Richard I. Cooper

CRYSTALS version 12: software for guided crystal structure analysis

The determination of small-molecule structures from single-crystal X-ray data is being carried out by researchers with little or no crys- tallographic training. At the same time, completely automatic crystal structure analysis can still only be achieved under very favourable conditions. Many of the problems that cause automatic systems to fail could be resolved with suitable chemical insight, and until this is built- in, programs continue to need human guidance. CRYSTALS version 12 contains a modern crystallographic human-interface design, and novel strategies incorporating chemical knowledge and sensible crystallographic guidance into crystal structure analysis software.

Retrieval of Crystallographically-Derived Molecular Geometry Information

The crystallographically determined bond length, valence angle, and torsion angle information in the Cambridge Structural Database (CSD) has many uses. However, accessing it by means of conventional substructure searching requires nontrivial user intervention. In consequence, these valuable data have been underutilized and have not been directly accessible to client applications. The situation has been remedied by development of a new program (Mogul) for automated retrieval of molecular geometry data from the CSD. The program uses a system of keys to encode the chemical environments of fragments (bonds, valence angles, and acyclic torsions) from CSD structures. Fragments with identical keys are deemed to be chemically identical and are grouped together, and the distribution of the appropriate geometrical parameter (bond length, valence angle, or torsion angle) is computed and stored. Use of a search tree indexed on key values, together with a novel similarity calculation, then enables the distribution matching any given query fragment (or the distributions most closely matching, if an adequate exact match is unavailable) to be found easily and with no user intervention. Validation experiments indicate that, with rare exceptions, search results afford precise and unbiased estimates of molecular geometrical preferences. Such estimates may be used, for example, to validate the geometries of libraries of modeled molecules or of newly determined crystal structures or to assist structure solution from low-resolution (e.g. powder diffraction) X-ray data.

CRYSTALS enhancements: dealing with hydrogen atoms in refinement

Because they scatter X-rays weakly, H atoms are often abused or neglected during structure refinement. The reasons why the H atoms should be included in the refinement and some of the consequences of mistreatment are discussed along with selected real examples demonstrating some of the features for hydrogen treatment that can be found in the software suite CRYSTALS.

The derivation of non-merohedral twin laws during refinement by analysis of poorly fitting intensity data and the refinement of non-merohedrally twinned crystal structures in the program CRYSTALS

Although non-merohedrally twinned crystal structures can normally be solved without difficulty, problems usually arise during refinement. Careful analysis of poorly fitting data reveals that they belong predominantly to certain distinct zones in which |Fo|2 is systematically larger than |Fc|2. In the computer program ROTAX, a set of data with the largest values of (|F_{o}^{\,2}| − |F_{c}^{\,2}|)/u(|F_{o}^{\,2}|) is identified and their indices transformed by rotations or roto-inversions about possible direct- and reciprocal-lattice directions. Matrices that transform the indices of the poorly fitting data to integers are identified as possible twin laws.

Report on the sixth blind test of organic crystal structure prediction methods

The results of the sixth blind test of organic crystal structure prediction methods are presented and discussed, highlighting progress for salts, hydrates and bulky flexible molecules, as well as on-going challenges.

Refinement of the structure of β-U4O9

β-U4O9 is a superlattice structure based on the fluorite arrangement of UO2. The U atoms occupy positions close to those in UO2 and the additional O atoms are accommodated in cuboctahedral clusters of \bar43m symmetry, which are centred on the special 12-fold sites of the cubic space group I\bar43d. The structure has been refined from single-crystal neutron data in accordance with the procedure described in the previous paper [Popa & Willis (2004). Acta Cryst. A60, 318–321].

ElectroShape: fast molecular similarity calculations incorporating shape, chirality and electrostatics.

We present ElectroShape, a novel ligand-based virtual screening method, that combines shape and electrostatic information into a single, unified framework. Building on the ultra-fast shape recognition (USR) approach for fast non-superpositional shape-based virtual screening, it extends the method by representing partial charge information as a fourth dimension. It also incorporates the chiral shape recognition (CSR) method, which distinguishes enantiomers. It has been validated using release 2 of the Directory of useful decoys (DUD), and shows a near doubling in enrichment ratio at 1% over USR and CSR, and improvements as measured by Receiver Operating Characteristic curves. These improvements persisted even after taking into account the chemotype redundancy in the sets of active ligands in DUD. During the course of its development, ElectroShape revealed a difference in the charge allocation of the DUD ligand and decoy sets, leading to several new versions of DUD being generated as a result. ElectroShape provides a significant addition to the family of ultra-fast ligand-based virtual screening methods, and its higher-dimensional shape recognition approach has great potential for extension and generalisation.

Compositional dependence of anomalous thermal expansion in perovskite-like ABX3 formates

The compositional dependence of thermal expansion behaviour in 19 different perovskite-like metal-organic frameworks (MOFs) of composition [A(I)][M(II)(HCOO)3] (A = alkylammonium cation; M = octahedrally-coordinated divalent metal) is studied using variable-temperature X-ray powder diffraction measurements. While all systems show essentially the same type of thermomechanical response-irrespective of their particular structural details-the magnitude of this response is shown to be a function of A(I) and M(II) cation radii, as well as the molecular anisotropy of A(I). Flexibility is maximised for large M(II) and small A(I), while the shape of A(I) has implications for the direction of framework hingeing.

Crystal structures of increasingly large molecules: meeting the challenges with CRYSTALS software

BackgroundThe size and complexity of molecules being studied by single crystal diffraction is growing year by year, resulting in an increase in the difficulties encountered during structure determination. From the crystallisation itself and sample handling, to structure solution and refinement, specific problems due to larger molecules are discussed.ResultsDuring refinement, several methods are available to deal with the problems encountered with large structures within the software Crystals. Hydrogens atoms can neither be found easily nor refined freely, but restraints can be applied automatically. Special scattering factors can be used to model complex disorder. Finally chemical information can be included in the form of restraints in order to help the determination of a good model.Multicollinearity problems are more likely in the refinement of large structures; to some extent more precise and accurate algorithms can help. Also, if the global minimum is less well defined, faster refinement enables more cycles to be carried out, a necessity for good convergence. The efficiency of the algorithms in Crystals have been increased to help address these issues.ConclusionsThus, crystal structures are getting larger and their complexity is increasing. Recent developments in precision and speed during the least squares in Crystals is helping the structural scientist to deal with larger structures more efficiently.

Will it crystallise? Predicting crystallinity of molecular materials

Predicting and controlling crystallinity of molecular materials has applications in a crystal engineering context, as well as process control and formulation in the pharmaceutical industry. Here, we present a machine learning approach to this problem which uses a large input training set which is classified on a single measurable outcome: does a substance have a reasonable probability of forming good quality crystals. While the related problem of crystal structure prediction requires reliable calculation of three dimensional molecular conformations, the method employed here for predicting crystallisation propensity uses only “two dimensional” information consisting of atom types and connectivity. We show that an error rate lower than 10% can be achieved against unseen test data. The predictive model was also tested in a blind screen of a set of compounds which do not have crystal structures reported in the literature, and we found it to have a 79% classification accuracy. Analysis of the most significant descriptors used in the classification shows that the number of rotatable bonds and a molecular connectivity index are key in determining crystallisation propensity and using these two measures alone can give 80% accurate classification of unseen test data.