Methyl Libration in Propane Measured with Neutron Inelastic Scattering

The $A_2$ and $B_2$ torsional vibrational frequencies in propane gas have been directly measured at 217 ± 8 and 265 ± 8 cm⁻¹, respectively, with inelastically scattered neutrons using the “small κ” method of neutron molecular spectroscopy. The theoretical basis of the scattering experiment is discussed, and factors affecting resolution and intensity are enumerated. Not subject to the same selection rules as optical spectroscopy, neutron molecular spectroscopy is capable of observing vibrational transitions which are otherwise forbidden by molecular symmetry. The vibrational frequencies are interpreted by numerically solving the two‐dimensional wave equation giving librational motion with a two‐dimensional Fourier expansion. In this approach, the potential energy is conveniently expanded also in Fourier form and we obtain a $V_3\text{\hspace{0.17em}=\hspace{0.17em}3680\hspace{0.17em}±\hspace{0.17em}190}\mathrm{cal}/\mathrm{mole}$ for individual methyl‐group librations and a $V_{33}$ or $V_6\text{\hspace{0.17em}=\hspace{0.17em}−\hspace{0.17em}280\hspace{0.17em}±\hspace{0.17em}130}\mathrm{cal}/\mathrm{mole}$ term which couples the two methyl tops. Evaluation of additional Fourier constants in the potential‐energy expansion must await additional spectroscopic data concerning higher vibrational levels. Intermolecular perturbations of the librational frequencies were observed in both liquid and solid propane. These are sufficiently small, however, that one can conclude, to a first approximation, that the librational motions are not greatly effected in condensed states of propane.