CELLOPT: improved unit-cell parameters for electron diffraction data of small-molecule crystals.

Electron diffraction enables structure determination of organic small molecules using crystals that are too small for conventional X-ray crystallography. However, because of uncertainties in the experimental parameters, notably the detector distance, the unit-cell parameters and the geometry of the structural models are typically less accurate and precise compared with results obtained by X-ray diffraction. Here, an iterative procedure to optimize the unit-cell parameters obtained from electron diffraction using idealized restraints is proposed. The cell optimization routine has been implemented as part of the structure refinement, and a gradual improvement in lattice parameters and data quality is demonstrated. It is shown that cell optimization, optionally combined with geometrical corrections for any apparent detector distortions, benefits refinement of electron diffraction data in small-molecule crystallography and leads to more accurate structural models.

New method to compute Rcomplete enables maximum likelihood refinement for small datasets.

The crystallographic reliability index [Formula: see text] is based on a method proposed more than two decades ago. Because its calculation is computationally expensive its use did not spread into the crystallographic community in favor of the cross-validation method known as [Formula: see text]. The importance of [Formula: see text] has grown beyond a pure validation tool. However, its application requires a sufficiently large dataset. In this work we assess the reliability of [Formula: see text] and we compare it with k-fold cross-validation, bootstrapping, and jackknifing. As opposed to proper cross-validation as realized with [Formula: see text], [Formula: see text] relies on a method of reducing bias from the structural model. We compare two different methods reducing model bias and question the widely spread notion that random parameter shifts are required for this purpose. We show that [Formula: see text] has as little statistical bias as [Formula: see text] with the benefit of a much smaller variance. Because the calculation of [Formula: see text] is based on the entire dataset instead of a small subset, it allows the estimation of maximum likelihood parameters even for small datasets. [Formula: see text] enables maximum likelihood-based refinement to be extended to virtually all areas of crystallographic structure determination including high-pressure studies, neutron diffraction studies, and datasets from free electron lasers.