Centrosymmetric groups

Tetragonal co-ordination with 2 chelating pn ligands and S-bonded NCS groups Centrosymmetric dimer. Each Cu surrounded by 7 atoms. Asymmetric bidentate NO 3 co-ordination Both have exactly trans planar co-ordination... 

The two exponential tenns are complex conjugates of one another, so that all structure amplitudes must be real and their phases can therefore be only zero or n. (Nearly 40% of all known structures belong to monoclinic space group Pl c. The systematic absences of (OlcO) reflections when A is odd and of (liOl) reflections when / is odd identify this space group and show tiiat it is centrosyimnetric.) Even in the absence of a definitive set of systematic absences it is still possible to infer the (probable) presence of a centre of synnnetry. A J C Wilson [21] first observed that the probability distribution of the magnitudes of the structure amplitudes would be different if the amplitudes were constrained to be real from that if they could be complex. Wilson and co-workers established a procedure by which the frequencies of suitably scaled values of F could be compared with the tlieoretical distributions for centrosymmetric and noncentrosymmetric structures. (Note that Wilson named the statistical distributions centric and acentric. These were not intended to be synonyms for centrosyimnetric and noncentrosynnnetric, but they have come to be used that way.)... 

Figure 11.19 Schematic diagram of the centrosymmetric dimer in [Cii2(NO ).i(py) lpy showing the two bridging nitrato groups each coordinated to the 2 Cii atoms by a single O atom the dimer also has an unsymmetrical bidentate nitrate group on each Cu.

An irreversible extinction of the SHG signal at 150-200°C is observed for a number of other fluoride and oxyfluoride compounds of tantalum and niobium that crystallize in centrosymmetric space groups. This phenomenon is especially typical for the compounds prepared by precipitation from solutions [206]. The appearance of the weak SHG signal for such compounds is related to imperfections in their crystal structure and the creation of dipoles. Nevertheless, appropriate thermal treatment improves the structure and leads to the disappearance of dipoles and to the irreversible disappearance of the corresponding SHG signal. 

Fig. 100. Irreversible extinction of SHG signal during heating of compounds that crystallize in centrosymmetric space groups. SHG signal is normalized by signal of alpha-quartz (a-SiO/f.

Few examples of chemical or enzymatic desymmetrizations of centrosymmetric molecules (point group S2 = Q) have been described [150]. The PLE-catalyzed hydrolysis of a centrosymmetric cyclohexanediacetate gave rise to an enantiomeri-cally pure (>99.5% ee) cyclohexanediol monoacetate in high yield [151] (Figure 6.57). 

Wavenumbers (unsealed cm ) and relative infrared/Raman intensities as follows. Infrared intensities very strong-strong-medium-weak-very weak-0. Raman intensities 0-100 (sh shoulder). In the case of the centrosymmetric point group C2h the rule of mutual exclusion applies... 

The nonmesogenic compound CB2 is described here, because it shows a reversible distortive solid-solid phase transition at 290.8 K (transition enthalpy 0.9 kj/mol) from the centrosymmetric low temperature phase I to the noncentrosymmetric high temperature phase II. The crystal structures of both solid phases I and II are very similar [45] as demonstrated in Fig. 2. The molecules are arranged in layers. The distances between the cyano groups of adjacent molecules are 3.50 A Ncyano-Ncyano and 3.35 A Ncyano-C ano for phase I and 3.55 A Ncyano-Ncyano and 3.43 A Ncyano-Ccyano for phase II. In the two... 

In 1985, Astheimer et al, [134] described the crystal structure of the mesogenic 4,4 -di(7S0-hexoxybenzalazine, Here, the centrosymmetric molecule is fully elongated with the hexoxy group in an aU-trans conformation and the phenyl rings are exactly coplanar. 

For this scheme, m, n, and p have been defined for minerals as being even numbers. Notice also that the formula for bismuthite and aikinite have been doubled in keeping with the reported model where only (l) = Cu and (ll) = Pb are known [78]. Also defined are the terms A (A=m/4) and B (B=n/2). It has been observed that for most mineralogical systems, when A-i-B is even, the corresponding space group was the non-centrosymmetric, Pmc2i, and when A-vB is... 

Ethyl a-cyano-4-[2-(2-pyridyl)ethenyl]cinnamate (7 OEt) also crystallizes with /3-centrosymmetric-type packing yielding photoreactive crystals and, upon photoirradiation (>410 nm), is converted into the /3-hetero-type dimer (7 OEt-dimer) nearly quantitatively. The 7 OEt-dimer (space group PT, triclinic) has the structure which is predicted from the crystal structure of 7 OEt (space group PT, triclinic). 

C16H2207 l,5-Anhydro-2,3,4-tri-0-benzoylxylitol (ATBXYL10)114 PI Z = 2 Dx = 1.32 R = 0.053 for 3,536 intensities. The crystal structure contains centrosymmetrically related d and l enantiomers. The pyranoid conformation is an almost ideal (d) [1C4(l)]i withQ = 60 pm, 0=1°, with normal bond-lengths and valence-angles. The benzoyl groups are equatorial, with their planes approximately normal to the mean plane of the pyranoid ring. 

Substitution of the dimethylsilyl group by bis(tert-butyl)-stannyl does not change the structure in solution, e.g. 33 is found to be monomeric. A very interesting dimer is 26. In contrast to the centrosymmetrical dimer of 1 (C-Symmetry), 26 has a twofold axis (C2, see Fig. 9). This special structure may be due to intramolecular Lewis acid-base interactions between the boron and nitrogen atoms 39). Nevertheless,... 

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