Planar projection

As planar projection diagrams indicate, considerable overcrowding occurs in 1-phenyldibenzothiophene between the hydrogen atoms on the phenyl substituent and the adjacent C-9 proton. To a lesser extent this is also true of the 4-phenyl derivative due to partial overlap of the phenyl substituent with the sulfur atom of the thiophene ring. A detailed study of the UV spectra of the four monophenyl derivatives and the association constants of their 2,4,7-trinitrofluorenone complexes reveals that both 1-phenyl- and 4-phenyldibenzothiophene have the phenyl substituent orthogonal to the plane of the heterocycle, while both 2-phenyl- and 3-phenyldibenzothiophene are essentially planar. 

In the formula shown below for rodorubicin (a cytostatic agent) convert the groups shown in the Haworth projection into a planar projection of the rings in which the substituents are shown with wedged bonds. 

Figure 2.3. Boat and chair forms of P-D-glucuronic acid, (a) Cj chair conformation (left) and planar projection (right) (b) Boat conformation and (c) 1C chair conformation of P-D-glucuronic acid.The latter two conformations are energetically less stable than the Ci chair conformation.

Figure 1. A schematic planar projection of the direct bonding of a water molecule in an ice lattice. A central site (0) has four first-neighbors (1), which are adjacent to the central site and to three other molecules (2). Each of the 12 second neighbors (2) of the central site (0) is adjacent to only one first-neighbor (1) of the central site. Some of the third-order neighbors (3) of the central site (molecules separated through three successive bondings by the central site) are, however, adjacent to two second neighbors. Only one of the third neighbors is drawn.

II.E.4. Evaluation of the Local Field. For a tetrahedral coordination of the water molecules, the distance between the two planar sublayers of the same layer of icelike structure is (1/3)/, l being the distance between the centers of two adjacent water molecules, while the distance between the centers of two adjacent layers is A = (4/3)l. The vertexes of the tetrahedron formed by the four first neighbors of a water molecule have the length zV8/3, while the planar projection of the tilted hexagonal lattice has the side zV8/9. The volume occupied in this structure by a water molecule is v = (8/3 3)Z8. 

Fig. 7 Using the underscore convention, the topological picture of B5H9 in Figure 6 is seen to be just the planar projection of the geometrical picture...

Figure 1.6 Configurational sequences, (a) Spatial representations of meso (m) and racemic (r) configurations, (b) Planar projections of m and r configurations, (c) Isotactic (mm), heterotactic (mr), and syndiotactic (rr) triads.

Special cases are discussed in some detail in the literature [112,197,198], where the shape representation P is chosen as a space curve representing a protein backbone and the topological descriptors Fj(s) on the local tangent plane projections are either graphs or knots defined by the crossing pattern on the planar projection at each tangent plane T(s) of the sphere S. 

Fio. 3.7. Planar projections of molecular graphs of hydrocarbon molecules generated from theoretical charge distributions. Bond critical points are denoted by black dots. Structures 1 to 4 are normal hydrocarbons from methane to butane, 5 is isobutane, 6 is pentane, 7 is neopentane, and 8 is hexane. The remaining structures are identified in Table 3.2. The structures depicted in these diagrams are determined entirely by information contained in the electronic charge density. 

Figure 2. Axial projection (top) and planar projection (bottom) of the crystal structure of cellulose I. The planar projection shows the hydrogen-bonding network within the layers. (Reproduced with permission from Ref. 8. Copyright 1974, Elsevier Scientific Publishing Company,...

FIGURE 22.1 Classes of silicate structures, (a) Symbol used for the SiOj" tetrahedron. This top view of the symbol shows a red circle to represent the fourth oxygen atom at the top of the tetrahedron. The black dot represents the silicon atom at the center of the tetrahedron. Bear in mind that all of these structures are actually three dimensional. Planar projections are used here for convenience of representation, (b) Disilicate, (c) Cyclosilicate, (d) Infinite single chain, (e) Infinite double chain, (f) Infinite sheet, (g) Infinite network (cristobalite, Si02). 

The theory of the hodograph transform and the relationship derived between the equations of the two lines given by this transform in the case of a binary mixture and those of the competitive equilibrium isotherms were briefly presented in Section 8.1.2. The theory is easily extended to multicomponent mixtures, although in this case we must represent the hodograph transform in an n-dimensional coordinate system, Ci, C2, , C , or in its planar projections. If the solution presents a constant state (Figure 8.1), it is a simple wave solution, and there is a relationship between the concentrations of the different components in the eluent at the column exit (Figure 8.2). This result is valid for any convex-upward isotherm. In the particular case in which the competitive Langmuir isotherm apphes, these relationships are linear. 

Fischer Projection (or Fischer-Pollens projection) A planar projection formula in which the vertical bonds lie behind the plane of the paper and the horizontal bonds lie above the plane. Used commonly in carbohydrate structures, where each carbon in turn is placed in the proper orientation for planar projection. 

The authors have estimated the intracrystalline volume of clinoptilolite from the water content of the Na form and conclude from their estimates of the ionic volumes of the organic cations used that 100% exchange is theoretically possible for all ions. They conclude from a consideration of the heulandite structure (41), which is isostructural with clinoptilolite, that partial ion sieving occurs because there are 2 different networks of channels that intersect. Diffusion into and through one network is via rings of 10 tetrahedra having a planar projection that... 

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