Molecular rotations and local modes

Rotational energy level structures of stretching vibrational states have been investigated in the XH2, XH3, and XH4 type symmetrical hydrides. Transformations from standard vibration–rotation normal coordinate Hamiltonians are made to internal coordinate representations which explicitly give the terms responsible for rotational coupling between the different local mode states. It is shown that the local mode relations between the vibration–rotation parameters as given by Lehmann [J. Chem. Phys. 95, 2361 (1991)] and by Halonen and Robiette [J. Chem. Phys. 84, 6861 (1986)] make these Hamiltonians diagonal in the local mode basis. The effective vibration–rotation parameters of overtones are then proved to obey the local mode relations closer and closer as the vibrational excitation increases. A simple vibrational model accounts well for the vibrational dependencies of vibration–rotation constants in the case of SiH4, GeH4, and SnH4.