Knowledge Bank

The theory of vibration-rotation interaction in polyatomic molecules has been developed using curvilinear internal coordinates for the vibrational degrees of freedom. After specification of an initial axis system for the molecule, a change in variables is used to remove the zeroth order Coriolis coupling. The usual perturbation expansion is used to obtain all of the vibration-rotation coefficients, $\alpha ki$, $\chi kk$, $\chi kk$ $\chi 11$, $\chi 1s1s\prime$, etc., for linear, symmetric top, and asymmetric top molecules, including the cases of Fermi and Fermi-Dennison resonances. Analysis has been made for several triatomic molecules. For those molecules where anharmonic forces have been previously determined by other formulations, the results compare favorably. The use of curvilinear internal coordinates for vibration-rotation interaction introduces enharmonic terms into the vibrational kinetic energy and gives second derivative terms for the moments of inertia that include the motion of an atom along its natural curved path during vibration. The anharmonic force constants that appear in the vibration-rotation coefficients are the ``real” force constants in the valence force approximation. The formulation is especially suited for vibration-rotation analysis when it is necessary to restrict the number of internal degrees of freedom because of molecular complexity, when there are obvious advantages to having the molecular kinetic energy in the obvious form. In the presentation, some attention will be devoted to the significance and limitations that may be inherent in application to the analysis of empirical parameters for particular molecules.