Crystal structure inverse

The ferrites generally have one of three crystal structures inverse spinel, gameL and hexagonal. The spinel structures (cf. 

The SSW form an ideal expansion set as their shape is determined by the crystal structure. Hence only a few are required. This expansion can be formulated in both real and reciprocal space, which should make the method applicable to non periodic systems. When formulated in real space all the matrix multiplications and inversions become 0(N). This makes the method comparably fast for cells large than the localisation length of the SSW. In addition once the expansion is made, Poisson s equation can be solved exactly, and the integrals over the intersitital region can be calculated exactly. 

The even-numbered degree of polymerization behaviour of 2 OEt can be interpreted from its crystal structure (Fig. 9), in which the molecule is related to its neighbouring molecules by two different inversion centres to make a plane-to-plane stack (Maekawa et al., 1991a). The ethylenic double... 

In ionic crystals with d = nearest neighbor distance, the ions repulse each other strongly when d becomes smaller than the equilibrium value d0. This can be described by an inverse power function, +l/dn, where n is a power of order, 9. As for the electrostatic attractions, these repulsions must be summed over the N molecules of the crystal structure, yielding another constant, D. The energy, < > per molecule (ion pair) is then ... 

From 2002 to 2007, Kubiak and Janczak [27-30] and Sun s [31] groups investigated various symmetrical MPcs with pyridine and its derivatives 4-CP and 4-MP as two axial ligands. Six complexes in this series with crystal structures are reported. The crystal structures of MnPc(Py)2 (M = Mg (4), Mn (5), Co (6) or Fe (7)) complexes with axial pyridine ligands are isostructural. Another two compounds [FenPc(4-CP)2] 2(4-CP) (8) and [RunPc(4-MP)2] -2CHC13 (9) have similar molecular structures to 4-7. The central metal ions in these complexes lie at the inversion centres thus, the molecules are centrosymmetric. In the six complexes, the central metal ion and the four Niso atoms of the Pc(2-) ligands lie on a strict plane. The... 

Mechanisms involving axial coordination of the optically active amine have also been invoked, and crystal structure data on RCo(DMG)2B complexes, where R is alkyl or (R)-l-(methoxycarbonyl)ethyl, and B is (R )-a-methylbenzylamine, were obtained (316, 317). Because deuteration of the (R)-methoxycarbonyl complex gave (5)-methylpropionate-2-d, it was concluded that Co—C bond cleavage occurred with inversion of configuration at the carbon (317). It would be useful to know the mechanistic details of this step, which could involve attack by D+, DCo(III), or coordinated D, as well as D2, for it is an unusual, if not unique, observation [contrast with the usual retention mechanism outlined in Eq. (39)]. 

The X-ray crystal structure of 6-chloro-2,3-dihydro-7-methyl-5-methyIene-2//, 3H, 5H- l,4-dithiepin-l,l,4,4-tetraoxide has been published and a short intermolecular contact across an inversion centre noted <00AX(Qel09>. An experimentally direct and efficient approach to 1,3-dithiepins has been reported using 1 qi-alkyldihalides and carbon disulfide and sodium borohydride, to generate the sulfide nucleophile . 

The 4,4 -bipy and bpe derivatives display a similar crystal structure to that of Cd(4,4 -bipy)2[Ag(CN)2]2 reported by Iwamoto et al. [89]. It consists of the interpenetration of two identical 3D networks. The knots of the networks are defined by the iron(II) and silver(I) atoms. Each iron(II) atom located on an inversion centre defines an elongated octahedron whose axial positions are occupied by the nitrogen atoms of two 4,4 -bipy ligands. In addition, each 4,4 -bipy ligand binds a silver atom so that it is three-coordinated. This is the reason why the [Ag(CN)2] group is bent (see Fig. 18). 

The crystal structure can be considered as a structure regularly stacked with bimolecular layers along the a-axis. Within the bimolecular layer, two molecules related by inversion symmetry face each other in the tail-to-tail fashion with their molecular axes inclined by about 26° to the bilayer surface. This inclination enables the head-to-tail arrangement of azobenzene chromophores as expected from the spectroscopic study. 

Figure 8. Crystal structure of alkynol 12 to show synthons IX and X. There are two symmetry independent molecules and each lies on an inversion centre. Hydrogen bonds are indicated. Notice here that the hydrogen-bonded and hydrocarbon regions are well insulated.

Figure 2. (a) Crystal structure ofCClfSb(OTeFs)f (b) A view of the CClf cation, with key bond lengths and bond angles, showing the two-fold positional disorder around the crystallographic inversion center.82... 

Finally, reference must be made to the important and interesting chiral crystal structures. There are two classes of symmetry elements those, such as inversion centers and mirror planes, that can interrelate. enantiomeric chiral molecules, and those, like rotation axes, that cannot. If the space group of the crystal is one that has only symmetry elements of the latter type, then the structure is a chiral one and all the constituent molecules are homochiral the dissymmetry of the molecules may be difficult to detect but, in principle, it is present. In general, if one enantiomer of a chiral compound is crystallized, it must form a chiral structure. A racemic mixture may crystallize as a racemic compound, or it may spontaneously resolve to give separate crystals of each enantiomer. The chemical consequences of an achiral substance crystallizing in a homochiral molecular assembly are perhaps the most intriguing of the stereochemical aspects of solid-state chemistry. 

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