Crystals phase problem with

In the crystallographic case, the limited radius of convergence of refinement arises not only from the high dimensionality of the parameter space, but also from what is known as the crystallographic phase problem . With monochromatic diffraction experiments on single crystals, one measures the amplitudes of the reflections, not the phases. The phases, however, are required to compute electron density maps, which are obtained by Fourier transformation of the structure factor (described by a complex number for each reflection). Phases for new crystal structures are usually obtained from experimental methods such as multiple isomorphous replacement. However, electron density maps computed from a combination of native crystal amplitudes and multiple isomorphous replacement phases are sometimes insufficiently accurate to allow a complete and unambiguous tracing of the macromolecule. Furthermore, electron density maps for macromolecules are... 

X-Ray diffraction from single crystals is the most direct and powerful experimental tool available to determine molecular structures and intermolecular interactions at atomic resolution. Monochromatic CuKa radiation of wavelength (X) 1.5418 A is commonly used to collect the X-ray intensities diffracted by the electrons in the crystal. The structure amplitudes, whose squares are the intensities of the reflections, coupled with their appropriate phases, are the basic ingredients to locate atomic positions. Because phases cannot be experimentally recorded, the phase problem has to be resolved by one of the well-known techniques the heavy-atom method, the direct method, anomalous dispersion, and isomorphous replacement.1 Once approximate phases of some strong reflections are obtained, the electron-density maps computed by Fourier summation, which requires both amplitudes and phases, lead to a partial solution of the crystal structure. Phases based on this initial structure can be used to include previously omitted reflections so that in a couple of trials, the entire structure is traced at a high resolution. Difference Fourier maps at this stage are helpful to locate ions and solvent molecules. Subsequent refinement of the crystal structure by well-known least-squares methods ensures reliable atomic coordinates and thermal parameters. 

This article reviews progress in the field of atomistic simulation of liquid crystal systems. The first part of the article provides an introduction to molecular force fields and the main simulation methods commonly used for liquid crystal systems molecular mechanics, Monte Carlo and molecular dynamics. The usefulness of these three techniques is highlighted and some of the problems associated with the use of these methods for modelling liquid crystals are discussed. The main section of the article reviews some of the recent science that has arisen out of the use of these modelling techniques. The importance of the nematic mean field and its influence on molecular structure is discussed. The preferred ordering of liquid crystal molecules at surfaces is examined, along with the results from simulation studies of bilayers and bulk liquid crystal phases. The article also discusses some of the limitations of current work and points to likely developments over the next few years. 

They have been prepared with several anions,332-335 the tetrafluoroborate salt exhibits SA and Sc phases332,333 but the triflate shows a nematic phase 334 One of the problems in studying these complexes was the very high temperatures at which the phases existed and the fact that decomposition was often observed in the upper reaches of the SA phases. Reduction of these temperatures was achieved by changing the small anions for dodecyl sulfate that also make that more materials exhibit nematic SA and Sc phases, and another more viscous phase appeared, named cubic phase So- With the anion octyl sulfate336 the crystal structure of one of the complex with 4-metoxystilbazole could be achieved (20), with this anion the cubic phase was not present. 

The use of blank-disc CBED patterns for solving crystal stmctures by electron diffraction (in conjunction with direct methods for the phase problem) would seem to have many advantages ... 

The Stevens group [20] performed the reaction under microreaction conditions using the previously mentioned CYTOS College System [18]. The main problem with this setup is the formation of crystals (as the final products are crystalline) that leads to clogging of the system. This was circumvented by injection of a fluorinated inert solvent (Fluorinert FC-70) after the micromixing unit and before the RTU, which prevented the clogging and allowed the authors to collect the desired compounds easily by phase separation. 

Nowadays computers are so absurdly fast that the phase problem can be solved by recursive computation the newly proposed charge-flipping algorithm [14] performs in absence of any information on the target crystal structure not even the molecular composition or the crystal symmetry is needed. The procedure starts with... 

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