Tunneling-rotational transitions

T. Baba, T. Tanaka, I. Morino, K. M. T. Yamada, and K. Tanaka, Detection of the tunneling rotation transitions of malonaldehyde in the submillimeter wave region. /. Chem. Phys. 110, 4131 4133 (1999). 

Typical energy-level schemes for dipolarly unstable systems with indications of the allowed rotational, tunneling, and tunneling-rotational transitions in two limit cases, when the rotational frequency is larger than the tunneling one and when the inverse inequality takes place, are presented in Figs. 1 and 2. The expected pure rotational spectra for three concrete sets of parameter values are shown in Figs. 3 to 5. If A = 0 (or... 

The dynamics of tunneling rotation of hindered rotors interacting with intra- and intermolecular vibrations has received much less attention than structural studies. Such interactions shift and broaden tunneling spectral lines and, when temperature is raised, lead to transitions from coherent tunneling to thermally activated hopping. 

Tunneling rotation of three-dimensional coupled rotors in solid methane is dealt with in many experimental and theoretical studies. The phase transition at 20.4 K turns this species from orientationally disordered phase I to partially oriented phase II. According to neutron... 

Fig. 1. Tunneling-rotational energy levels and allowed transitions for A < B. The dashed lines divide the transitions of different branches.

Spectroscopically, tunneling will manifest itself in a doubling of the observed vibrational-rotational transitions. In the case of finite barriers the wave function... 

The organic linker here is 5-sulfoisophthalate (SIPA). At the lowest loading of H2, a strong peak is observed in the rotational tunneling spectra (Figure 5.14) at 4.2 meV along with a weaker peak at 17.3 meV from hindered rotational transitions of the bound H2 molecule. 

Each rotational transition is split into up to four closely lying components and can be assigned to the lowest vibration-rotation-tunneling substates resulting from the motion of the water molecules in the trimer. The four components are labelled S, S , W, W in the order of increasing energy. 

Figure Bl.4.9. Top rotation-tunnelling hyperfine structure in one of the flipping inodes of (020)3 near 3 THz. The small splittings seen in the Q-branch transitions are induced by the bound-free hydrogen atom tiiimelling by the water monomers. Bottom the low-frequency torsional mode structure of the water duner spectrum, includmg a detailed comparison of theoretical calculations of the dynamics with those observed experimentally [ ]. The symbols next to the arrows depict the parallel (A k= 0) versus perpendicular (A = 1) nature of the selection rules in the pseudorotation manifold.

In spin relaxation theory (see, e.g., Zweers and Brom[1977]) this quantity is equal to the correlation time of two-level Zeeman system (r,). The states A and E have total spins of protons f and 2, respectively. The diagram of Zeeman splitting of the lowest tunneling AE octet n = 0 is shown in fig. 51. Since the spin wavefunction belongs to the same symmetry group as that of the hindered rotation, the spin and rotational states are fully correlated, and the transitions observed in the NMR spectra Am = + 1 and Am = 2 include, aside from the Zeeman frequencies, sidebands shifted by A. The special technique of dipole-dipole driven low-field NMR in the time and frequency domain [Weitenkamp et al. 1983 Clough et al. 1985] has allowed one to detect these sidebands directly. 

As seen from this table, the WKB approximation is reasonably accurate even for very shallow potentials. At 7 = 0 the hindered rotation is a coherent tunneling process like that studied in section 2.3 for the double well. If, for instance, the system is initially prepared in one of the wells, say, with cp = 0, then the probability to find it in one of the other wells is P( jn, t) = 5sin (2Ar), while the survival probability equals 1 — sin ( Ar). The transition amplitude A t), defined as P( + t) = A t), is connected with the tunneling frequency by... 

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