Symmetry and Structural Parameters

Tetravinylmethane (TVM) is a very interesting compound with respect to its conformational and structural parameters. All the assumptions on the symmetry of TVM are based on D2d and S4 conformations10,11. Surprisingly, none of these conformations is observed in the crystalline state instead, C symmetry was found in an orthorhombic crystal lattice (space group Pbca). If one of the vinyl groups (C3-C8-C9) is rotated by ca 150°, the Ci symmetry can be transferred to S4 symmetry (or vice versa). This is evident from Figure 2 where DVC is also shown in the same projection which demonstrates that the C1 symmetry is no coincidence of packing effects. 

SCHEME 22. MO-Schemee), PES data (eV), and structural parameters of the Group 14-decamethyl-metallocenes X-ray 6gED two independent molecules dtwo conformers in the unit cell in orbital notation for C2v symmetry... 

The species [B,HS]2 with D3h symmetry and nine equal B—B distances was predicted to be stable by Lipscomb et al. however, thus far the species has eluded preparation74 . Of the dicarbapentaborane analogues, three isomers are possible but the only unsubstituted isomer known is 1,5-C2B3H5. The structure, which has been determined by electron diffraction99 , is shown in Fig. 8 and structural parameters are shown inset. 

High-Symmetry/Temperature and Low-Symmetry/Temperature Structural Parameters of KO2... 

Earlier, in Chapter 3, the existence of the nematic phase was presented as an example of an order-disorder phenomenon. The symmetry and structure of the nematic phase were used to identify the natural order parameter , where P2 (cos d) is the second Legendre polynomial and the angular brackets denote a statistical average over the orientational distribution function /(cos 6). The orientational potential energy of a single molecule was shown, in the mean field approximation, to be... 

The symmetry and structure of the smectic-A liquid crystals are reviewed the natural order parameters are identified. The relationship of the smectic-A phase to the nematic (or cholesteric) and isotropic phases in homologous series is also examined. The McMillan form of the single molecule potential function is then deduced starting from the Kabayashi form of the potentiaP and using the formal development presented earlier. The derivation of the statistical thermodynamics then follows, along with a presentation of McMillan s numerical results and a comparison with experiment. Improvements in the theory introduced by Lee et al are also considered. In the last section, the important question of whether the smectic-A to nematic (cholesteric) phase transition can ever be second order is examined. 

LEED [44] - implemented in the computer code [51] used in this study, in particular, the combination of geometrical and chemical perturbations [38] - the element-specific positions of atoms in the surface could additionally be determined (this is in spite of the average structure being of (1 x 1) symmetry). The structural parameters that, by input to model intensity calculations, reproduce the experimental intensities best (as j udged by a reliability factor, here the Pendry J -factor [42]) correspond to the experimentally determined parameter values. By comparison with their theoretical counterparts calculated by first-principles as described earlier, the reliability of the present theoretical approach can be judged. 

Structural parameters and interatomic distances derived from electron diffraction (7) (77JST(42)l2i) and X-ray diffraction (8) studies (76AX(B)3178) provide unequivocal evidence that pyrazine is planar with >2a symmetry. There is an increased localization of electron density in the carbon-nitrogen bonds, with carbon-carbon bonds being similar in length to those in benzene. ... 

Phenazine also exhibits D h symmetry and numerous reports on the X-ray structure of a-phenazine have appeared (54AX129). The parameters determined at 80 K are shown in... 

Having determined the effect of the diffusive interfaces on the structure parameters, we now turn to the calculation of H and K in microemulsions. In the case of oil-water symmetry three-point correlation functions vanish and = 0. In order to calculate K from (77) and (83) we need the exphcit expressions for the four-point correlation functions. In the Gaussian approximation... 

The symbolic variables show explicit which parameters are constrained to have the same values, i.e. He and H7 are symmetry equivalent and must therefore have the same distances and angles, and a sign difference in the torsional angle. Although the R4 and R5 (and A3 and A4) parameters have the same values initially, they will be different in the final optimized structure. 

The phase transiton from a paraelectric to a ferroelectric state, most characteristic for the SbSI type compounds, has been extensively studied for SbSI, because of its importance with respect to the physical properties of this compound (e.g., J53, 173-177, 184, 257). The first-order transition is accompanied by a small shift of the atomic parameters and loss of the center of symmetry, and is most probably of a displacement nature. The true structure of Sb4S5Cl2 106), Bi4S5Cl2 194), and SbTel 108,403) is still unknown. In contrast to the sulfides and selenides of bismuth, BiTeBr 108) and BiTel (JOS, 390) exhibit a layer structure similar to that of the Cdl2 structure, if the difference between Te, Br, and I (see Fig. 36) is ignored. 

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