Projections along

Measurements of Stark splittings in microwave and radiofrequency spectra allow tliese components to be detennined. The main contribution to tire dipole moment of tire complex arises from tire pennanent dipole moment vectors of tire monomers, which project along tire axes of tire complex according to simple trigonometry (cosines). Thus, measurements of tire dipole moment convey infonnation about tire orientation of tire monomers in tire complex. It is of course necessary to take account of effects due to induced dipole moments and to consider whetlier tire effects of vibrational averaging are important. 

Now, we have besides the vibrational, the electronic angular momentum the latter is characterized by the quantum number A corresponding to the magnitude of its projection along the molecular axis, L. Here we shall consider A as a unsigned quantity, that is, for each A 7 0 state there will be two possible projections of the electronic angular momentum, one corresponding to A and the other to —A. The operator Lj can be written in the form... 

This section discusses some of the items considered in the start-up costs for a coal gasification project, along with the methods of estimating each item. 

Figure 10.2 Crystal structure of GeF2 (a) projection along the chains, and (b) environment of Ge (pseudo trigonal bipyramidal). The bond to the unshared F is appreciably shorter (179 pm) than those in the chain and there is a weaker interaction (257 pm) linking the chains into a 3D structure.

Problem 3.18 Draw a Newman projection along the C2-C3 bond of the following conformation of 2,3-dimethylbutane, and calculate a total strain energy ... 

Figure 4.4 The structure of cyclopropane, showing the eclipsing of neighboring C-H bonds that gives rise to torsional strain. Part (b) is a Newman projection along a C-C bond.

Figure 4.5 The conformation of cyclobutane. Part (c) is a Newman projection along the C1-C2 bond, showing that neighboring C—H bonds are not quite eclipsed.

In Fig. 6 the arrangement of the manganese atoms is shown in a projection along the a-axis. The unit cells are marked by the shaded regions. It can easily be seen, that no lattice distortion is necessary to form... 

Figure 7. Crystal structures of (a) hollandite, (b) romanechite (psilomelane), and (c) todorokite. The structures arc shown as three-dimensional arrangements of the MnO() octahedra (the tunnel-tilling cations and water molecules, respectively, are not shown in these plots) and as projections along the short axis. Small, medium, and large circles represenl the manganese atoms, oxygen atoms, and the foreign cations or water molecules, respectively. Open circles, height z. = 0 fdled circles, height z = Vi.

Figure 16. Crystal structure of a-MnOOH. The structure is shown as a three-dimensional arrangement of the Mn(0,0H)6 octahedra with the protons filling the [2 x 1] tunnels, and as a projection along the short crystallographic oaxis. Small circles, manganese atoms large circles, oxygen atoms open circles, height z - 0 filled circles, height z = A The shaded circles represent the hydrogen ions.

Fig. 1 a, b. Projection along the chain axis and side view of models of syndiotactic polystyrene in the a) trans-planar conformation b) s(2/l)2 helical conformation... 

Fig. 2 a, b. Side view and projection along the chain axis of models of isotactic polystyrene in the a) s(3/l) helical conformation b) nearly /raw-planar conformation, proposed for the crystalline gels [12]... 

An analogous case, of identical chain conformations as well as of similar unit cell dimensions, have been described for the two crystalline forms of poly-p-phenylene terephtalamide [33-36] (better known with the trade name of Kevlar). The projections along the c axis of the packing of the chains proposed for the two forms [36] has been sketched in Fig. 8, corresponding to the localization of the chain axes in (0,0, z) and (1/2,1/2, z) for the more common polymorph, in (0, 0, z) and (1/2,0, z) for the other polymorph. 

Fig. 9. — Antiparallel packing arrangement of the 3-fold helices of (1— 4)-(3-D-xylan (7). (a) Stereo view of two unit cells roughly normal to the helix axis and along the short diagonal of the ab-plane. The two helices, distinguished by filled and open bonds, are connected via water (crossed circles) bridges. Cellulose type 3-0H-0-5 hydrogen bonds stabilize each helix, (b) A view of the unit cell projected along the r-axis highlights that the closeness of the water molecules to the helix axis enables them to link adjacent helices.

Fig. 35. (continued)—(b) Antiparallel packing arrangement of two double helices, drawn in open and filled bonds, in the trigonal unit-cell projected along the c-axis. 

Fig. 37. (continued)—(b) An axial view projected along the r-axis shows the packing arrangement of three welan double helices in the trigonal unit cell. The helix drawn in solid bonds is antiparallel to the remaining helices (open bonds). Note that calcium ions are positioned between the helices and each water molecule (large open circle) shown here is connected to all three surrounding helices. The interstitial space is occupied by several other ordered water molecules (not shown). 

Figure 3. Common 4.3. 4.3 metal layers and crystallographic relation between the structure types of (a) U3Si2, YB2C and ThB4 (upper row), (b) Ti3Co5B2 and SC2RU5B4 (middle rows), (c) Nd2Fe,4B (lower part) all structures are seen in projection along [001].

Figure 1. Crystallographic relation (schematic) between the structure types of RhB (anti-NiAs type), TaFeB (ordered Fe2P type) and ZrIrjB4 type. Numbers given indicate heights in projection along [001]. Large circles are metal atoms, small circles are B atoms. Metal sublattice of RhB and different modes of filling the voids (squares) generate the different structure types (see text).

Figure 2. Structural series of Cr-AI borides and mode of formation Crn. AlB2 = CrAI + nCrB2, n = 1,2. The structures are projected along [001] the B net and Al atoms in z = 1 /2 Cr atoms are in z = 0.

Figure 3. Relation between the orthorhombic structure types of CrB and UBC (projected along [100]) as well as between the tetragonal structure types of a-MoB and ThBC (projected along [100]). Boron atoms are at the centers of trigonal metal prisms, carbon atoms at the centers of MjB-Oj,. The numbers given indicate the heights in projection.

Figure 3. Comparison of boron net-type diboride structures, ThMoB4, YCrB4, Y2ReBg, ErNiB4, Er4NiB,3, and AIB2 projected along [001].

Figure 4. Comparison between the structure types of CeCrjBj and W2lr3Bg, (x 1) as seen in a projection along [001].

Figure 1. The crystal structure of ThB4-type tetraborides. (a) The covalent boron skeleton, (b) Atomic arrangement in MB4 (projected along 5).

Fig. 29.—Newman Projection along the N-S Bond for Saccharin and Two Cyclohexyl-sulfamates. ...

Figure 5.6 If proton broad-band decoupling is applied in the evolution period, t, then the resulting 2D spectrum contains only chemical shift information in the F, domain, while both chemical shift and coupling information is present in the F domain. Projection onto the /-j-axis therefore gives the H-decoupled C spectrum, whereas projection along F. gives the fully coupled C spectrum.

FIGURE 3. The conformation of dimethyl sulfoxide projection along one of the S—C bonds. 

Fig. 4.6.7 Projections along the secondary diagonal from the 2D VEXSY experiments presented partly in Figure 4.6.5 and 4.6.6. (a) Distribution of velocity change obtained among others from Figure 4.6.5 (a, d) of the SMC module, (b) Distribution of velocity change obtained among others from Figure 4.6.6(a, d) of the SPAN module, (c) Three out of six distributions presented in (a) and (b) are displayed as the distribution of acceleration, which is obtained by dividing the velocity...

Fig. 5.5.14 Schematic diagram showing how the double-phase encoded DEPT sequence achieves both spatial and spectral resolution within the reactor, (a) A spin-echo ]H 2D image taken through the column overlayed with a grid showing the spatial location within the column of the two orthogonal phase encoded planes (z and x) used in the modified DEPT sequence. The resulting data set is a zx image with a projection along y. In-plane spatial resol-ution is 156 [Am (z) x 141 [xm (x) for a 3-mm slice thickness. The center of each volume from which the data have been acquired is identified by the intersection of the white lines. The arrow indicates the direction of flow.

Figure 1. Induced spin density map for MnCu(pba)(H20)j. 2H20 at 10K under 5 T in projection along the perpendicular to the basal plane. Solid and dashed lines are used respectively for negative and positive spin densities. Contour steps are 5 mpB/A2. The spin delocalisation is more pronounced toward the N atom than the O atoms.

Fig. 6. Comparative projections along the c axis of the diol molecules and the canals they enclose in 1, 2,3,8 and 9. The bond thickening signifies depth in individual molecules only, because the helical characteristic is absent from these projections of the lattice. The canal boundaries are marked as the intersecting projected van der Waals spheres of the hydrogen atoms which line the canals. All five diagrams are presented on the same scale. Significant hydrogen atoms are marked as filled circles, and the spines are circled...

---