Higher-Order Rotation-Vibration Energies of Polyatomic Molecules. V

The Schrödinger equation for the energies of a rotating-vibrating polyatomic molecule is not exactly soluable. The common procedure is to expand the Hamiltonian for the problem in orders of magnitude, the parameter of smallness being of the order of (Be(αα)/ωs)½, where Be(αα) is a rotational constant and ωs is a vibration frequency, and to arrive at energy expressions by successive approximations. The actual order of magnitude of a term in the Hamiltonian will depend upon the values of (Be(αα)/ωs) and the values of the rotational quantum numbers relative to the vibration quantum numbers. One may, therefore, use different expansions for the quantum mechanical Hamiltonian corresponding to the values of J and K taken under consideration, in which case the ``index'' of magnitude of the matrix element of an operator O belonging to the Hamiltonian operator hm, expansion for the Hamiltonian H as has been done by Goldsmith et al., whatever the values of the quantum numbers may be, accepting then that the true ``index'' of magnitude is not necessarily equal to m. Adopting the latter scheme and using the expansion of the Hamiltonian proposed by Goldsmith et al. the contributions to the energy of the various terms comprising it are considered for various ranges of J and K and an assignment of the order of magnitude to which the contribution belongs is made.