Internal coordinate formulation for the vibration-rotation energies of polyatomic molecules. III. Tetrahedral and octahedral spherical top moleculesa)

Abstract

The theory of vibration-rotation interactions in tetrahedral and octahedral spherical top molecules has been developed using curvilinear internal coordinates for the vibrational degrees of freedom. Integral to the development has been a derivation of the vibrational kinetic energy for configurations away from equilibrium when redundant coordinates are present in the symmetry coordinate basis. General expressions for the inertial coefficients, Coriolis coupling coefficients, and vibrational kinetic energy anharmonicity coefficients have been derived for both the tetrahedral and octahedral molecules. A Van Vleck transformation is used to obtain both the diagonal and off-diagonal theoretical vibration-rotation and vibration anharmonic spectroscopic coefficients to second order. Comparisons with the earlier work on methane by Gray and Robiette are good. Application is made in the partial determination of the anharmonic potential energy coefficients for SF6 and CF4. As has been found in our previous work, the curvilinear internal coordinate approach has definite advantages over the Cartesian displacement approach for the angle bending modes in the molecules.