Torsion–Vibration–Rotation Interactions in Methanol. I. Millimeter Wave Spectrum

Abstract

In a study of internal rotation in methanol, the millimeter wave spectra of CH₃OH, CD₃OH, and CH₃OD have been investigated between 90 and 200 Gc/sec. In the analysis of the spectra, torsion–vibration–rotation interactions were treated as adjustable parameters in semiempirical formulas. Kivelson's formula for a‐type $\text{ΔK\hspace{0.17em}=\hspace{0.17em}0}$ transitions was tested over a wide range of quantum numbers. It reproduced the CH₃OH and CD₃OH spectra quite well, but the approximations used in the calculations appear to start breaking down for the larger asymmetry of CH₃OD. For assignment of b‐type $\text{ΔK\hspace{0.17em}=\hspace{0.17em}±\hspace{0.17em}1}$ transitions, a method was developed based on the wide spectral range of the millimeter wave spectrometer. Sufficient b‐type data were obtained for CH₃OH to permit a test of Kirtman's formula for origins of $Q$ branches. Convergence difficulties in the Q‐branch least‐squares fit prompted a re‐examination of the theory, which revealed an interesting linear relation coupling six of the parameters. This relation shows that for any molecule the torsional barrier terms $V_3$ and $V_6$ , the two moments of inertia about the near‐symmetry axis, and two of the adjustable interaction parameters cannot be independently determined from the spectrum of a single isotopic species. This casts some doubt on values previously reported for $V_6$ in other molecules and adds further uncertainty to $V_3$ determinations. The effective $V_3$ obtained by ignoring torsion–vibration–rotation interactions was found to decrease slightly on deuteration, values of 375.6, 371.8, and 370.3 cm^− 1 being obtained for CH₃OH, CD₃OH, and CH₃OD, respectively. Although it is impossible to determine $V_6$ unambiguously from the spectrum of CH₃OH alone, a qualitative argument suggests that $V_6$ lies between 0 and −0.8 cm⁻¹. The geometry of the molecule has been completely determined from the experimental data.