International Tables For Crystallography Research Articles

A novel algorithm for calculation of Fourier and asymmetric units.

A new method is presented for determining asymmetric and Fourier units based on plane groups for all space groups. These units are specifically designed to improve the calculation of fast Fourier transforms compared with the units derived from asymmetric units in the International Tables for Crystallography, Vol. A. The algorithm can be easily implemented into existing crystallographic programs using a short computer code.

Revisited relativistic Dirac-Hartree-Fock X-ray scattering factors. I. Neutral atoms with Z = 2-118.

In this first of a series of publications, the X-ray scattering factors for neutral atoms are revisited. Using the recently developed DBSR_HF program [Zatsarinny & Froese Fischer (2016). Comput. Phys. Comm. 202, 287-303] the fully relativistic Dirac-Hartree-Fock ground-state wavefunctions for all atoms with Z = 2-118 (He-Og) have been calculated using the extended average level scheme and including both the Breit interaction correction to the electronic motion due to magnetic and retardation effects, and the Fermi distribution function for the description of the nuclear charge density. The comparison of our wavefunctions with those obtained in several previous studies in terms of the total and orbital (spinor) electronic energies, and a number of local and integrated total and orbital properties, confirmed the quality of the generated wavefunctions. The employed dense radial grid combined with the DBSR_HF's B-spline representation of the relativistic one-electron orbitals allowed for a precise integration of the X-ray scattering factors using a newly developed Fortran program SF. Following the established procedure [Maslen et al. (2006). International Tables for Crystallography, Vol. C, Section 6.1.1, pp. 554-589], the resulting X-ray scattering factors have been interpolated in the 0 ≤ sin θ/λ ≤ 2 Å-1 and 2 ≤ sin θ/λ ≤ 6 Å-1 ranges using the recommended analytical functions with both the four- (which is a current convention) and five-term expansions. An exhaustive comparison of the newly generated X-ray scattering factors with the International Union of Crystallography recommended values and those from a number of previous studies showed an overall good agreement and allowed identification of a number of typos and inconsistencies in the recommended quantities. A detailed analysis of the results suggests that the newly derived values may represent an excellent compromise among all the previous studies. The determined conventional interpolating functions for the two sin θ/λ intervals show, on average, the same accuracy as the recommended parametrizations. However, an extension of each expansion by only a single term provides a significant improvement in the accuracy of the interpolated values for an overwhelming majority of the atoms. As such, an updated set of the fully relativistic X-ray scattering factors and the interpolating functions for neutral atoms with Z = 2-118 can be easily incorporated into the existing X-ray diffraction software with only minor modifications. The outcomes of the undertaken research should be of interest to members of the crystallographic community who push the boundaries of the accuracy and precision of X-ray diffraction studies.

AFLOW-XtalFinder: a reliable choice to identify crystalline prototypes

The accelerated growth rate of repository entries in crystallographic databases makes it arduous to identify and classify their prototype structures. The open-source AFLOW-XtalFinder package was developed to solve this problem. It symbolically maps structures into standard designations following the AFLOW Prototype Encyclopedia and calculates the internal degrees of freedom consistent with the International Tables for Crystallography. To ensure uniqueness, structures are analyzed and compared via symmetry, local atomic geometries, and crystal mapping techniques, simultaneously grouping them by similarity. The software (i) distinguishes distinct crystal prototypes and atom decorations, (ii) determines equivalent spin configurations, (iii) reveals compounds with similar properties, and (iv) guides the discovery of unexplored materials. The operations are accessible through a Python module ready for workflows, and through command line syntax. All the 4+ million compounds in the AFLOW.org repositories are mapped to their ideal prototype, allowing users to search database entries via symbolic structure-type. Furthermore, 15,000 unique structures — sorted by prevalence — are extracted from the AFLOW-ICSD catalog to serve as future prototypes in the Encyclopedia.

Derived crystal structure of martensitic materials by solid-solid phase transformation.

A mathematical description of crystal structure is proposed consisting of two parts: the underlying translational periodicity and the distinct atomic positions up to the symmetry operations in the unit cell, consistent with the International Tables for Crystallography. By the Cauchy-Born hypothesis, such a description can be integrated with the theory of continuum mechanics to calculate a derived crystal structure produced by solid-solid phase transformation. In addition, the expressions for the orientation relationship between the parent lattice and the derived lattice are generalized. The derived structure rationalizes the lattice parameters and the general equivalent atomic positions that assist the indexing process of X-ray diffraction analysis for low-symmetry martensitic materials undergoing phase transformation. The analysis is demonstrated in a CuAlMn shape memory alloy. From its austenite phase (L21 face-centered cubic structure), it is identified that the derived martensitic structure has orthorhombic symmetry Pmmn with the derived lattice parameters ad = 4.36491, bd = 5.40865 and cd = 4.2402 Å, by which the complicated X-ray Laue diffraction pattern can be well indexed, and the orientation relationship can be verified.

A Minimal Generating Set of Cubic Fedorov Groups

Computer minimization of generating subsets (subsets of generators) of cubic Fedorov groups listed in the International Tables for Crystallography has been performed. The structure and fuzziness of the obtained minimal subsets are discussed. It is established that the allowable number of elements for almost half the minimized subsets is not the least one, which suggests that the generating subsets of Fedorov groups in the International Tables for Crystallography should be improved.

A Minimal Generating Set of Intermediate-Symmetry Fedorov Groups

Minimization of generating sets (sets of generators) indicated in the International Tables for Crystallography has been performed for tetragonal, trigonal, and hexagonal space groups. It is established that generating sets of some groups cannot be minimized to a set of minimally possible power (minimal set) for a given group, which suggests that the generating set used in the International Tables for Crystallography should be improved.

Using Mathematica as a platform for crystallographic computing

A comprehensive Mathematica package for crystallographic computations, MaXrd, has been developed. It comprises space-group representations based on International Tables for Crystallography, Vol. A, together with scattering factors from XOP and cross sections from xraylib. Featured functionalities include calculation of structure factors, linear absorption coefficients and crystallographic transformations. The crystal data used by MaXrd are normally generated from external .cif files. The package comes with a dynamic documentation seamlessly integrated with the Mathematica system, including code, examples, details and options. From the onset, minimal Mathematica experience is required to make use of the package. It may be a helpful supplement in research and teaching where crystallography and X-ray diffraction are essential. Although Mathematica is a proprietary software, all the code of this package is open source. It may easily be extended to cover user-specific applications.

Using Mathematica as a platform for crystallographic computing

A comprehensive Mathematica package for crystallographic computations, MaXrd, has been developed. It comprises space-group representations based on International Tables for Crystallography, Vol. A, together with scattering factors from XOP and cross sections from xraylib. Featured functionalities include calculation of structure factors, linear absorption coefficients and crystallographic transformations. The crystal data used by MaXrd are normally generated from external .cif files. The package comes with a dynamic documentation seamlessly integrated with the Mathematica system, including code, examples, details and options. From the onset, minimal Mathematica experience is required to make use of the package. It may be a helpful supplement in research and teaching where crystallography and X-ray diffraction are essential. Although Mathematica is a proprietary software, all the code of this package is open source. It may easily be extended to cover user-specific applications.

Application of various methodological approaches for assessment of soil micromorphology due to VESTA program applicable to prediction of the soil structures formation

Application of various methodological approaches for assessment of soil micromorphology due to VESTA program applicable to prediction of the soil structures formation

The atomic anisotropic displacement tensor – completing the picture.

A simplified approach for calculating the equivalent isotropic displacement parameter is presented and the transformation property of the tensor representation U to point-group operations is analysed. Complete tables have been compiled for the restrictions imposed upon the tensor owing to the site symmetry associated with all special positions as listed in Hahn [(2011), International Tables for Crystallography, Vol. A, Space-group Symmetry, 5th revised ed. Chichester: John Wiley and Sons, Ltd].

Density- and wavefunction-normalized Cartesian spherical harmonics for l ≤ 20.

The widely used pseudoatom formalism [Stewart (1976). Acta Cryst. A32, 565-574; Hansen & Coppens (1978). Acta Cryst. A34, 909-921] in experimental X-ray charge-density studies makes use of real spherical harmonics when describing the angular component of aspherical deformations of the atomic electron density in molecules and crystals. The analytical form of the density-normalized Cartesian spherical harmonic functions for up to l ≤ 7 and the corresponding normalization coefficients were reported previously by Paturle & Coppens [Acta Cryst. (1988), A44, 6-7]. It was shown that the analytical form for normalization coefficients is available primarily for l ≤ 4 [Hansen & Coppens, 1978; Paturle & Coppens, 1988; Coppens (1992). International Tables for Crystallography, Vol. B, Reciprocal space, 1st ed., edited by U. Shmueli, ch. 1.2. Dordrecht: Kluwer Academic Publishers; Coppens (1997). X-ray Charge Densities and Chemical Bonding. New York: Oxford University Press]. Only in very special cases it is possible to derive an analytical representation of the normalization coefficients for 4 < l ≤ 7 (Paturle & Coppens, 1988). In most cases for l > 4 the density normalization coefficients were calculated numerically to within seven significant figures. In this study we review the literature on the density-normalized spherical harmonics, clarify the existing notations, use the Paturle-Coppens (Paturle & Coppens, 1988) method in the Wolfram Mathematica software to derive the Cartesian spherical harmonics for l ≤ 20 and determine the density normalization coefficients to 35 significant figures, and computer-generate a Fortran90 code. The article primarily targets researchers who work in the field of experimental X-ray electron density, but may be of some use to all who are interested in Cartesian spherical harmonics.

Vision of a knowledge economy in IYCr2014

The research landscape is changing at an alarming rate, it is now impossible to talk to any professional engaged in the research community without mentioning open data, big data, new search optimisation tools, or tools geared for the digital age. Without a doubt these developments and new tools are fostering change which is revolutionising the way researchers work, share their results and interact with colleagues across the crystallographic community. Publishers too are embracing the technology shift and evidence of this can be found in many new product launches which focus on new innovative open access models, tools for analysing and quantifying masses of data, right through to bringing experts from different research departments together to discuss common problems and hopefully find novel solutions. At the International Union of Crystallography (IUCr) we have a wealth of current and historical data relevant to today's research arena in our 9 journals. What many researchers may not know however is we also have novel tools for writing and submitting articles, such as publBio and publCIF, communities such as the world directory of crystallographers and solutions such as the International Tables for Crystallography. All of these products, tools and services help our research community across a broad range of disciplines find answers they can trust in a timely manner. This presentation will explore some of the opportunities currently being explored to expand our crystallographic communities, and how we can share with and embrace other scientists employing crystallographic methods. The presentation will also look at how we can provide new and smarter products and services so we can truly reflect the interdisciplinary nature of crystallography in 2014 and beyond.

Open Meeting of the Commission on International Tables for Crystallography

The development of the seriesInternational Tables for Crystallographysince the 2011 Congress in Madrid will be discussed. The series includes eight published volumes with a ninth expected before the end of 2014 and definite plans for a tenth. A new edition of Volume A (Space-group symmetry, Editor Mois Aroyo) is nearly ready. A great deal of work has been done on the associated onlineSymmetry Database. Volume A1 (Symmetry relations between space groups, 2011, editors Hans Wondratschek and Ulrich Müller) is the companion volume. Work on a revision of theBrief Teaching Editionwill begin once the new Volume A is finished. Volume B (Reciprocal space, 2010; Editor Gervais Chapuis, who succeeded Uri Shmueli in 2011) and Volume C (Mathematical, physical and chemical tables, 2006, Editor Richard Welberry) are undergoing revisions, which will be major. The volumes will be reorganized with those topics connected to reciprocal space in B and those connected to direct space in C. A new edition of Volume D (Physical properties of crystals, Editor André Authier) was completed in 2013. A new edition of Volume F (Crystallography of biological macromolecules, Editors Eddy Arnold, Daniel Himmel, and Michael Rossmann) appeared in 2012. A new Volume H onPowder diffraction(Editors Chris Gilmore, Jim Kaduk, and Henk Schenk) is nearing completion. A new Volume I onXAFS(Editors Chris Chantler, Federico Boscherini, and Bruce Bunker) is in the planning stage. The Commission on Magnetic Structures is developing plans for a volume. In the meantime Danny Litvin's compilation of 1-, 2-, and 3-dimensional magnetic subperiodic groups and space groups was published as an e-book by the IUCr in 2013. Ideas for future developments will be welcome.

Nicotine and 4-(Methylnitrosamino)-1-(3-pyridyl)-1-butanone Binding and Access Channel in Human Cytochrome P450 2A6 and 2A13 Enzymes

Cytochromes P450 (CYP) from the 2A subfamily are known for their roles in the metabolism of nicotine, the addictive agent in tobacco, and activation of the tobacco procarcinogen 4-(methylnitrosamino)-1-(3-pyridyl)-1-butanone (NNK). Although both the hepatic CYP2A6 and respiratory CYP2A13 enzymes metabolize these compounds, CYP2A13 does so with much higher catalytic efficiency, but the structural basis for this has been unclear. X-ray structures of nicotine complexes with CYP2A13 (2.5 Å) and CYP2A6 (2.3 Å) yield a structural rationale for the preferential binding of nicotine to CYP2A13. Additional structures of CYP2A13 with NNK reveal either a single NNK molecule in the active site with orientations corresponding to metabolites known to form DNA adducts and initiate lung cancer (2.35 Å) or with two molecules of NNK bound (2.1 Å): one in the active site and one in a more distal staging site. Finally, in contrast to prior CYP2A structures with enclosed active sites, CYP2A13 conformations were solved that adopt both open and intermediate conformations resulting from an ∼2.5 Å movement of the F to G helices. This channel occurs in the same region where the second, distal NNK molecule is bound, suggesting that the channel may be used for ligand entry and/or exit from the active site. Altogether these structures provide multiple new snapshots of CYP2A13 conformations that assist in understanding the binding and activation of an important human carcinogen, as well as critical comparisons in the binding of nicotine, one of the most widely used and highly addictive drugs in human use.

Maturation in Action: CryoEM Study of a Viral Capsid Caught during Expansion

Bacteriophage HK97 maturation involves discrete intermediate particle forms, comparable to transitional states in protein folding, before reaching its mature form. The process starts by formation of a metastable prohead, poised for exothermic expansion triggered by DNA packaging. During maturation, the capsid subunit transitions from a strained to a canonical tertiary conformation and this has been postulated to be the driving mechanism for initiating expansion via switching hexameric capsomer architecture from skewed to 6-fold symmetric. We report the subnanometer electron-cryomicroscopy reconstruction of the HK97 first expansion intermediate before any crosslink formation. This form displays 6-fold symmetric hexamers, but capsid subunit tertiary structures exhibit distortions comparable to the prohead forms. We propose that coat subunit strain release acts in synergy with the first crosslinks to drive forward maturation. Finally, we speculate that the energetic features of this transition may result from increased stability of intermediates during maturation via enhanced inter-subunit interactions.

Open meeting of the Commission on International Tables for Crystallography

Open meeting of the Commission on International Tables for Crystallography

Seitz notation for symmetry operations of space groups

Space-group symmetry operations are given a geometric description and a short-hand matrix notation in International Tables for Crystallography, Volume A, Space-Group Symmetry. We give here the space-group symmetry operations subtables with the corresponding Seitz (R∣t) notation for each included symmetry operation.

Exact direct-space asymmetric units for the 230 crystallographic space groups.

It is well known that the direct-space asymmetric unit definitions found in the International Tables for Crystallography, Volume A, are inexact at the borders. Face- and edge-specific sub-conditions have to be added to remove parts redundant under symmetry. This paper introduces a concise geometric notation for asymmetric unit conditions. The notation is the foundation for a reference table of exact direct-space asymmetric unit definitions for the 230 crystallographic space-group types. The change-of-basis transformation law for the conditions is derived, which allows the information from the reference table to be used for any space-group setting. We also show how the vertices of an asymmetric unit can easily be computed from the information in the reference table.

How to read (and understand) Volume A ofInternational Tables for Crystallography: an introduction for nonspecialists

Since fewer and fewer students get proper crystallographic education at the undergraduate level, the responsibility to promote and propagate this knowledge must be directed to alternative channels. It is not a marginal issue, because the language of crystallography is rather hermetic and, without proper support, it might disappear from the collective scientific knowledge, so that in the next generation there would be no-one able to use it properly, to say nothing about advancing the field. Black-box crystallography might be useful in some situations, but it cannot replace well informed, conscious scientific pursuits by properly trained specialists. Without sufficient understanding of crystallographic terms and principles, the now thriving branch of structural research would wither, and this could have particularly lamentable consequences for structural biology. The purpose of this article is to teach non-initiated persons, primarily structural biologists, how to interpret the information contained in the fundamental Volume A of International Tables for Crystallography (ITA). An excellent and comprehensive overview of many issues concerning crystal symmetry is presented in a book by Burns & Glazer (Space Groups for Solid State Scientists, 2nd ed. New York: Academic Press, 1990), also explaining the contents of ITA, but this text is unfortunately not popular among structural biologists. There are several superb handbooks explaining the foundations of structural crystallography but they usually do it without direct reference to ITA. There is also a comprehensive introduction included in ITA, but it is written in rather hermetic language and is, therefore, not suitable for nonspecialists with no training in exact sciences. This article, which uses simple language to explain all the terms encountered on the space-group pages of ITA, is meant to bridge this growing gap in crystallographic instruction. The explanations are illustrated with actual examples taken directly from the pages of ITA.

Disorientation angles and compatible walls for phase transition hexagonal to monoclinic phase

Orientation of compatible domain walls and magnitude of disorientation angle of a ferroelastic domain twin resulting from phase transition hexagonal to monoclinic phases is expressed in crystallographic unit-cell parameters of the low-symmetry phase. These two characteristics, the orientation of the compatible wall and the disorientation angle, depend on the spontaneous strain in two single-domain states R 1, R 2 from which the domain twin is formed. They have been determined for all classes of the compatible domain walls as a function of the strain-tensor components [A. Authier, International Tables for Crystallography, in Physical Properties of Crystals, Chapter 3.4, Vol. D, A. Authier, ed., Kluwer Academic Publishers, Dordrecht, 2003, pp. 449–505]. If relative changes of crystal lattice are small, then the second rank symmetrical strain tensor u can be calculated from the crystallographic unit-cell parameters before and after the deformation [J.L. Schlenker, G.V. Gibbs, and M.B. Boisen Jr, Strain-tensor components expressed in terms of lattice parameters, Acta. Cryst. A 34 (1978), pp. 52–54; L. Jian and C.M. Wayman, Domain boundary and domain switching in a ceramic rare-earth Orthoniobate LaNbO4 , J. Am. Ceram. Soc. 79 (1996), pp. 1642–1648]. An alternative approach expresses the disorientation angle and orientation of the compatible domain wall [J. Přívratská, Disorientation angle expressed in terms of lattice parameters, Ferroelectrics 291 (2003), pp. 197–204] in terms of the crystallographic unit-cell parameters of the low-symmetry phase.