Expansion and Transformations of the Vibration-Rotation Hamiltonian

The effect of molecular deformations on the rotational energy is accounted for by expanding the elements of the inverse molecular inertia tensor, occurring in the vibration-rotation Hamiltonian, in powers of normal coordinates. A similar expansion is applied to the vibrational potential function. Then the terms of the expanded Hamiltonian can be classified according to their expected degrees of magnitude. The interactions within a set of levels which are close in energy can be dealt with by calculation of the matrix elements of the expanded Hamiltonian, followed by matrix diagonalization. The interactions between levels far apart in energy can be handled by subjecting the Hamiltonian to contact transformations, leading to a transformed Hamitonian, or by application of the Van Vleck perturbation theory. This procedure eliminates the matrix elements between far lying levels, generating new matrix elements within each set of close lying vibration-rotation levels.