Rotation barrier, inversion splitting

Inversion doubling has been observed in microwave spectrum of methylamine CH3NH2. This splitting depends on the quantum numbers of rotation and torsion vibrations [Shimoda et al., 1954 Lide, 1957 Tsuboi et al., 1964]. Inversion of NH2 alone leads to the eclipsed configuration corresponding to the maximum barrier for torsion. Thus, the transition between equilibrium configurations involves simultaneous NH2 inversion and internal rotation of CH3 that is, inversion appears to be strongly coupled with internal rotation. The inversion splits each rotation-vibration (n, k) level into a doublet, whose components, in turn, are split into three levels with m = 0, 1 by internal rotation of the... 

We shall divide these molecules into two categories (i) molecules with one large amplitude motion (inversion) which will be dealt with in Section 6.1 (ii) molecules with inversion and internal rotation (Section 6.2). Only such molecules will be considered, where the inversion barrier is low enough that inversion splittings can be resolved by microwave or infrared spectroscopy. As for the pyramidal inversion with higher barriers, description of the methods for determination of the barrier heights and the chemical consequences of the existence of the so-called invertomers, the reader is referred to review papers ... 

The infrared and especially microwave spectra of methylamine and its deuterated species have been studied in considerable detail [see paper for further references]. The potential barriers to internal rotation and inversion are both relatively high [Table 6 internal rotation barrier is 684 cm in the ground state of CH3NH2] but the splittings of the energy levels are measurable. 

Torsional barriers are referred to as n-fold barriers, where the torsional potential function repeats every 2n/n radians. As in the case of inversion vibrations (Section 6.2.5.4a) quantum mechanical tunnelling through an n-fold torsional barrier may occur, splitting a vibrational level into n components. The splitting into two components near the top of a twofold barrier is shown in Figure 6.45. When the barrier is surmounted free internal rotation takes place, the energy levels then resembling those for rotation rather than vibration. 

---