Noncentrosymmetric structures

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.)... 

The first and third order terms in odd powers of the applied electric field are present for all materials. In the second order term, a polarization is induced proportional to the square of the applied electric field, and the. nonlinear second order optical susceptibility must, therefore, vanish in crystals that possess a center of symmetry. In addition to the noncentrosymmetric structure, efficient second harmonic generation requires crystals to possess propagation directions where the crystal birefringence cancels the natural dispersion leading to phase matching. 

It has been known that alternating LB films consisting of two different amphiphiles have noncentrosymmetric structures, and therefore, are expected to provide piezoelectric, pyroelectric and nonlinear optical properties. Therefore, we prepared alternating LB films consisting of 5-(p-dodecyloxyphenyl)pyrazine-2-carboxylic acid (DOPC)... 

For the establishment of a preparation method for LB films with well-defined noncentrosymmetric structure, quantitative evaluation of noncentrosymmetric molecular orientation is essential. The linear Stark effect, which is observed only in noncentrosymmetric materials, is expected to be helpful for the characterization of noncentrosymmetric molecular orientation in LB films [5], In this section, we describe the quantitative evaluation of noncentrosymmetric molecular orientation in LB films by the linear Stark effect measurement. 

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]. 

In order to bridge the gap between an SHG-active material and one optimized for use in an optoelectronic device, many compounds have been synthesized, characterized, modified and then ultimately rejected during the past decade (i-3). This is not surprising, since the ideal material must fulfil a plethora of stringent requirements (4-7). The most critical condition for an SHG-active material is that it must form noncentrosymmetric structures however, thermal stability, in volatility, transparency, lack of colour, mechanical strength and crystal habit are also crucial properties for materials to be incorporated into practical devices. 

Ashwell, G.J. (1999) Langmuir-blodgett films Molecular engineering of noncentrosymmetric structures for second order nonlinear optical applications. Journal of Materials Chemistry, 9, 1991-2003. 

For a centrosymmetric structure, Uhki can equal only 0 or 180° (i.e. F having signs + or respectively), for a noncentrosymmetric structure it can have any value. Owing to the translational symmetry of crystals, p xyz) can be considered as a periodic function in three-dimensional space and expressed by the Fourier transform of equation (8),... 

Other variables refined in the LS procedure are the scale factor K (Section 3.3.5) always, atomic site occupancies in the cases of disorder and/or nonstoichiometric composition and the absolute structure parameter for noncentrosymmetric structures. If the sample contains atoms with sufficiently strong anomalous scattering, the latter parameter indicates whether the assumed absolute structure of the crystal is right or wrong. 

The phase problem is more extensive for noncentrosymmetric structures. because then most of the structure factors have phase angles with any value between 0° and 360°. The number of relative phase combinations is, then, infinite. If, however, the relative phase angle is in the correct quadrant (0 to 90°, 90 to 180°, etc.), the map is generally interpretable. Therefore, as an approximation, the number of possibilities is reduced from infinity to 4. Of these, only one is totally correct, several are essentially correct, while the majority are incorrect. 

The derivation of phases for noncentrosymmetric structures is more difficult, because the values are not restricted to 0° or 180°. In addition to the origin-defining phases, an enantiomorph-defining phase must be selected. Usually phases are derived by the tangent formula ... 

The set of anisotropic displacement parameters, obtained from the least-squares refinement of the crystal structure (as described by Chapter 10) can be analyzed to obtain T, L and S. It has been assumed that there is no correlation between the motion of different atoms. Values of Uij are analyzed (again by an additional least-squares analysis) in such a way that good agreement is obtained between the refined values and those predicted when constants have been obtained for the T, L, and S tensors. The total number of anisotropic displacement parameters (6 per atom) is the input, and a total of 12 parameters for a centrosymmetric structure, or 20 parameters for a noncentrosymmetric structure, is the output of this least-squares analysis. The results consist of the molecular translational (T), librational (L), and screw (S) tensors. This treatment leads to estimates of corrections that should be made to bond distances. On the other hand, this type of analysis cannot be used for intermolec-ular distances because the correlation between the motion of different molecules is not known. 

Certain physical phenomena, such as piezoelectric or pyroelectric effects, or second harmonic generation, are found only for noncentrosymmetric structures [see Table 4.6 (Chapter 4) and Chapter 5]. The statistics of the intensities will usually tell if a crystal structure is centrosymmetric or noncentrosymmetric (see Chapter 8). 

Umemura, Y.. Yamagishi, A., Schoonheydt, R., Persoons, A., De Schryver, F. Langmuir-Blodgett films of a clay mineral and ruthenium(II) complexes with a noncentrosymmetric structure. J. Am. Chem. Soc. 124. 992-997 (2002)... 

Linear organic molecules were firstly considered for the design of TPA efficient molecules. This family can be divided into two groups (Fig. 1) (1) dipolar molecules constituted by a noncentrosymmetric structure, with a linear delocaUzed electrons system substituted at each end by electron donor D and acceptor groups A (push-pull molecules) (2) quadrupolar systems, consisting of symmetric molecules with a n electrons system substituted by donor or acceptor groups. 

For those protein models for which structure amplitudes have been calculated, R values are usually in the range 0.4-0.5 even for the limited data available for these noncentrosymmetric structures.1S 18 There would appear to be no in principle reason why a protein model should not refine within the limits imposed by the extent and accuracy of the data and, in fact, efforts were made to refine myoglobin, the first protein to be solved. Considerable effort was invested and progress was made, but the work has never been fully reported. It is clear from what has been reported, however, that the effort was an extensive one but that the methods used were not sufficiently effective. 

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