Accurate charge density of the tripeptide Ala-Pro-Ala with the maximum entropy method (MEM): influence of data resolution

2007 ◽  
Vol 63 (4) ◽  
pp. 633-643 ◽  
Author(s):  
Andreas Hofmann ◽  
Roman Kalinowski ◽  
Peter Luger ◽  
Sander van Smaalen

The accurate electron density of Ala-Pro-Ala is determined by the maximum entropy method (MEM), employing the same reflection data measured at 100 K which was used for a multipole refinement by Kalinowski et al. [(2007), Acta Cryst. Accepted for publication]. Properties of the electron density are compared with the corresponding properties of the static electron density from the multipole model and to the dynamic MEM electron density of trialanine at 20 K. It is thus shown that the increased thermal smearing at 100 K leads to lower electron densities in the bond critical points and atomic charges closer to zero for Ala-Pro-Ala than has been obtained for trialanine at 20 K. The influence of the resolution of the data is investigated by a series of MEM calculations. Atomic charges and atomic volumes are found not to depend on the resolution, but the charge density in the BCPs decreases with decreasing resolution of the dataset. The origin of this dependence is found to lie mostly in the more accurate estimate of the atomic displacement parameters (ADPs) for the higher-resolution datasets. If these effects are taken into account, meaningful information on chemical bonding can be obtained with data at a resolution better than d min = 0.63 Å. Alternatively, low-resolution X-ray diffraction data can be used in accurate electron-density studies by the MEM, if another source of accurate values of the ADPs is available, e.g. from refinements with multipole parameters from a database of transferable multipole parameters.

2004 ◽  
Vol 37 (5) ◽  
pp. 698-702 ◽  
Author(s):  
H. Yamada ◽  
W. S. Shi ◽  
C. N. Xu

The crystal structure of a strontium europium aluminate, Sr0.864Eu0.136Al2O4, with a novel hexagonal form was investigated by a combination of Rietveld analysis and the maximum-entropy method (MEM) with synchrotron X-ray powder diffraction data. The electron density image calculated by the MEM/Rietveld method revealed that the apical oxygen ion in the AlO4tetrahedron has a broad distribution corresponding to an extraordinarily large atomic displacement parameter. This structure could be expressed by a split-atom model, with which the Rietveld refinement gaveRwp= 2.99% andRB= 4.16%. Subsequently, MEM-based pattern fitting (MPF) decreased theRfactors toRwp= 2.81% andRB= 2.34% and the electron density image clearly showed that the apical oxygen ions of the AlO4tetrahedra are split over three sites around a threefold axis involving an elongated distribution of the residual O ions along thecaxis. These results suggest that AlO4tetrahedra in Sr0.864Eu0.136Al2O4are orientationally disordered.


2007 ◽  
Vol 63 (2) ◽  
pp. 285-295 ◽  
Author(s):  
Andreas Hofmann ◽  
Jeanette Netzel ◽  
Sander van Smaalen

An accurate charge density study of trialanine is presented with the maximum entropy method (MEM), on the basis of the same reflection data as was used for a multipole refinement [Rödel et al. (2006). Org. Biomol. Chem. 4, 475–481]. With the MEM, the optimum fit to the data is found to correspond to a final value of χ2 which is less than its statistical expectation value N Ref, where N Ref is the number of reflections. A refinement strategy is presented that determines the optimal goal for χ2. It is shown that the MEM and the multipole method are on a par with regard to the reproduction of atomic charges and volumes, general topological features and trends in the charge density in the bond critical points (BCPs). Regarding the values of the charge densities in the BCPs, agreement between quantum chemical calculations, the multipole method and MEM is good, but not perfect. In the case of the Laplacians, the coincidence is not as good and especially the Laplacians of the C—O bonds differ strongly. One of the reasons for the observed differences in the topological parameters in the BCPs is the fact that MEM densities still include the effects of thermal motion, whereas multipole densities are free from the effects of thermal motion. Hydrogen bonds are more convincingly reproduced by the MEM than by multipole models.


1993 ◽  
Vol 48 (1-2) ◽  
pp. 75-80 ◽  
Author(s):  
Masaki Takata ◽  
Yoshiki Kubota ◽  
Makoto Sakata

Abstract The nature of the bonding in Be metal was studied by investigating the MEM map, which is the electron density distribution obtained by the Maximum-Entropy Method. In order to avoid extinc-tion effects, 19 Bragg reflections were measured by a new powder-diffraction experiment that utilizes Synchrotron Radiation as an incident X-ray and an Imaging Plate as detector. The experiment was carried out at the Photon Factory BL6A2. In spite of the limited number of reflections used in the MEM analysis, the electron density distribution of Be was obtained accurately and reliably. The structure factors for unmeasured reflections were calculated and compared with the values observed by Larsen and Hansen [Acta Cryst. B40, 169 (1984)]. The agreement is very good. Furthermore, the MEM map revealed that Be metal forms an electronic layer in the shape of a honeycomb that is parallel to the basal plane.


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