How to get maximum structure information from anisotropic displacement parameters obtained by three-dimensional electron diffraction: an experimental study on metal–organic frameworks

Abstract

Three-dimensional electron diffraction (3D ED) has been used for ab initio structure determination of various types of nanocrystals, such as metal–organic frameworks (MOFs), zeolites, metal oxides and organic crystals. These crystals are often obtained as polycrystalline powders, which are too small for single-crystal X-ray diffraction (SCXRD). While it is now possible to obtain accurate atomic positions of nanocrystals by adopting kinematical refinement against 3D ED data, most new structures are refined with isotropic displacement parameters (U eq), which limits the detection of possible structure disorders and atomic motions. Anisotropic displacement parameters (ADPs, Uij ) obtained by anisotropic structure refinement, on the other hand, provide information about the average displacements of atoms from their mean positions in a crystal, which can provide insights with respect to displacive disorder and flexibility. Although ADPs have been obtained from some 3D ED studies of MOFs, they are seldom mentioned or discussed in detail. We report here a detailed study and interpretation of structure models refined anisotropically against 3D ED data. Three MOF samples with different structural complexity and symmetry, namely ZIF-EC1, MIL-140C and Ga(OH)(1,4-ndc) (1,4-ndcH2 is naphthalene-1,4-dicarboxylic acid), were chosen for the studies. We compare the ADPs refined against individual data sets and how they are affected by different data-merging strategies. Based on our results and analysis, we propose strategies for obtaining accurate structure models with interpretable ADPs based on kinematical refinement against 3D ED data. The ADPs of the obtained structure models provide clear and unambiguous information about linker motions in the MOFs.

In Situ Study of the Activation Process of MOF-74 Using Three-Dimensional Electron Diffraction

“…Even with residual electrostatic potentials within the pores, R -factors <15 were achieved through dynamical refinement. These are similar to those obtained for other MOFs from 3DED data in literature …”

Making ripples in the comparison of calculated and experimental maps for real-space refinement and assessment by analytic modelling of local resolution

“…Enhancing the quantitative comparison of calculated and experimental maps will be decisive in extricating unbiased experimental information beyond prior knowledge and the authors -along with the contribution in this paper -raise a number of questions remaining to be addressed. These include the inverse problem of calculating their parameters from the experimental map, the extension of the model to anisotropic displacement parameterization or subatomic resolution scenarios in charge-density studies or the current limitations in the absence of complete data and the need for optimally accounting for atomic scattering where unaccounted environmental effects or dynamic effects occur (Gruza et al, 2020;Samperisi et al, 2022). None of these considerations detracts from the interest of their proposed map calculation and application in refinement but rather adds to the debate.…”