Direct Space (direct + space)

Distribution by Scientific Domains


Selected Abstracts


Occupation numbers for atomic shells in direct space bounded by the maxima of the one-electron potential

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 6 2001
M. Kohout
Abstract Atomic shells defined as wells of the one-electron potential bounded by successive maxima of this electron density function give reasonable electron numbers for the occupation of shells with empty d orbitals. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 83: 324,331, 2001 [source]


FOX, `free objects for crystallography': a modular approach to ab initio structure determination from powder diffraction

JOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 6 2002
Vincent Favre-Nicolin
A new program has been developed for ab initio crystal structure determination from powder diffraction data (X-ray and neutron). It uses global-optimization algorithms to solve the structure by performing trials in direct space. It is a modular program, capable of using several criteria for evaluating each trial configuration (e.g. multi-pattern). It is also modular in the description of the crystal content, with the possibility of describing building blocks in the sample, such as polyhedra or molecules, and with automatic adaptive handling of special positions and sharing of identical atoms between neighbouring building blocks. It can therefore find the correct structure without any assumption about the connectivity of the building blocks and is suitable for any kind of material. Several optimization algorithms (simulated annealing, parallel tempering) are available, with the possibility of choosing the convergence criterion as a combination of available cost functions. This program is freely available for Linux and Windows platforms; it is also fully `open source', which, combined with an object-oriented design and a complete developer documentation, ensures its future evolution. [source]


The application of eigensymmetries of face forms to anomalous scattering and twinning by merohedry in X-ray diffraction

ACTA CRYSTALLOGRAPHICA SECTION A, Issue 3 2010
H. Klapper
The face form (crystal form) {hkl} which corresponds to an X-ray reflection hkl is considered. The eigensymmetry (inherent symmetry) of such a face form can be used to derive general results on the intensities of the corresponding X-ray reflections. Two cases are treated. (i) Non-centrosymmetric crystals exhibiting anomalous scattering: determination of reflections hkl for which Friedel's rule is strictly valid, i.e.I(hkl) = I() (Friedel pair, centric reflection), or violated, i.e.I(hkl) , I() (Bijvoet pair, acentric reflection). It is shown that those reflections hkl strictly obey Friedel's rule, for which the corresponding face form {hkl} is centrosymmetric. If the face form {hkl} is non-centrosymmetric, Friedel's rule is violated due to anomalous scattering. (ii) Crystals twinned by merohedry: determination of reflections hkl, the intensities of which are affected (or not affected) by the twinning. It is shown that the intensity is affected if the twin element is not a symmetry element of the eigensymmetry of the corresponding face form {hkl}. The intensity is not affected if the twin element belongs to the eigensymmetry of {hkl} (`affected' means that the intensities of the twin-related reflections are different for different twin domain states owing to differences either in geometric structure factors or in anomalous scattering or in both). A simple procedure is presented for the determination of these types of reflections from Tables 10.1.2.2 and 10.1.2.3 of International Tables for Crystallography, Vol. A [Hahn & Klapper (2002). International Tables for Crystallography, Vol. A, Part 10, edited by Th. Hahn, 5th ed. Dordrecht: Kluwer]. The application to crystal-structure determination of crystals twinned by merohedry (reciprocal space) and to X-ray diffraction topographic mapping of twin domains (direct space) is discussed. Relevant data and twinning relations for the 63 possible twin laws by merohedry in the 26 merohedral point groups are presented in Appendices A to D. [source]


Correcting electron-density resolution bias in reciprocal space

ACTA CRYSTALLOGRAPHICA SECTION A, Issue 3 2009
Angela Altomare
Fourier syntheses are always affected by series-termination errors, which generate sets of positive and negative ripples around each main peak in the map. The interaction among the ripples distorts the profile of the map and moves peaks away from their correct positions. In a previous paper [Altomare et al. (2008). Acta Cryst. A64, 326,336] an algorithm was described which reduces the resolution bias by removing the effects of the ripples in direct space. In this paper the correction is performed in reciprocal space: the effect of the ripples on the atomic scattering factors is calculated and subtracted from the usual atomic scattering factors. The modified scattering factors are used to calculate new structure factors, from which more accurate electron-density maps may be obtained. The experimental tests show that the procedure minimizes the effects of the resolution bias and provides atomic positions that are more accurate than those provided by traditional approaches. [source]


Diffraction with a coherent X-ray beam: dynamics and imaging

ACTA CRYSTALLOGRAPHICA SECTION A, Issue 2 2007
Frédéric Livet
Methods for carrying out coherent X-ray scattering experiments are reviewed. The brilliance of the available synchrotron sources, the characteristics of the existing optics, the various ways of obtaining a beam of controlled coherence properties and the detectors used are summarized. Applications in the study of the dynamics of speckle patterns are described. In the case of soft condensed matter, the movement of inclusions like fillers in polymers or colloidal particles can be observed and these can reflect polymer or liquid-crystal fluctuations. In hard condensed-matter problems, like phase transitions, charge-density waves or phasons in quasicrystals, the study of speckle fluctuations provides new time-resolved methods. In the domain of lensless imaging, the coherent beam gives the modulus of the sample Fourier transform. If oversampling conditions are fulfilled, the phase can be obtained and the image in the direct space can be reconstructed. The forthcoming improvements of all these techniques are discussed. [source]


Structure and conformational analysis of a bidentate pro-ligand, C21H34N2S2, from powder synchrotron diffraction data and solid-state DFTB calculations

ACTA CRYSTALLOGRAPHICA SECTION B, Issue 5 2009
Edward E. Ávila
The molecular and crystalline structure of ethyl 1,,2,,3,,4,,4a,,5,,6,,7,-octahydrodispiro[cyclohexane-1,2,-quinazoline-4,,1,,-cyclohexane]-8,-carbodithioate (I) was solved and refined from powder synchrotron X-ray diffraction data. The initial model for the structural solution in direct space using the simulated annealing algorithm implemented in DASH [David et al. (2006). J. Appl. Cryst.39, 910,915] was obtained performing a conformational study on the fused six-membered rings of the octahydroquinazoline system and the two spiran cyclohexane rings of (I). The best model was chosen using experimental evidence from 1H and 13C NMR [Contreras et al. (2001). J. Heterocycl. Chem.38, 1223,1225] in combination with semi-empirical AM1 calculations. In the refined structure the two spiran rings have the chair conformation, while both of the fused rings in the octahydroquinazoline system have half-chair conformations compared with in-vacuum density-functional theory (DFT) B3LYP/6-311G*, DFTB (density-functional tight-binding) theoretical calculations in the solid state and other related structures from X-ray diffraction data. Compound (I) presents weak intramolecular hydrogen bonds of the type N,H...S and C,H...S, which produce delocalization of the electron density in the generated rings described by graph symbols S(6) and S(5). Packing of the molecules is dominated by van der Waals interactions. [source]