Crystal structures accuracy

The parameters in the original parameterization are adjusted in order to reproduce the correct results. These results are generally molecular geometries and energy differences. They may be obtained from various types of experimental results or ah initio calculations. The sources of these correct results can also be a source of error. Ah initio results are only correct to some degree of accuracy. Likewise, crystal structures are influenced by crystal-packing forces. 

P2j Z = 4 D,= 1.073 R = 0.116 for 3,095 intensities. The crystal structure contains two symmetry-independent molecules having very similar conformations. The main interest in this low-accuracy structure lies in the long-chain packing of the molecules, which forms a typical,... 

Brunger AT (1992) Free R-value - a novel statistical quantity for assessing the accuracy of crystal-structures. Nature 355(6359) 472 t75... 

Modern theories of electronic structure at a metal surface, which have proved their accuracy for bare metal surfaces, have now been applied to the calculation of electron density profiles in the presence of adsorbed species or other external sources of potential. The spillover of the negative (electronic) charge density from the positive (ionic) background and the overlap of the former with the electrolyte are the crucial effects. Self-consistent calculations, in which the electronic kinetic energy is correctly taken into account, may have to replace the simpler density-functional treatments which have been used most often. The situation for liquid metals, for which the density profile for the positive (ionic) charge density is required, is not as satisfactory as for solid metals, for which the crystal structure is known. 

For both structures, all final Si positions were obtained with reasonable accuracy (0.1 -0.2 A) by a 3D reconstruction of HRTEM images followed by a distance least-squares refinement. This kind of accuracy is sufficient for normal property analysis, such as catalysis, adsorption and separation, and as a starting point for structure refinement with X-ray powder diffraction data. The technique demonstrated here is general and can be applied not only to zeolites, but also to other complicated crystal structures. 

Most of the crystal-structure analyses report hydrogen-atom positions these are less accurate than those of the non-hydrogen atoms by a factor of ten, except in the case of neutron diffraction, where the accuracies are comparable. 

T.E. Weirich, R. Ramlau, A. Simon, S. HovmdUer, X.D. Zou. A crystal structure determined to 0.02 A accuracy by electron crystallography. Nature 382 144-146, 1996. J.M. Cowley. Diffraction Physics. 2nd edition, North-HoUand, Amsterdam, 1984. 

A complete structure determination contains the two distinct steps solving and refining the structure. The refinement can only be started after the structure has been solved. By solving a structure we mean that most of the most strongly scattering atoms are found to within an accuracy of 0.2 to 0.3 A. All methods for solving crystal structures from X-ray diffraction data in most cases give just a fraction of the complete structure. Patterson... 

The theoretician uses these programs to predict structure, either of single molecules or of assemblages of molecules, using X-ray or NMR data, when available, to test his predictions (13-15). It has been known for a long time that even the earlier molecular mechanics programs can predict the structures of certain types of molecules with excellent reliability. For the cyclic alkanes, an accuracy comparable to that of the best X-ray crystal structure analysis can be obtained. In fact, the method is more widely applicable since neither compound nor crystals are necessary (1 . 

The PIXEL code and documentation (OPiX package) can be downloaded at the author s site http //users.unimi.it/gavezzot. Computing times on an ordinary PC are of the order of a few seconds for a molecular dimer, to a few minutes for a complete crystal structure. PIXEL has been repeatedly shown to give results of accuracy comparable to ab initio MO methods [51]. For an example. Fig. 5 [52] shows a comparison between MP2, PIXEL, uncorrected and corrected periodic-orbital... 

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