H^{\prime}_{1}$ are, to first order of approximation, those for the unperturbed Hamiltonian $H_{a}$. The matrix elements of $E_{A^{\prime}}$ have been evaluated for fundamental “parallel” vibrations, for fundamental “perpendicular” vibrations and for the pure rotation spectrum. The selection rules for the parallel type transition remain $\Delta$J$\pm 1.0; \Delta{K}=0$. The significant selection rules for the perpendicular type transition remain $\Delta{J}=\pm 1.0; \Delta{K}=\Delta l=\pm 1$. Certain other transitions are allowed in this case, but they are almost certainly negligible. In all instances, the relations for the matrix elements of the electric moment consist of the usual unperturbed term plus correction terms depending in a more or less complicated manner upon the rotational quantum numbers J and K. On inspection one sees that the relations are hybrid functions showing the effect discussed by $Nielsen^{2}$ and the effect discussed by Herman and $Wallis^{3}$.”
Description
$^{1}$H. Hanson, H. H. Nielsen, J. Waggoner, and W. H. Shaffer, J. Chem. Phys. (in press). $^{2}$H. H. Nielsen, Bull. de la Societe Royale des Sciences de Liege, p. 440. Nos. 6--7, (1951). 3R. C. Herman and R. F. Wallis, J. Chem. Phys., 23, 637, (1955).
Author Institution: Department of Physics and Astronomy, The Ohio State University
Author Institution: Department of Physics and Astronomy, The Ohio State University