Hindered Rotation in Molecules with Relatively High Potential Barriers

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Abstract
The theory of hindered rotation has been applied to the type of asymmetric molecule in which the hindering barrier is high enough so that the hindered rotation splittings of the energy levels are small compared with the rotational energies but yet large enough to be observable in the microwave spectrum. The specific type of molecule considered consists of a rigid asymmetric component which may undergo a hindered rotation about the symmetry axis of a rigid symmetric component where the symmetric component is in addition assumed to have threefold symmetry and the asymmetric component at least a plane of symmetry containing the symmetry axis of the symmetric component. An example might be the acetaldehyde molecule, CH3CHO. In principle, the theory developed by Burkhard and Dennison can be used directly but in practice the method is difficult to apply to such a molecule since the matrix elements of the Hamiltonian used previously do not degenerate naturally or easily to those for the rigid asymmetric rotator in the infinite barrier limit. In the present treatment a transformation is made on the Hamiltonian whereby this complication is avoided and the resulting calculations are greatly simplified. It is found that the spectrum is essentially that of the rigid rotator with the important exception that all the strong lines are split into two components. For the low J transitions specific formulas have been derived for these splittings which are relatively simple functions of the barrier height, the principal moments of inertia, and two additional parameters involving the molecular dimensions and the masses. The barrier height can thus be deduced from the observed splittings without the use of the somewhat cumbersome machinery needed in the general case.