Non-centrosymmetric space groups

In contrast to sulfurous acid, H2S03, which is not known as pure substance, the respective selenium compound can be obtained in crystalline form. H2Se03 crystallizes with the non-centrosymmetric space group P2 2,2] and contains pyramidal H2Se03 molecules.54 Within the molecules the bond lengths Se-O and SeOH differ by about 10 pm and the molecules are connected to puckered layers by strong hydrogen bonds. 

Karle, J. Hauptman, H.A. (1956). A theory for the four types of non-centrosymmetric space groups 1P222, 2P22, 3Pi2, 3P22- Acta Cryst. 9, 635-651. 

In a second step d5mamical effects must be taken into account. For dynamical refinement we used a multi-slice least squares (MSLS) procedure [21], where the centre of laue circle, crystal thickness and scaling factor were refined for each zone separately with fixed atom positions. In the case of non-centrosymmetric space groups the enantiomorph used for refinement can be chosen for each zone, additionally. After the basic parameters have been derived satisfactorily, the atom positions can be refined. The R-values (see Eq. 2) refined by MSLS usually dropped down to 6-13%. 

In the 25 analyzed dpg/dpg+ eompounds 10 crystallize in non-centrosymmetric space groups (5 are chiral). In HOFDAH the chiralization is forced by introducing a chiral negative ion in the structure (L-tartrate, Figure. 5). In other cases, chiralization is spontaneous and it can be achieved either by... 

However, FriedeFs law no longer holds if a compound containing an anomalous scatterer, besides other elements, crystallizes in a non-centrosymmetric space group then the following inequalities between Friedel pairs apply ... 

An X-ray crystallographic analysis of DAD single crystals shows a triclinic system with the non-centrosymmetric space group P1 and that the direction of polarization of DAD in the molecular crystal is perfectly aligned in one dimension. 

Molecular and crystal structure of DAD are shown in Figure 3 and 4. DAD crystallize in a triclinic system with the non-centrosymmetric space group P1. The direction of polarization of DAD in the molecular crystal is perfectly aligned in one dimension as shown in Figure 4. X-ray crystal analysis of DAD also shows the existence of two hydrogen bonds between adjacent molecules, 0 1--H... 

However, up to now, no fuUy clear mechanism by which TL occurs has been presented. Some works suggest that TL is a consequence of a recombination of charges separated during fracture of a crystal belonging to a non-centrosymmetric space group . On the other hand. Cotton and coworkers showed that centric compounds can exhibit TL, and they pointed to two non-centric compounds, at least, which show no TL at room temperature. However, TL in centrosymmetric compounds have been generally assigned to impurities or disorder of some atoms in the molecular structure . 

AgFj with ASF5 in AHF (4). X-ray diffraction data were obtained at 186 K the structure was solved and refined in the non-centrosymmetric space group Pnl a (nonstandard setting of Pnal ). Besides the well... 

Perutz, M. F. Isomorphous replacement and phase determination in non-centrosymmetric space groups. Acta Cryst. 9, 867-873 (1956). 

J. Karle and H. Hauptman, A theory of phase determination for the four types of non-centrosymmetric space groups, Acta Cryst. 9, 635 (1956). Jerome Karle, US crystallographer, and Herbert A. Hauptman, US mathematician, laid a foundation towards the development of modem direct phase determination techniques. They won 1985 Nobel Prize in Chemistry for their outstanding achievements in the development of direct methods for the determination of crystal stmctures - http //www.nobel.se/ chemistry/laureates/1985/. 

M. A. Spackman and P. G. Byrom, Retrieval of structure-factor phases in non-centrosymmetric space group. Model studies using multipole refinement, Acta Cryst. B53, 553-564 (1997). 

The substantial difference in the pressure dependence of the frequency of the Raman V2 multiplet will be discussed later. The pressure dependences of the Raman and infrared frequencies are compared in the inset of Fig. 6. We find that Raman and infrared frequencies do not coincide (cf Ref. [9]) suggesting a non-centrosymmetric space group. Unlike the Raman data, our infrared frequencies are in good agreement with those reported in Ref. [9] in the pressure range overlapped by the two studies (to 25.2 GPa). 

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