ROTATION--VIBRATION LINE INTENSITIES IN PARALLEL BANDS OF SYMMETRIC TOPS. THE QUADRATIC FORCE FIELD FOR $NH_{3}$

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1960

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Ohio State University

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“Terms involving the dependence of the moment of inertia on normal coordinates have been included in the Hamiltonian for a symmetric top molecule. When treated by perturbation theory these terms lead to a first order change in the rotation-vibration line intensity of the parallel bands. The second order Coriolis effect leads to intensities in the second order only. The perturbation introduces a factor \[ [1+\delta^{B}_{n} (1-4 \theta^{B}_{n}) (J+1)] \] into the line intensity formula for the R-branch and a factor \[ [1-\delta^{B}_{n} (1-4 \theta^{B}_{n}) J] \] for the P-branch. These apply to the $n^{th}$--- parallel band. The results are independent of the quantum number, K. These extra factors found here are very similar to those found by Herman and Wallis $^{1}$ for diatomic molecules and by $Gallup^{2}$ for linear $C_{\infty v}$ molecules. In the above expressions $\delta^{B}_{n}=2B_{0}/\nu_{n}$ and $\theta^{B}_{n}=|\mu_{0}| \xi^{B}_{n}/(|\partial_{\mu}/\partial Q_{n}|)$, and other symbols have their standard meanings. $\xi^{B}_{n}$ is a quantity dependent on the geometry and quadratic force field of the molecule. Some sum rules involving the $\xi^{B}_{n}$ have been derived. Schatz and McKean have measured $\partial_{\mu}/\partial Q_{n}$ for the bands of $NH_{3}{^{2}}$. Using these values and data on the intensities of the lines in the $950 cm^{-1}$ band of $NH_{3}, \xi^{B}$ has been measured for this band. Knowledge of $\xi^{B}$ for this band allows one to calculate the force constant matrix for parallel vibrations. The force constants for perpendicular vibrations have long been known from a measurement of the first order Coriolis effect in those bands. Together, these two sets of force constants lead unequivocally to the bond stretching, angle deformation and all interaction force constants. A discussion of the results will be presented.”

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$^{*}$ Present Address: Poly chemicals Department, E. I. Dupont Corp., Wilmington, Delaware. $^{1}$ R. Herman, R. F. Wallis, J. Chem. Phys. 23, 637 (1955). $^{2}$ G. A. Gallup. J. Chem. Phys. 27, 1338 (1957). $^{3}$ D. C. McKean and P. N. Schatz, J. Chem. Phys. 24, 316 (1956).
Author Institution: Department of Chemistry, University of Nebraska

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