J. Appl. Cryst.の発刊に際して

One of the most exciting tools that have entered the material science toolbox in recent years is machine learning. This collection of statistical methods has already proved to be capable of considerably speeding up both fundamental and applied research. At present, we are witnessing an explosion of works that develop and apply machine learning to solid-state systems. We provide a comprehensive overview and analysis of the most recent research in this topic. As a starting point, we introduce machine learning principles, algorithms, descriptors, and databases in materials science. We continue with the description of different machine learning approaches for the discovery of stable materials and the prediction of their crystal structure. Then we discuss research in numerous quantitative structure–property relationships and various approaches for the replacement of first-principle methods by machine learning. We review how active learning and surrogate-based optimization can be applied to improve the rational design process and related examples of applications. Two major questions are always the interpretability of and the physical understanding gained from machine learning models. We consider therefore the different facets of interpretability and their importance in materials science. Finally, we propose solutions and future research paths for various challenges in computational materials science.

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Recent advances and applications of machine learning in solid-state materials science

The efficiency of the successive dichotomy method for powder diffraction pattern indexing [Louer & Louer (1972). J. Appl. Cryst. 5, 271–275] has been proved over more than 30 years of usage. Features implemented in the new version of the computer program DICVOL04 include (i) a tolerance to the presence of impurity (or inaccurately measured) diffraction lines, (ii) a refinement of the `zero-point' position, (iii) a reviewing of all input lines from the solution found from, generally, the first 20 lines, (iv) a cell analysis, based on the concept of the reduced cell, to identify equivalent monoclinic and triclinic solutions, and (v) an optional analysis of input powder data to detect the presence of a significant `zero-point' offset. New search strategies have also been introduced, e.g. each crystal system is scanned separately, within the input volume limits, to limit the risk of missing a solution characterized by a metric lattice singularity. The default values in the input file have been extended to 25 A for the linear parameters and 2500 A3 for the cell volume. The search is carried out exhaustively within the input parameter limits and the absolute error on peak position measurements. Many tests with data from the literature and from powder data of pharmaceutical materials, collected with the capillary technique and laboratory monochromatic X-rays, have been performed with a high success rate, covering all crystal symmetries from cubic to triclinic. Some examples reported as `difficult' cases are also discussed. Additionally, a few recommendations for the correct practice of powder pattern indexing are reported.

Powder pattern indexing with the dichotomy method

The past couple of years have witnessed a remarkable burst in the development of organic field-effect transistors (OFETs), with a number of organic semiconductors surpassing the benchmark mobility of 10 cm2/(V s). In this perspective, we highlight some of the major milestones along the way to provide a historical view of OFET development, introduce the integrated molecular design concepts and process engineering approaches that lead to the current success, and identify the challenges ahead to make OFETs applicable in real applications.

Integrated materials design of organic semiconductors for field-effect transistors

How do molecules aggregate in solution, and how do these aggregates consolidate themselves in crystals? What is the relationship between the structure of a molecule and the structure of the crystal it forms? Why do some molecules adopt more than one crystal structure? Why do some crystal structures contain solvent? How does one design a crystal structure with a specified topology of molecules, or a specified coordination of molecules and/or ions, or with a specified property? What are the relationships between crystal structures and properties for molecular crystals? These are some of the questions that are being addressed today by the crystal engineering community, a group that draws from the larger communities of organic, inorganic, and physical chemists, crystallographers, and solid state scientists. This Perspective provides a brief historical introduction to crystal engineering itself and an assessment of the importance and utility of the supramolecular synthon, which is one of the most important concepts in the practical use and implementation of crystal design. It also provides a look to the future from the viewpoint of the author, and indicates some directions in which this field might be moving.

Crystal engineering: from molecule to crystal.

In the 2007 blind test of crystal structure prediction hosted by the Cambridge Crystallographic Data Centre (CCDC), a hybrid DFT/MM method correctly ranked each of the four experimental structures as having the lowest lattice energy of all the crystal structures predicted for each molecule. The work presented here further validates this hybrid method by optimizing the crystal structures (experimental and submitted) of the first three CCDC blind tests held in 1999, 2001, and 2004. Except for the crystal structures of compound IX, all structures were reminimized and ranked according to their lattice energies. The hybrid method computes the lattice energy of a crystal structure as the sum of the DFT total energy and a van der Waals (dispersion) energy correction. Considering all four blind tests, the crystal structure with the lowest lattice energy corresponds to the experimentally observed structure for 12 out of 14 molecules. Moreover, good geometrical agreement is observed between the structures determined by the hybrid method and those measured experimentally. In comparison with the correct submissions made by the blind test participants, all hybrid optimized crystal structures (apart from compound II) have the smallest calculated root mean squared deviations from the experimentally observed structures. It is predicted that a new polymorph of compound V exists under pressure.

Revisiting the blind tests in crystal structure prediction: accurate energy ranking of molecular crystals.

The results of the application of a density functional theory method incorporating dispersive corrections in the 2010 crystal structure prediction blind test are reported. The method correctly predicted four out of the six experimental structures. Three of the four correct predictions were found to have the lowest lattice energy of any crystal structure for that molecule. The experimental crystal structures for all six compounds were found during the structure generation phase of the simulations, indicating that the tailor-made force fields used for screening structures were valid and that the structure generation engine, which combines a Monte Carlo parallel tempering algorithm with an efficient lattice energy minimiser, was working effectively. For the three compounds for which the experimental crystal structures did not correspond to the lowest energy structures found, the method for calculating the lattice energy needs to be further refined or there may be other polymorphs that have not yet been found experimentally.

Progress in Crystal Structure Prediction

Methane is the simplest organic molecule, and like many supposedly simple molecular materials it has a rich phase diagram. While crystal structures could be determined for two of the solid phases, that of the low temperature phase III remained unsolved. Using high-resolution neutron powder diffraction and a direct-space Monte Carlo simulated annealing approach, this fundamental structure has now finally been solved. It is orthorhombic with space group Cmca, and 16 molecules in the unit cell. The structure is closely related to that of phase II, yet is no subgroup of it.

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The crystal structure of methane phase III

Crystal structure prediction methods have been used to explore the potential energy landscape for crystals of a melatonin agonist (MA). All known experimental polymorphs were found in the search for crystal packing alternatives with a single molecule in the asymmetric unit, and the predicted order of stability agrees with experiment. The crystal structure corresponding to the global minimum has not been observed experimentally, but analysis of the crystal structures of similar molecules in the Cambridge Structural Database (CSD) indicates that the packing motif present in the predicted structure is also found in nature. To date it has not been experimentally possible to crystallize the most stable polymorph of the biologically active R-enantiomer, whereas the S-enantiomer readily crystallizes in the stable form. Analysis of the results shows that this polymorph has an uncommon packing motif which is found just once among the 12 lowest energy predicted structures but is seen in two crystal structures of MA...

Crystal Structure Prediction of a Flexible Molecule of Pharmaceutical Interest with Unusual Polymorphic Behavior

The results of an extensive in silico polymorph screen with the program GRACE of paracetamol in all 230 space groups with one and two molecules in the asymmetric unit are presented. The three experimentally known forms I, II and III are found in the list of predicted crystal structures in the correct stability order with rank 1, 3 and 6, respectively. Structures with ranks 3 to 8 exhibit the same motif of 2-D hydrogen-bonded sheets. The hydrogen-bonding scheme of the rank 2 structure is markedly different from the known forms, consisting of two interpenetrating 3-D hydrogen-bonded networks. The excellent agreement with experiment and the prediction of one and only one new packing motif within the lattice energy window delimited by the known forms confirms the fitness for crystal structure prediction of the employed methodology. Analysis of the structure at rank 2 is used to propose experimental strategies that may lead to a new form IV of paracetamol.

Marcus A. Neumann

Papers

Revisiting the blind tests in crystal structure prediction: accurate energy ranking of molecular crystals.

Progress in Crystal Structure Prediction

The crystal structure of methane phase III

Crystal Structure Prediction of a Flexible Molecule of Pharmaceutical Interest with Unusual Polymorphic Behavior

Can crystal structure prediction guide experimentalists to a new polymorph of paracetamol