VIBRATION-ROTATION INTERACTION IN SYMMETRIC TOP MOLECULES AND THE SPLITTING OF $A_{1}$ AND $A_{2}$ LEVELS.

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1965

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Ohio State University

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Analytical expressions for the splitting of the $A_{1}$ and the $A_{2}$ rovibrational states in symmetric top molecules are derived with emphasis on the symmetry properties of the Hamiltonian and the wavefunctions. A perturbation technique employing interaction diagrams is used instead of the contact transformation which has been used by previous $workers.^{1, 2, 3}$ Also a few revisions on the existing theory of vibration rotation interaction are made. It is stressed that the observed l-type doubling constants in symmetric top molecules provide information about those anharmonicity potential constants which are not involved in the expression for $\alpha$. A numerical example is given for the ammonia molecule and the magnitude of the anharmonicity term is estimated. The possibility of observing the direct transition between the split levels is discussed.

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$^{1}$ H. H. Nielsen, Revs. Modern Phys. 23, 90 (1951). $^{2}$ M. L. Grenier-Besson, J. Physique Rad. 21, 555 (1960). $^{3}$ G. Amat and H. H. Nielsen, J. Mol. Spectroscopy 2, 152 (1958).
Author Institution: Division of Pure Physics, National Research Council

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