Is electron crystallography possible? The direct determination of organic crystal structures

Electron Diffraction of 3D Molecular Crystals

Electron crystallography has a storied history which rivals that of its more established X-ray-enabled counterpart. Recent advances in data collection and analysis have sparked a renaissance in the field, opening a new chapter for this venerable technique. Burgeoning interest in electron crystallography has spawned innovative methods described by various interchangeable labels (3D ED, MicroED, cRED, etc.). This Review covers concepts and findings relevant to the practicing crystallographer, with an emphasis on experiments aimed at using electron diffraction to elucidate the atomic structure of three-dimensional molecular crystals.

Single-Crystal Poly[4-(4,4-dihexadecyl-4H-cyclopenta[1,2-b:5,4-b']dithiophen-2-yl)- alt-[1,2,5]thiadiazolo[3,4- c]pyridine] Nanowires with Ultrahigh Mobility

We fabricated single-crystal poly[4-(4,4-dihexadecyl-4H-cyclopenta[1,2-b:5,4-b']-dithiophen-2-yl)- alt-[1,2,5]thiadiazolo-[3,4- c]pyridine] (PCDTPT) nanowires with ultrahigh mobility using a liquid-bridge-mediated nanotransfer molding method. The structural analysis of the single-crystal PCDTPT nanowires reveals that PCDTPT crystals have a triclinic structure, and the nanowires grow parallel to PCDTPT backbone chains, which provide important insights into its intrinsic charge transport. The single-crystal PCDTPT nanowire exhibits a superior charge carrier mobility of 72.94 ± 18.02 cm² V^-1 s^-1 (maximum mobility up to 92.64 cm² V^-1 s^-1), which is a record high value among conjugated polymers to date. In the single-crystal PCDTPT nanowire, the backbone chains in the linear structure along the nanowire growth axis lead to strong backbone delocalization, resulting in highly conductive polymer backbones and a drastic increase in charge carrier mobility. In addition, the single-crystal PCDTPT nanowire shows good environmental stability under air conditions compared to small-molecule organic semiconductors.

Electron crystallography of organic materials

The application of electron crystallography to the study of organic materials is reviewed, mainly in context of the author's own experience. Direct methods for crystallographic phase determination have been shown to be very effective for ab initio structure analyses with electron diffraction intensities, permitting the elucidation of previously uncharacterized crystal structures. Fruitful applications areas have included chain-folded linear polymers, pigments, polydisperse linear chain arrays and, surprisingly, the subgroup assembly of certain proteins.

Maximum entropy methods in electron crystallography

The maximum entropy (ME) method of solving crystal structures in two or three dimensions from electron diffraction data is described. Applications to organic and inorganic molecules, membrane proteins and surface structures are outlined, and the power of the ME formalism to deal with incomplete and error prone data is demonstrated.

Applications of the maximum entropy method to powder diffraction and electron crystallography

A new multisolution phasing method based on entropy maximization and likelihood ranking, proposed for the specific purpose of increasing the accuracy and sensitivity of probabilistic phase indications compared with conventional direct methods, has been implemented and applied to a wide variety of problems. The latter comprise the determination of small crystal structures from X-ray diffraction data obtained from single crystals or from powders, and from electron diffraction data, both with and without partial phase information obtained by image processing of electron micrographs; the ranking of phase sets for a small protein; and the improvement of poor quality phases for a larger protein at medium resolution under constraint of solvent flatness. The main components of the method are (1) a tree-directed search through a space of trial phase sets; (2) the saddlepoint method for calculating joint probabilities of structure factors, using entropy maximization; (3) likelihood-based scores to rank trial phase sets and prune the search tree; (4) a statistical analysis of the scores for automatically selecting reliable phase indications. Their use is illustrated here on structure determinations from powder X-ray diffraction data and from electron diffraction data.

Electron crystallography of organic and biological molecules--techniques and comparison to X-ray crystallographic results

In this review, it is shown how ab initio analyses of molecular crystal structures can be carried out with electron diffraction intensities and high-resolution, low-dose, electron micrographs, dispelling the long-held myth that such determinations are not possible. The results for small organics, polymethylene compounds, various polymers, and even intregral membrane proteins, are in good agreement with independent X-ray crystal structure determinations, which, however, were not needed to solve the crystallographic phase problem from the electron scattering data. The concept of electron crystallography benefits from the utility of electron micrographs for providing phase information, in addition to the standard 'direct' methods used nowadays by all crystallographers.