Knowledge Bank

The vibration-rotation Hamiltonians for the planar and non planar $XY3$ symmetric top and $XY4$ and $XY6$ spherical top molecules have been derived to second order using curvilinear internal coordinates for the vibrational degrees of freedom. Expressions for the anharmonic vibrational spectroscopic coefficients and the vibration-rotation spectroscopic coefficients have been obtained from the Hamiltonians. For these coefficients, the anharmonicities on both the rotational and vibrational kinetic energies have been derived from the molecular geometries for all of the types of molecules mentioned above. Quantative results have been obtained from application to some typical symmetric top and spherical top molecules.