Internal Rotation in Completely Asymmetric Molecules. II. Interactions between Vibration and Internal Rotation

Abstract

The theory of internal rotation for molecules with asymmetric internal rotors is extended to include the interactions of normal vibrations with the hindered internal rotation. The Sayvetz condition is derived for separation of internal rotation and vibration in zeroth order in the kinetic energy. Then the complete Hamiltonian is developed which includes the effect of the α dependence of the vibrational kinetic energy as well as those terms which are introduced through the reduction in symmetry of the vibrationally distorted molecule. An effective internal, over‐all rotation Hamiltonian is isolated for the vth vibrational state by a Van Vleck transformation. The behavior of various terms in the Hamiltonian are examined in detail in the case of molecules for which both the framework and top possess planes of symmetry. Particular attention is devoted to the use of symmetry properties in discussing the α dependent properties of the Hamiltonian. Perturbation theory is used to obtain an effective rotational Hamiltonian for the nth torsional state. It is found that the structure of some rotational transitions is sensitive to particular new terms which are introduced by vibration. The microwave spectra of CH₂DCOH and CHD₂COH are analyzed on a parametric basis.