Errors, in crystal structures

Serious errors in crystal structures are very rare, and are usually associated with the first structure determination of a novel target, in particular when only low resolution data are available (3.0-5.0A). Small errors and inaccuracies, however, are very common and virtually unavoidable. These errors are often underestimated, and small details of crystal structures are frequently overinterpreted by non-crystallo-graphers. Medicinal chemists making use of crystal structures should be well aware of their limitations. ... 

Using crystal structures quality criteria A Errors in crystal structures B Quality criteria... 

Errors in crystal structures can be divided into three categories ... 

The number of reflection intensities measured in a crystallographic experiment is large, and commonly exceeds the number of parameters to be determined. It was first realized by Hughes (1941) that such an overdetermination is ideally suited for the application of the least-squares methods of Gauss (see, e.g., Whittaker and Robinson 1967), in which an error function S, defined as the sum of the squares of discrepancies between observation and calculation, is minimized by adjustment of the parameters of the observational equations. As least-squares methods are computationally convenient, they have largely replaced Fourier techniques in crystal structure refinement. 

There has been much discussion of the probable limits of error of atomic coordinates in crystal structures, the upshot of which is the conclusion that earlier estimates of accuracy were too optimistic. Cruickshank (1949) showed that the relation between the standard deviation a x) of a coordinate of an atom and the differences between... 

The same data collection and reduction techniques are commonly used by the same workers for many different polymers. Therefore, data for these other polymers may contain errors on a similar scale, but that the errors have usually, but not always, gone undetected (8). If more than 500 reflections are observed, from single crystals of simple molecules, recognizable electron-density distributions have been derived from visually estimated data classified only a "weak", "medium" or "strong". The calculation of the structure becomes more sensitive to the accuracy of the intensity data as the number of data points approaches the number of variables in the structure. One problem encountered in crystal structure analyses of fibrous polymers is that of a very limited number of reflections (low data to parameter ratio). In addition, fibrous polymers usually scatter x-rays too weakly to be accurately measured by ionization or scintillation counter techniques. Therefore, the need for a critical study of the photographic techniques of obtaining accurate diffraction intensities is paramount. 

The internal structure of a polyatomic ligand is obtained as an additional result in these investigations. Its high concentration and the sharp intramolecular distances often result in dominant contributions to the diffraction curves and make possible a precise determination of its bonding distances. When careful analyses have been made, no significant differences from values found in crystals have been found, however. Therefore, the derived structure for the ligand can serve as an internal check on the quality of the data. Large deviations from values found in crystal structures may be an indication of errors in the data or in the method of analysis. 

Also crystallizing in space group P2 ]c, uranocene has two molecules per unit cell, so that the U(CsH8)2 molecule occupies a special position of site symmetry 1. In other words, the molecule has an eclipsed conformation, and it may be assigned to special position 2(a). Similarly, the two halves of the [Re2Clg]2- dianion in K2 [Rc2C lmolecular dimensions (indicating that the symmetry of the dianion is Z>4h within experimental error) and crystal structure are shown in Fig. 9.6.5. 

Preliminary three-dimensional atomic coordinates of atoms in crystal structures are usually derived from electron-density maps by fitting atoms to individual peaks in the map. The chemically reasonable arrangement of atoms so obtained is, however, not very precise. The observed structure amplitudes and their relative phase angles, needed to calculate the electron-density map, each contain errors and these may cause a misinterpretation of the computed electron-density map. Even with the best electron-density maps, the precisions of the atomic coordinates of a preliminary structure are likely to be no better than several hundredths of an A. In order to understand the chemistry one needs to know the atomic positions more precisely so that better values of bond lengths and bond angles will be available. The process of obtaining atomic parameters that are more precise than those obtained from an initial model, referred to as refinement of the crystal structure, is an essential part of any crystal structure analysis. 

The main cause of the existence of errors in protein structure coordinates is that x-ray structure determination consists of a long series of complicated steps. Starting with the exposure of imperfect crystals to x-rays, reflections are obtained which, after several... 

Water molecules are an essential aspect of protein structures. Without knowledge of the location of all tightly bound waters, many aspects of the structure, function, and stability of proteins cannot be properly studied. Unfortunately, waters are often abused in crystal structure determination. From the kinds of errors we detect, we assume that some crystallographers, shortly before they manually place waters in the density map, use software that places a water molecule close to each alpha carbon (in a well-determined structure there is about 1 bound water molecule visible per residue). Unfortunately, it regularly occurs that a few waters that are not moved to another position are forgotten, and remain part of the structure. 

Figure 5. H -O frequency distributions in crystals for hydrogen bonds from C=C-H donors to (top) C=0 acceptors, n = 33, and (bottom) C-OH acceptors, n = 31. Database analysis perform for this article [CSD, June 1997 update with 167797 entries, ordered and error-free crystal structures with R < 0.10, normalized H-atom position based on a linear C=C-H group, and a C-H bond distance of 1.08 A neither donor nor acceptor group directly bonded to a metal atom, H -O < 2.95 A for three-center hydrogen bonds, only the short component is considered).

The direct experimental result of a crystallographic analysis is an electron-density map, and not the atomic model everybody looks at If errors occur in crystal structures, they most often occur at the level of the (subjective) interpretation of the electron-density maps by the crystallographer. A severe problem, especially at low resolution (lower than 3.0 A), is the so-called model bias. To calculate an electron-density map, one needs amplitudes and phases. The amplitudes are determined experimentally, but the phases cannot be measured directly. In later stages of refinement, they are calculated from the model, which means that if the model contains errors, the phases will contain the same errors. Since phases make up at least 50% of the information which is used to calculate the electron-density maps, wrong features may still have reasonable electron density because of these phase errors. 

There are various theoretical methods for calculating the lattice energy of a molecular crystal. It is important to note that the accuracy of these methods is key to the correct prediction of co-crystal stability. Some verification of the accuracy of the method for calculating the lattice energy is possible using experimental information. If the method, when used in crystal structure prediction, fails to predict the known polymorphs of the molecular crystals as low energy structures, then it is clear that, unless there is some fortuitous cancellation of errors, the method will not be able to predict co-crystal stability reliably. 

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. 

The next step is to obtain geometries for the molecules. Crystal structure geometries can be used however, it is better to use theoretically optimized geometries. By using the theoretical geometries, any systematic errors in the computation will cancel out. Furthermore, the method will predict as yet unsynthesized compounds using theoretical geometries. Some of the simpler methods require connectivity only. 

In general, the R factor is between 0.15 and 0.20 for a well-determined protein structure. The residual difference rarely is due to large errors in the model of the protein molecule, but rather it is an inevitable consequence of errors and imperfections in the data. These derive from various sources, including slight variations in conformation of the protein molecules and inaccurate corrections both for the presence of solvent and for differences in the orientation of the microcrystals from which the crystal is built. This means that the final model represents an average of molecules that are slightly different both in conformation and orientation, and not surprisingly the model never corresponds precisely to the actual crystal. 

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