Structure refinement methods

Molecular force fields and chemical shift pseudo-forces 

The time constant r has to be chosen in such way that the influences of rapid motions like vibrations are averaged out while slow conformational changes prevail. 

To account for experimental constraints, in most calculations the following pseudo-energy term is added to the total energy  

The index k runs over all measured values of the intensity I. This equation does not contain the index i of the experimental chemical shift, because to the intensity at some points of the spectrum may consist of contributions from several nuclear sites. On the other hand, we can only analyze spectra in which the intensities are not biased by experimental conditions such as cross polarization effects. Furthermore, the method only seems to make sense in solid state NMR investigations with broad overlapping lines. 

In MD simulations or geometry optimizations pseudo-forces are needed in addition to the pseudo-energies  

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Evidence exists that some of the softest normal modes can be associated with experimentally determined functional motions, and most studies apply normal mode analysis to this purpose. Owing to the veracity of the concept of the normal mode important subspace, normal mode analysis can be used in structural refinement methods to gain dynamic information that is beyond the capability of conventional refinement techniques. 

A Structure Refinement Method Based on Molecular Dynamics in Four Spatial Dimensions. 

Soper, A.K., Tests of the empirical potential structure refinement method and a new method of application to neutron diffraction data on water, Mol. Phys., 99, 1503-1516,2001. 

The whole-pattern-fitting structure-refinement method, which was first introduced by Rietveld and used for neutron diffraction powder patterns, does yield from x-ray diffraction patterns correct, refined structural information for linear polymers. Remarkably precise lattice parameters are obtained incidentally in the use of the method. The method lends itself to improved estimations of the fraction of amorphous and crystalline materials, or of two polymorphic forms, present. As improved profile functions come in to use, the method promises to provide crystallite size information, almost as a spin-off benefit. 

The whole-pattern-fitting structure-refinement method is not limited to specimens containing randomly oriented crystallites. The method does permit an orientation parameter to be refined, though it was not done in this work. Crystallites in the molded polypropylene specimen probably were oriented to some small extent nevertheless, the refinement method worked well. The sensitivity of the method to crystallite orientation and the applicability of the method to polymers with oriented crystallites such as in drawn films or fibers are yet to be determined. 

The whole-pattern-fitting structure-refinement method can give correct, refined structural information for linear polymers. Use of generalized coordinates, in which accurately known structural information can be introduced as known parameters, makes the least-squares fitting problem tractable. Excellent fits of x-ray diffraction data for isotactic polypropylene permitted the selection of the correct space group and a preferred model. 

R.A. Young, P.E. Mackie, and R.B. Von Dreele, Application of the patternfitting structure-refinement method of x-ray powder diffractometer patterns, J. Appl. Cryst. 10, 262 (1977) C.P Khattak and D.E. Cox, Profile analysis of x-ray powder diffractometer data structural refinement of Lao.vsSro jsCrOs. J. Appl. Cryst. 10, 405 (1977). 

In the above scheme, step B is expected to be the slowest. However, the increased accuracy of the theoretical electronic density is likely to reduce the number of iterations within the structure refinement process substantially. Whereas the estimated overall computer time requirement of the (JCR-AFDF approach is comparable to that of the standard structure refinement method, some improvements in speed as well as in accuracy are expected. 

Application of the Rietveld Crystal Structure Refinement Method to Cellotetraose... 

SAKTHIVEL ET AL. Rktveld Crystal Structure Refinement Method... 

The conventional crystal structure refinement method by means of the Rietveld method suffers from considerable uncertainty largely because of the unfavorable data-to-parameter ratios. The complexity of the problem generally depends on the number of atoms located in the asymmetric unit. For nonstoichiometric guest-host materials, the difficulty in structural determination of crystalline powders lies in how to determine dynamical disorder and partial... 

Recent developments in molecular dynamics techniques allow consideration of values and NOE restraints as an ensemble property (Lindorff-Larsen et al. 2005 Richter et al. 2007). The obtained ensembles represent a more realistic view of these flexible molecules in solution than those calculated with conventional NMR structure refinement methods. The dynamically restrained ensembles occupy a considerably larger conformational space than the conventionally calculated ones, and reproduce independent NMR parameters (e.g., chemical shifts) much better. 

Young, R. A., P. E. Mackie and R. B. Von Dreele (1977). Application of the Pattern-Fitting Structure Refinement Method for X-Ray Powder Diffractometer Patterns ./oMrwa/ of Applied Crystallography 10 262-269. 

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