The Dynamics of Ammonium Ions in NMR Spectra

The general form of the effective spin Hamiltonian, shown in Eq. (4), is valid also for NX4 rotors. Therefore, in an unsymmetrical environment, the corresponding QEC term can be formulated as follows  

A consistently quantum mechanical theory describing the coherent and stochastic dynamics of tetrahedral rotors has not been reported yet. Nevertheless, in the extreme situations where the facile re-orientations involve only one axis, the DQR theory will be rigorously valid also for such rotors. Specifically, if the unique axis is a three-fold axis, the stochastic term will have the same form as in Eq. (8) [or the equivalent form in Eq. (10)]. In the case of a two-fold axis, the AB term such as that in Eq. (5) will be obtained, but with the pair-permutation operator P replaced by the operator R defined above. One can thus reasonably expect that even in the cases where there are more than one facile re-orientation axes, applicability of the phenomenological AB approach will suffer similar restrictions as those specified in Subsection 4.4 for methyl-like rotors. 

As far as experimental investigations of the ammonium ion dynamics are concerned, the present authors are aware of only two reports where both the coherent and stochastic effects are taken into account in the interpretation of the observed spectra. Both the reports involve H spectra of a single crystal of variously deuterated ammonium persulfate. For this material it was found that at temperatures below 40 K, the relevant dynamics are dominated by re-orientations about one of the possible re-orientation axes of the ND4 ions. Since it is a three-fold axis, the picture seen in the spectra is essentially similar to that for a deuterated methyl group. The experimental H spectra concerned could be fairly reproduced in terms of the AB model (see Fig. 19). 

However, when the values of feciass obtained in this way (fits based on visual similarity criteria) are displayed in an Arrhenius plot, a characteristic tooth can be seen at 28 K (see Fig. 20). In view of the discussion of Subsection 4.4, its occurrence may reflect a basic 

This is, however, a provisional interpretation. Apart from the primary re-orientation mentioned above, the authors quoted managed to identify another facile re-orientation route in the system, which involves one of the remaining three three-fold axes. The secondary coherent tunnelling, whose maximum low-temperature frequency was estimated at 4.5 kHz, produces additional tiny splittings that affect the p multiplet. With increasing temperature, the frequency of the secondary tunnelling decreases to zero and, in the temperature range of interest in the present discussion (above 23 K, see 

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