Knowledge Bank

“Vibration-rotation interaction manifests itself in the Hamiltonian of the linear symmetric X-Y-X molecule through the terms $q1(P2-Pz2$) and ($P-P+P\cdot P-2P42$) where $q1$ is the normal coordinate for the breathing mode, P is the total angular momentum operator, $P$ is the internal vibrational angular momentum operator, and the z coordinate axis lies along the equilibrium internuclear axis. Corrections to the dipole moment matrix elements due to these terms are obtained; the contact transformation method of Hanson, Nielson, Shaffer, and $Waggoner1$ is used to simplify the calculations. The resulting intensity expressions indicate, just as the results of Herman and $Wallis2$ for the diatomic molecule, that vibration-rotation interaction gives rise to band asymmetry.”