Diagonal planes

If you have arrived at point group 0, your molecule must have n (diagonal) planes of symmetry in addition to the horizontal one. If n is odd, there is also a center of symmetry. The simplest case is that with n = 2. Look at the seams on a baseball or a tennis ball and verify that its symmetry is that of 02a-... 

Projection of the structure Projection of the structure on the base plane (001) on the diagonal plane (110)... 

Fig. 23. The form of the reduced three-dimensional DICO experiment.52 The experiment produces a two-dimensional experiment that is in effect, the projection of the full three-dimensional exchange spectrum onto the diagonal plane shown. This spectrum is then sufficient to determine whether two different motional processes revealed by the experiment are correlated.

Fig. 5. Methyl 3,4-difluorocubane-l-carboxylate difference density maps in various diagonal planes of the cubane cage. The maxima of the bond densities lie outside, implying that the cage bonds are bent (reproduced with permission from Imgartinger et al. [45]).

Pig. Symmetry elements and point groups of three type of molecules, <7, av ad denote verticalhorizontal and diagonal plane of symmetry. 

The point groups V d have, in addition to the axes defining Vn, n diagonal planes Od which bisect the angles between successive twofold axes. The ad and C2 axes imply that there is also an S2n and, if n is odd, a center of symmetry Molecules of T>2d symmetry have the shape of two equivalent halves twisted b 90°, for example, allene and spiran shown here ... 

It is natural to enquire why different AX compounds should possess different structures, and, in particular, why CsCl, CsBr and Csl should have a structure different from that of the other alkali halides. We can answer this question if we consider fig. 3.07a, which represents a section through the caesium chloride unit cell on a vertical diagonal plane. The ions in this diagram are shown in their correct relative sizes for Cs+ and Cl-, and anions and cations are seen to be in contact at the points P. Now let us suppose that the cations are replaced by others of... 

Fig. 3.07. Section through a unit cell of the caesium chloride structure on a vertical diagonal plane. The solid circles represent the cations. In (a) the ions are shown in their correct relative sizes for CsCl (b) corresponds to the critical radius ratio for anion-anion contact.

Fig. 14.20. (a) Plan of four unit cells of the tetragonal structure of w-propylammonium chloride, CH3(CH2)2NH3C1, projected on a plane perpendicular to the z axis, (b) Plan of the same structure projected on a vertical diagonal plane and referred to the cell indicated by inclined broken lines in (a), (c) Plan of the unit cell of the monoclinic structure of w-propylammonium chloride projected on a plane perpendicular to the y axis. The cell can be regarded as derived from that shown in (6) by a shear in the direction of the arrows. 

Fig. 12.28. Reaction cube locating the butadiene conical intersection in relation to rotation at each of the bonds. The shaded area in the center represents the location of the conical intersection with all bond rotations near 90°. The open circles represent initial excited states. The energy surface in Figure 12.27 represents the diagonal plane bisecting the cube. Reproduced from J. Am. Chem. Soc., 115, 3710 (1993), by permission of the American Chemical Society.

CTi, = horizontal plane of symmetry cr = diagonal plane of symmetry. 

Fig. 3.6. Geometrical interpretation of the effects of the 2 factorial design. The main effects are contrasts between opposite faces (a), and the interaction effects are contrasts between diagonal planes (b).

Figure 10.12 (a) Slip in a rod, characterised by diagonal planes across which atoms in the crystal have sheared because of an applied load (b) shp band, in which slip planes are aggregated into narrow regions (c) mechanical twin planes, across which the atoms in the crystal are reflected because of an apphed load (d) twin band, in which twin planes are aggregated. Note slip and twimiing are both caused by stress and are difficult to distinguish in macroscopic samples... 

The shear strain is thus equivalent to a tensile and a compressive strain of 6/2 each at 45° to the original axes. Figure (b) shows that the shear stress is equivalent to a tensile and a compressive force parallel to these directions equal to 2 x ct/-J2 — -v/2[Pg.405]

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