Ideal structures, deviations from

An energy minimization of the complex between V and naphthalene indeed showed a tight fit between the van der Waals surfaces in a nearly equatorial conformation (Figure 2). The force field minimized structure deviates from the idealized one shown in Chart II, which, however, represents a time-averaged picture of the ring. Although the computer models... 

Figure 4.4. Schematic representations of base-pair structural deviations from the ideal coordinate frame of the upper and middle left. The most important rotations for the purposes of this chapter are propeller twist, twist, and roll. [Adapted from Figs. 7 and 8 (erroneously listed as Fig. 9 in its caption) of Ref. 13, with permission].

Anything which makes the structure deviate from the ideal one or defects or irregular structure elements may then be inunediately sorted out as ... 

If we assume that there are certain ideal val ues for bond angles bond distances and so on itfol lows that deviations from these ideal values will destabilize a particular structure and increase its po tential energy This increase in potential energy is re ferred to as the strain energy of the structure Other terms for this increase include steric energy and steric strain Arithmetically the total strain energy ( ) of an alkane or cycloalkane can be considered as... 

The deviation from planarity that is present in a structure such as 1 raises the question of how severely a conjugated system can be distorted from the ideal coplanar alignment of p orbitals and still retain aromaticity. This problem has been analyzed by determining the degree of rehybridization necessary to maximize p orbital overlap in 1. It is found that rehybridization to incorporate fractional amounts of s character can improve orbital alignment substantially. Orbitals with about 6% s character are suggested to be involved... 

Figure 15.6 Various representations of the molecular structure of ryclc-Si2 showing S atoms in three parallel planes. I he idealized point group symmetry is and the mean dihedral angle is 86.1 5.5 . In the crystal the symmetry is slightly distorted to C21, and the central group of 6 S atoms deviate from eoplanarily by 14pm.

Analysis of data pertaining to the modulus of PEO gels obtained by the polyaddition reaction [90] shows that even in this simplified case the network structure substantially deviates from the ideal one. For all samples studied, the molecular weight between crosslinks (M p) exceeds the molecular weight of the precursor (MJ. With decreasing precursor concentration the M xp/Mn ratio increases. Thus, at Mn = 5650 a decrease in precursor concentration from 50 to 20% increases the ratio from 2.3 to 12 most probably due to intramolecular cycle formation. 

In Fig. 3.1, several ideal structures are also plotted with the + mark. All of these structures have no adjustable parameter and most of them lose some of the symmetry elements when they are distorted. As shown in the figure, most of the ideal structures have some deviation from the fitting curve. It may be related to the fact that some of these ideal structures are deformed in real binary compounds. 

The analysis of XRPD patterns is an important tool studying the crystallographic structure and composition of powder compounds including the possibility to study deviation from ideal crystallinity, i.e. defects. Looking at an X-ray powder diffractogram the peak position reflects the crystallographic symmetry (unit cell size and shape) while the peak intensity is related to the unit cell composition (atomic positions). The shape of diffraction lines is related to defects , i.e. deviation from the ideal crystallinity finite crystallite size and strain lead to broadening of the XRPD lines so that the analysis of diffraction line shape may supply information about sample microstructure and defects distribution at the atomic level. 

All real crystals have deviation from the ideal crystallographic structure due to atomic displacements from their ideal positions in the unit cell. These displacements may... 

When the variation of any colligative property of a surfactant in aqueous solution is examined, two types of behavior are apparent. At low concentrations, properties approximate those to be expected from ideal behavior. However, at a concentration value that is characteristic for a given surfactant system (critical micelle concentration, CMC), an abrupt deviation from such behavior is observed. At concentrations above the CMC, molecular aggregates called micelles are formed. By increasing the concentration of the surfactant, depending on the chemical and physical nature of the molecule, structural changes to a more... 

Practical Value. The presented analytical expressions are very useful, predominantly for the analysis of the scattering from weakly distorted nanostructures. Because of their detailed SAXS curves, direct fits to the measured data return highly significant results (cf. Sect. 8.8.3). Nevertheless, some important corrections have to be applied [84], They comprise deviations from the ideal multiphase structure as well as thorough consideration of the setup geometry and machine background correction (cf. Sect. 8.8). 

Ruland and Smarsly [84] study silica/organic nanocomposite films and elucidate their lamellar nanostructure. Figure 8.47 demonstrates the model fit and the components of the model. The parameters hi and az (inside H ) account for deviations from the ideal two-phase system. Asr is the absorption factor for the experiment carried out in SRSAXS geometry. In the raw data an upturn at. s o is clearly visible. This is no structural feature. Instead, the absorption factor is changing from full to partial illumination of the sample. For materials with much stronger lattice distortions one would mainly observe the Porod law, instead - and observe a sharp bend - which are no structural feature, either. 

Although we have described the structures of several molecules in terms of hybrid orbitals and VSEPR, not all structures are this simple. The structures of H20 (bond angle 104.4°) and NH3 (bond angles 107.1°) were described in terms of sp3 hybridization of orbitals on the central atom and comparatively small deviations from the ideal bond angle of 109° 28 caused by the effects of unshared pairs of electrons. If we consider the structures of H2S and PH3 in those terms, we have a problem. The reason is that the bond angle for H2S is 92.3°, and the bond angles in PH3 are 93.7°. Clearly, there is more than a minor deviation from the expected tetrahedral bond angle of 109° 28 caused by the effect of unshared pairs of electrons ... 

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