Theoretical Description of the Proton Magnetic Resonance Line Shapes of Ammonium Ions under the Influence of Tunneling

A theoretical treatment for the NMR absorption line shape of a tetrahedral group of protons under the influence of tunneling has been developed for the particular case of NH₄⁺ ions. For the applied field parallel to a twofold axis of the ion the derived line shapes depend on a single splitting parameter J. This is a measure of the tunneling splitting of the torsional ground state in comparison to the dipolar energy of the ion. As J varies from 0 to ∞ the calculated line shapes are found to vary between the limiting cases of the distinguishable proton (four spin {}) and indistinguishable proton (spin isomeric) situations, respectively. These theoretical line shapes are compared with the observed "rigid-lattice" line shapes reported for the halides NH₄Cl, NH₄Br, and NH₄I. NH₄Cl and NH₄Br are found to be consistent with $J=0$ although the line shape of the latter exhibits an unexplained departure near the center of the resonance. NH₄I is found to exhibit observable splitting effects ($J=3.3$) in which tunneling has displaced one absorption component sufficiently into the wings to be resolved.