Rotational tunneling incoherent

In Ch. 21 Buntkowsky and Limbach review recent NMR work on the dynamics of dihydrogen and dideuterium in the coordination sphere of transition metals. In addition to inelastic neutron scattering and liquid state NMR, the effects of coherent (exchange couplings) and incoherent rotational tunneling of D2 pairs in transi-... 

The rest of the paper is organized as follows The second chapter gives an introduction into the theoretical description of tunneling phenomena and chemical kinetics. After a short summary about the connection of symmetry and tunneling, the basic properties of coherent and incoherent rotational tunneling and their relation to NMR spectroscopy are discussed and the empiric Bell [77] tunnel model is introduced, which is a powerful semi-empirical tool for the description of chemical kinetics in the transition from the coherent to the incoherent regime. 

A. Rotational Tunneling Coherent Tunneling of Symmetric and Incoherent Tunneling Relaxation of Asymmetric Rotors, 159... 

In the theory of deuteron spin-lattice relaxation we apply a simple model to describe the relaxation of the magnetizations T and (A+E), for symmetry species of four coupled deuterons in CD4 free rotators. Expressions are derived for their direct relaxation rate via the intra and external quadrupole couplings. The jump motion between the equilibrium positions averages the relaxation rate within the same symmetry species. Spin conversion transitions couple the relaxation of T and (A+E). This mixing is included in the calculations by reapplying the simple model under somewhat different conditions. The results compare favorably with the experimental data for the zeolites HY, NaA and NaMordenite [6] and NaY presented here. Incoherent tunnelling is believed to dominate the relaxation process at lowest temperatures as soon as CD4 molecules become localized. 

In contrast with the chain of coupled oscillators, the translational invariance of a chain of coupled rotors leads not to a continuous spectrum, but to two branches of tunneling states determined by Eqs. (7.83). These states are coherent, whereas the space-localized breather states (7.80) are incoherent. In this respect, the transitions between breather states are similar to thermally activated rotation of a single group, though the number of rotors lying within the breather envelope and participating in the collective motion is greater than unity ( 20). The above discussion of collective rotation, which is based on the paper of Fillaux and Carlile [1990], demonstrates that the spectrum of a chain of coupled rotors is much richer than the spectrum one can expect from the traditional band model. 

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