Knowledge Bank

“The microwave spectrum of propylene oxide has been observed in order to study the hindered internal rotation of the methyl group. Because “tunnelling” through the hindering harrier splits each torsional state v into two sublevels (species A and E of symmetry group $C3$) the rotational lines appear as doublets with strongly barrier dependent separation. The barrier is high enough that these doublets were not resolvable for most ground torsional state transitions of low J, but small splittings ($\sim 0.2$ mc) were observed for one Q branch series. However, the splittings are magnified by factors of fifty and twelve hundred in the first and second excited torsional states, respectively, and a large number of satellite lines from molecules in these states were assigned. Both the splittings and transition frequencies of the low J lines from the $v=0,1,2$ torsional states are in good agreement with the theory of hindered internal rotation developed by Wilson and co-workers, for a barrier $V(a)V3(1-\cos 3a)/2$ of $V3=2560$ cal/mole ($895cm-1$). For the ground torsional state one $rP$ branch and three $pP$ branches extending from $J=1$ to 45 and $K-1=1$ to 23 were also studied. For high K, the contributions from asymmetry $(\kappa =-0.88)$, centrifugal distortion, and internal rotation can to good approximation be treated separately. When grouped according to the average value of $\tau =K-1-K+1$, the transitions within each branch are nearly equally spaced. The centrifugal distortion shifts follow the symmetric rotor formula, and increase with the average value of $\tau$. Internal rotation here produces a triplet fine structure (1.0 me in extent) consisting of two E lines and a single A line of twice the intensity: since the rigid rotor asymmetry splitting is negligible for high K, the A line is nearly K-degenerate, but this degeneracy is split by the internal angular momentum present for the E level. The relative position of the three lines is periodic in K, following the pattern predicted by Koehler and Dennison for a symmetric hindered rotor (selection rules prevent its observation for a true symmetric rotor), and the splittings agree well with the barrier determined from the low J spectra.”