An equation between structure factors for structures containing unequal or overlapped atoms. II. An application to structure determination

1958 ◽  
Vol 11 (6) ◽  
pp. 393-397 ◽  
Author(s):  
M. M. Woolfson
Keyword(s):  
Structure Determination ◽  
Structure Factors

scholarly journals The Extended PLATON/SQUEEZE Tool in the Context of Twinning and SHELXL2014

2014 ◽  
Vol 70 (a1) ◽  
pp. C1436-C1436 ◽  
Author(s):  
Anthony Spek
Keyword(s):  
Structure Determination ◽  
Fourier Transformation ◽  
Ad Hoc ◽  
Solvent Mixtures ◽  
Density Peaks ◽  
Difference Density ◽  
Valence States ◽  
Structure Factors ◽  
Density Map ◽  
Solvent Molecules

The completion of a single crystal structure determination is often hampered by the presence of disordered solvent molecules of crystallization. The often not interesting details of that solvent disorder and its contribution to the calculated structure factors has to be modelled in some way in order to obtain publishable results. Current refinement programs include suitable constraints and restraints for a stable refinement of a discrete disorder model. This is often the preferred procedure, in particular when charge balances and valence states are relevant. Unfortunately, a discrete disorder model is not always feasible. Examples include solvent molecules in infinite channels or structures including unknown solvents or solvent mixtures. In such cases the iterative back-Fourier transformation of the content of the disordered solvent volume in a difference density map can be attempted as the contribution to the calculated structure factors. Back-Fourier transformation of disordered solvent regions was prototyped by us nearly 25 years ago (van der Sluis & Spek, 1990) around the, at that time widely used, SHELX76 refinement program. The original reason for its development was the structure determination of a pharmaceutical that contained infinite channels filled with ridges of electron density in the difference density map rather than discrete density peaks (van der Sluis & Spek, 1990). The preliminary implementation of a successful prototype procedure (called BYPASS) was complex and found not to be easily distributable due to its dependence on many (local) ad-hoc programs. A new distributable version, compatible with the next generation refinement program SHELXL97, was implemented as the SQUEEZE tool in the program package PLATON Spek, 2009). The new SHELXL2014 refinement program allows for an even more elegant implementation of the SQUEEZE tool including the possibility to apply it also for twinned structures. Examples and restrictions will be discussed.

Crystal structure determination by convergent-beam electron diffraction

1989 ◽  
Vol 47 ◽  
pp. 476-477
Author(s):  
R. Vincent ◽  
D. J. Exelby
Keyword(s):  
Crystal Structure ◽  
Electron Diffraction ◽  
Structure Determination ◽  
Convergent Beam Electron Diffraction ◽  
Crystal Structure Determination ◽  
Large Set ◽  
Beam Electron ◽  
X Ray ◽  
Structure Factors ◽  
Convergent Beam

In recent years, significant progress has been made towards a solution for the general problem of crystal structure determination by convergent beam electron diffraction (CBED). Even if we consider only perfectly ordered, periodic crystals defined by one of the conventional space groups, diffraction methods based on a focussed sub-micron beam of electrons are applicable to several related sets of structural problems that are not accessible to conventional X-ray or neutron diffraction techniques. We assume here that the space group either is known or has been determined from CBED patterns and that phases and amplitudes for some subset of the structure factors are required. Two limiting cases have been explored in some detail. For crystals where the atomic parameters and Debye-Waller factors are known accurately from high quality X-ray data, information on the charge redistribution for bonding electrons is available from precise measurements of the low order structure factors. Following the original research of Kambe, some recent work has demonstrated that accurate structure amplitudes and three-beam phase invariants can be extracted from the dynamical intensity distribution in CBED reflections. In principle, this approach is completely general but considerable labour would be required to extract sufficient data to solve the structure of an unknown crystal, whereas a large set of kinematic intensities is acquired from a single X-ray pattern.

Crystal structure determination by neutron powder diffraction using structural and packing constraints

1991 ◽  
Vol 24 (6) ◽  
pp. 1005-1008 ◽  
Author(s):  
P. G. Byrom ◽  
B. W. Lucas
Keyword(s):  
Crystal Structure ◽  
Powder Diffraction ◽  
Structure Determination ◽  
Direct Methods ◽  
Neutron Powder Diffraction ◽  
Crystal Structure Determination ◽  
Diffraction Profile ◽  
Peak Separation ◽  
Structure Factors ◽  
Structure Solution

In the past, crystal structure determination of solids consisting of molecules (or atom groups) whose geometry and size are known approximately has often been attempted using neutron powder diffraction profile refinement techniques, but without inclusion of this information. A method of structure solution has therefore been developed to include it. The proposed method does not require a set of structure factors and thus avoids the problems encountered in separating peaks in a powder diffraction scan. A successful test was conducted with a previously determined (yet treated as unknown) crystal structure, where direct methods had failed to solve the structure due to incorrect peak separation. Two computer programs, MODEL and PARAM, that implement the method are described.

The derivation of trial structures. I. Analytical methods for direct phase determination

2010 ◽  
Author(s):  
Jenny Pickworth Glusker ◽  
Kenneth N. Trueblood
Keyword(s):  
Crystal Structure ◽  
Structure Determination ◽  
Direct Methods ◽  
Analytical Techniques ◽  
Patterson Function ◽  
Structure Factors ◽  
Term Trial ◽  
Trial Structure ◽  
Electron Density Map ◽  
True Structure

As indicated at the start of Chapter 4, after the diffraction pattern has been recorded and measured, the next stage in a crystal structure determination is solving the structure—that is, finding a suitable “trial structure” that contains approximate positions for most of the atoms in the unit cell of known dimensions and space group. The term “trial structure” implies that the structure that has been found is only an approximation to the correct or “true” structure, while “suitable” implies that the trial structure is close enough to the true structure that it can be smoothly refined to give a good fit to the experimental data. Methods for finding suitable trial structures form the subject of this chapter and the next. In the early days of structure determination, trial and error methods were, of necessity, almost the only available way of solving structures. Structure factors for the suggested “trial structure” were calculated and compared with those that had been observed. When more productive methods for obtaining trial structures—the “Patterson function” and “direct methods”—were introduced, the manner of solving a crystal structure changed dramatically for the better. We begin with a discussion of so-called “direct methods.” These are analytical techniques for deriving an approximate set of phases from which a first approximation to the electron-density map can be calculated. Interpretation of this map may then give a suitable trial structure. Previous to direct methods, all phases were calculated (as described in Chapter 5) from a proposed trial structure. The search for other methods that did not require a trial structure led to these phaseprobability methods, that is, direct methods. A direct solution to the phase problem by algebraic methods began in the 1920s (Ott, 1927; Banerjee, 1933; Avrami, 1938) and progressed with work on inequalities by David Harker and John Kasper (Harker and Kasper, 1948). The latter authors used inequality relationships put forward by Augustin Louis Cauchy and Karl Hermann Amandus Schwarz that led to relations between the magnitudes of some structure factors.

scholarly journals Diffraction before destruction

2014 ◽  
Vol 369 (1647) ◽  
pp. 20130313 ◽  
Author(s):  
Henry N. Chapman ◽  
Carl Caleman ◽  
Nicusor Timneanu
Keyword(s):  
Diffraction Pattern ◽  
Structure Determination ◽  
High Dose ◽  
X Ray ◽  
Dose Rates ◽  
Structure Factors ◽  
Serial Crystallography ◽  
The Many ◽  
Dose Tolerance

X-ray free-electron lasers have opened up the possibility of structure determination of protein crystals at room temperature, free of radiation damage. The femtosecond-duration pulses of these sources enable diffraction signals to be collected from samples at doses of 1000 MGy or higher. The sample is vaporized by the intense pulse, but not before the scattering that gives rise to the diffraction pattern takes place. Consequently, only a single flash diffraction pattern can be recorded from a crystal, giving rise to the method of serial crystallography where tens of thousands of patterns are collected from individual crystals that flow across the beam and the patterns are indexed and aggregated into a set of structure factors. The high-dose tolerance and the many-crystal averaging approach allow data to be collected from much smaller crystals than have been examined at synchrotron radiation facilities, even from radiation-sensitive samples. Here, we review the interaction of intense femtosecond X-ray pulses with materials and discuss the implications for structure determination. We identify various dose regimes and conclude that the strongest achievable signals for a given sample are attained at the highest possible dose rates, from highest possible pulse intensities.

Structure determination from powder data using anomalous scattering: difference and partial, Patterson densities, and phases of structure factors

1997 ◽  
Vol 212 (7) ◽  
Author(s):  
K. Burger ◽  
W. Prandl ◽  
S. Doyle
Keyword(s):  
Structure Determination ◽  
Maximum Entropy Method ◽  
Algebraic Theory ◽  
Resonant Scattering ◽  
Entropy Method ◽  
Anomalous Scattering ◽  
Atom Type ◽  
X Ray ◽  
Structure Factors ◽  
Iron Garnet

AbstractFor structure determination from X-ray powder data, anomalous (resonant) scattering can be used to obtain difference Patterson and partial Patterson densities as well as phases of structure factors. Usually tuneable synchrotron radiation is used, and two or more powder patterns near and far the absorption edge of an atom type contained in the crystal are recorded.The algebraic theory together with some novel and efficient approximations is given in detail. Also symmetry restrictions, experimental and scaling procedures, and the use of the Maximum-Entropy method (MEM) are discussed. The application to the structure of an iron garnet FeFrom an MEM calculation of the electron-density, using the signed structure factors

scholarly journals Xtrapol8: automatic elucidation of low-occupancy intermediate-states in crystallographic studies

2022 ◽  
Author(s):  
Elke De Zitter ◽  
Nicolas Coquelle ◽  
Thomas R.M. Barends ◽  
Jacques-Philippe Colletier
Keyword(s):  
Bayesian Statistics ◽  
Structure Determination ◽  
Intermediate State ◽  
Time Resolved ◽  
Structure Factors ◽  
Intermediate States ◽  
Conventional Methods ◽  
Unstable States

Unstable states studied in kinetic, time-resolved and ligand-based crystallography are often characterized by a low occupancy, hindering structure determination by conventional methods. To automatically extract such structures, we developed Xtrapol8, a program which (i) applies various flavors of Bayesian-statistics weighting to generate the most informative Fourier difference maps; (ii) determines the occupancy of the intermediate state; (iii) calculates various types of extrapolated structure factors, and (iv) refines the corresponding structures.

Crystal Structure Determination of Glycerol-Containing Lipids from Electron Diffraction Data. Use of Analog Compounds Based upon Configurational Isomers of Cyclopentane-1, 2, 3-TRIOL

1977 ◽  
Vol 35 ◽  
pp. 24-25
Author(s):  
Douglas L. Dorset ◽  
Anthony J. Hancock
Keyword(s):  
Crystal Structure ◽  
Electron Diffraction ◽  
Diffraction Data ◽  
Structure Determination ◽  
Crystal Surface ◽  
Coherent Scattering ◽  
Crystal Structure Determination ◽  
Electron Diffraction Data ◽  
Polar Group ◽  
Axis Orientation

Lipids containing long polymethylene chains were among the first compounds subjected to electron diffraction structure analysis. It was only recently realized, however, that various distortions of thin lipid microcrystal plates, e.g. bends, polar group and methyl end plane disorders, etc. (1-3), restrict coherent scattering to the methylene subcell alone, particularly if undistorted molecular layers have well-defined end planes. Thus, ab initio crystal structure determination on a given single uncharacterized natural lipid using electron diffraction data can only hope to identify the subcell packing and the chain axis orientation with respect to the crystal surface. In lipids based on glycerol, for example, conformations of long chains and polar groups about the C-C bonds of this moiety still would remain unknown.One possible means of surmounting this difficulty is to investigate structural analogs of the material of interest in conjunction with the natural compound itself. Suitable analogs to the glycerol lipids are compounds based on the three configurational isomers of cyclopentane-1,2,3-triol shown in Fig. 1, in which three rotameric forms of the natural glycerol derivatives are fixed by the ring structure (4-7).

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