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The theory of hindered $rotation1,2,3$ has been applied to those molecules in which the hindering potential barrier is so high that the positions of the rotation lines are given in first order through the rigid rotator energy levels alone. It has been shown that the chief effect of the hindered rotation is to produce a splitting of these lines. The specific type of molecule considered consists of a rigid asymmetric component with at least a plane of symmetry which may undergo a hindered rotation about the symmetry axis of a three-fold rigid symmetric component. An example might be $ClH2CCH3$. In principle, the theory developed by Burkhard and $Dennison2$ can be used, but in practice the method is clumsy and exceedingly difficult to apply since the matrix elements of their hamiltonian do not degenerate easily or naturally to those for the rigid asymmetric rotator in the case of an infinitely high barrier although they have shown that the energy levels do eventually so degenerate. The difficulty arises from the fact that the Burkhard-Dennison hamiltonian contains cross products between the momentum associated with the hindered rotator and the components of total angular momentum. In the present treatment a contact transformation is made which removes these terms. The matrix elements of the hamiltonian for high barriers now become those of a rigid rotator plus those of a simple hindered rotator plus a small number of perturbation terms. The results of a perturbation treatment show mainly that in the limit of high barriers all rigid rotator lines are split into two components which have comparable intensity. From these splittings the barrier height can be deduced if the moments of inertia are known from an analysis of the gross features of the spectrum. The splittings are complicated functions of the moments of inertia mainly because the symmetry axis of the hindering potential does not in general coincide with one of the principal axes of inertia of the rigid molecule. However, the splictings for the lower J values can be tabulated in a form such that they can readily be used for the interpretation of experimental data. The work is being extended to more asymmetric types of molecules.