Determination of rotational symmetry elements in NMR crystallography

摘要

In this work we present a consistent set of NMR experiments including high-resolution as well as wideline techniques, which allow to determine crystallographic rotational symmetry elements in crystalline solids. ID spectra acquired with fast sample spinning about the magic angle provide the number of crystallographically inequivalent nuclei. By making use of the anisotropic properties of the chemical shift interaction the sets of crystallographically equivalent nuclei can be divided into subgroups of magnetically equivalent spins by means of radio-frequency-driven spin-diffusion wide-line exchange experiments. Maximum information can be achieved from these experiments by a combination of time- and frequency-domain analyses. We could demonstrate that the number of subgroups is equal to the order of the rotational symmetry element in which the crystallographically equivalent nuclei are arranged. From the evolution of the polarisation transfer as a function of the mixing time distances of these spins can be estimated quite accurately. Furthermore, it is often possible to distinguish between rotation and rotoinversion axes. The potential of this strategy for ab initio structure determination is demonstrated on the crystal structure of triphenyl phosphite, where eighteen molecules are arranged in a R-centred trigonal unit cell.