Hindered rotational energy levels of the ammonium ion in alkali halide lattices

Abstract

The hindered rotational energy levels of the ammonium ion in alkali halide lattices have been computed by assuming a ’’single approach model,’’ i.e., that one of the N–H bonds points toward the halide ion. The barrier to rotation about the threefold axis is small. Therefore, the tunneling frequencies for these solids are much larger than for other ammonium compounds. The Hamiltonian that describes the motion of the ammonium ion in alkali halide lattices is invariant under the direct product group ?×C3, where ? is the tetrahedral group of rotations around body-fixed axes and C3 the trigonal group of rotations about space-fixed axes. For high barriers to rotation, closed mathematical expressions have been derived for the librational frequencies. Experimental determination of the low temperature heat capacity or the mean square value of the nuclear angular momentum <I (I+1) ≳ is shown to provide a method for determining the barrier to rotation.