Internal coordinate formulation for the vibration-rotation energies of polyatomic molecules. II. Symmetric top molecules with a threefold axis

The theory of vibration-rotation interactions in symmetric top molecules with a threefold axis has been developed using curvilinear internal coordinates for the vibrational degrees of freedom. General expressions for the inertial coefficients, Coriolis coupling coefficients, and vibrational kinetic energy anharmonic coefficients have been derived for planar and nonplanar XY3 molecules. A Van Vleck perturbation scheme is used to obtain the theoretical vibration-rotation and vibration anharmonic spectroscopic coefficients. Applications are made in the analyses of the empirical spectroscopic coefficients for BF3 and NH3 in the determination of incomplete sets of improved anharmonic potential energy coefficients. In many respects it is found that the curvilinear internal coordinate approach to vibration-rotation interactions has advantages over the Cartesian displacement coordinate approach for angle bending modes in the symmetric top molecules.