Knowledge Bank

“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 $nth$--- 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 $\mathrm{<mrow\; data-mjx-texclass="ORD">1</mrow>}$ for diatomic molecules and by $Gallup2$ for linear $C\infty v$ molecules. In the above expressions $\delta nB=2B0/\nu n$ and $\theta nB=|\mu 0|\xi nB/(|\partial \mu /\partial Qn|)$, and other symbols have their standard meanings. $\xi nB$ is a quantity dependent on the geometry and quadratic force field of the molecule. Some sum rules involving the $\xi nB$ have been derived. Schatz and McKean have measured $\partial \mu /\partial Qn$ for the bands of $NH3\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}$. Using these values and data on the intensities of the lines in the $950cm-1$ band of $NH3,\xi B$ 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.”