PMR spectroscopy of the tunneling ammonium ion: Generalized line shape theory and some experimental examples

Abstract

The site symmetry of the NH4+ ion is low in many crystal structures of ammonium compounds. This renders inadequate the commonly considered theoretical models of the tunnel-split ground librational state of NH4+, which are based on a perfectly tetrahedral crystal field due to assumption of equivalent threefold, and neglect of twofold, axes of symmetry. A general treatment of the NMR line shape theory is therefore considered and Hamiltonian matrix elements for tunneling are explicitly calculated in terms of the seven overlap-integral parameters related to the four C3– and three C2–symmetry axes of a tetrahedron. The model allows us to discuss all possible ground torsional level structure of the tunneling ammonium ion. The proton NMR line shapes are calculated for all representative cases, and the results are used in comparison with experimental data to elucidate the ground torsional level structures of NH4VO3, (NH4)2ZrF6, (HN4)2TiF6, (NH4)2TeO4, and (NH4) IO4.