Structure centrosymmetric

PhN(H))2(tBuO)LiNaK(TMEDA)2]2 406.425 The centrosymmetric structure is composed of a 12-vertex cage in which two Li and two Na cations are four-coordinate in a distorted tetrahedron, while the K cations are six coordinate and octahedral. While Na binds only to N, the Li and K cations bond with 2N/20 and 4N/20, respectively. In a now familiar pattern, the Li cations occupy the core while the structure periphery is comprised of a (K- -N- -Na- N- K- N- -Na- -N) cycle of atoms, though an alternative description is of a (KO)2 ring sandwiched between two heterometallic (LiNNaN) rings. 

Diphenyl-l,3,4-oxadiazole is polymorphic (centrosymmetric monoclinic structure with space group P21/c and monoclinic non-centrosymmetric structure with space group P21/c). DSC investigations showed an irreversible transition from the first to the second form at 97 °C <2003JST219>. 

In the case of MAP, the concept of chirality was used so as to prevent centrosymmetry a chiral molecule cannot be superimposed on its image by a mirror or center of symmetry so that a crystal made only of left or right-handed molecules can accomodate neither of these symmetry elements. This use of the chirality concept ensures exclusion of a centrosymmetric structure. However as we shall see in the following, the departure of the actual structure from centrosymmetry may be only weak, resulting in limited nonlinear efficiencies. A prerequisite to the introduction of a chiral substituent in a molecule is that its location should avoid interfering with the charge-transfer process. 

MAP has a non-centrosymmetric structure (24) P2- leading to four non-vanishing crystalline nonlinear coefficients. According to the previously defined two-level model, there are also four non-vanishing molecular nonlinearity coefficients which are linearly related to the crystalline coefficients. (3)... 

Theoretical estimations and experimental investigations tirmly established (J ) that large electron delocalization is a perequisite for large values of the nonlinear optical coefficients and this can be met with the ir-electrons in conjugated molecules and polymers where also charge asymmetry can be adequately introduced in order to obtain non-centrosymmetric structures. Since the electronic density distribution of these systems seems to be easily modified by their interaction with the molecular vibrations we anticipate that these materials may possess large piezoelectric, pyroelectric and photoacoustic coefficients. 

ABC triblock copolymers have recently proven to be useful in constructing the so-called three-layer, onion, or core-shell-corona micelles, as described in Sect. 7.2. These micelles are characterized by a centrosymmetric structure and a micellar core with two different concentric compartments. Noncentrosymmetric structures from ABC triblock copolymers blended with AC diblocks have, however, been reported in bulk by Goldacker et al. [290]. 

HOMO) and the subjacent HOMO - 1 depicted in Chart 3. As such, the centrosymmetric structures above accord with the optimum overlap of the naphthalene HOMO and HOMO - 1 of au and bIu symmetry, respectively, with the degenerate pair of tropylium e i lowest unoccupied molecular orbitals (LUMOs) of the same gross symmetry. On the basis of similar considerations of orbital symmetry, the EDA complexes of tropylium with neither benzene nor anthracene donors would be centrosymmetric. 

We may describe the centrosymmetric structure in Scheme 10c in terms of the alternative, left-handed axial system by choosing the reverse vectors —a, -b, -c as the axial set, as shown in Scheme lOg. The whole arrangement remains unchanged, the only difference being that the molecules S and R are now described by coordinate sets x y z, and —x —y —z respectively. By symmetry the same applies to the nonisometric arrangement (Schemes IQf and h). 

Figure 10.2 The procedure of convolution, represented graphically, (a) A one-dimensional centrosymmetric structure, (b) A Gaussian distribution, which could potentially be an atomic shape function.

The true phases of the structure factors will, in general, be different from the phases calculated with the independent-atom model. In centrosymmetric structures, with phases restricted to 0 or n, only very few weak reflections are affected. In acentric structures, only the reflections of centrosymmetric projections, such as the hkO, hOl, and Okl reflections in the space group P212,21, are invariant. 

Inconclusive results are likely to be obtained for light-atom structures because of the low amount of anomalous scattering, as well as for nearly centrosymmetric structures, especially if the heavy atoms are distributed nearly centrosymmetrically 27. In the latter case the rj value may even refine to a false minimum with a deceptively small error estimate59. This led to the development of an alternative test by Flack which also overcomes these problems39-59. Flack introduced an absolute structure parameter x, which is defined by structure factor equation 12, and which is treated as a variable in the least-squares refinement. 

Fig. 21S. Determination of the absolute configuration of a non-centrosymmetric structure by using anomalous scattering. Left—Scattering by anomalously scattering atom JP and by the rest of the molecule, E. Centre—Representation of amplitudes and phases ot waves. Right—Corresponding vector representation (scale of amplitudes doubled).

The first important step in this direction was taken by Harker and Kasper (1948), who derived relations between pairs or small groups of reflections in a centrosymmetric structure in the form of inequality expressions. The simplest of these says that if Uhkl is the unitary structure amplitude —the structure amplitude expressed as a fraction of what it would be if the waves from all atoms were exactly in phase with each other f—then... 

The Correlation Field Approximation. In some cases it is not possible to explain experimental observations in terms of the site symmetry approximation, whereby the surroundings of a given molecule are treated as static. A clear example is provided by the crystalline form of the trans isomer of [(C5H5)Fe(CO)2]2, which has the centrosymmetric structure and the IR spectrum shown in Figure 10.13. The trans molecule (other isomers exist) has inherent Cy, symmetry when rotational orientation of the C5H5 rings about... 

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