A qualitative discussion of the near and far infrared spectrum of methyl alcohol shows that the rotational states, including the hindered rotation, may be well represented by a model consisting of a rigid hydroxyl and a rigid methyl group. These groups may perform a mutual rotation with respect to each other about the symmetry axis of the methyl group subject to a hindering potential which is assumed to have the form $V=\frac{1}{2}H(1-cos3x)$ where $x$ is the angle of mutual rotation. A series of lines in the microwave spectrum, discovered by Hershberger and Turkevich, have recently been measured with great accuracy by Coles who also determined their Stark splitting. The positive identification of these lines leads at once to an estimate of the barrier height $H$.

The wave equation for the rotation of methyl alcohol is obtained and the matrix elements of the hamiltonian are evaluated using the wave functions derived by Koehler and Dennison on the basis of a simplified model. Diagonalizing the hamiltonian yields the energy levels which are found to predict correctly the principal features of the microwave spectrum. A quantitative comparison serves to fix the moments and product of inertia to have the values, $A=34.28\mathrm{}$, $C_1=1.236\mathrm{}$ and $D=-0.107\mathrm{}$ all times ${10}^{-40\mathrm{}}$ g ${\mathrm{cm}.\mathrm{}}^2$ The two components of the electric moment are determined, ${\mu }_{\parallel }=0.893\mathrm{}$ and ${\mu }_{\perp }=1.435\mathrm{}\times {10}^{-18\mathrm{}}$ esu. A relation is obtained between the barrier height $H$ and the moment of inertia $C_2$ of the methyl group about its symmetry axis. Assuming $C_2$ to be equal to the methane moment of inertia, then $H=380\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$. If, in addition to taking a methane-like structure for the methyl group, it is assumed that the OH distance is the same as in water, namely 0.958A, one finds that (1) the CO distance is 1.421A, (2) the symmetry axis of the methyl group lies between the O and H atoms with the O displaced 0.084A from it and (3) the COH bond angle is 110° 15′. This latter angle is 5° 44′ greater than the apex angle in water vapor.

• Received 28 May 1951

DOI:https://doi.org/10.1103/PhysRev.84.408