Point group designation

Consider the molecule CIFjOj (with chlorine the central atom). How many isomers are possible Which is the most stable Assign point group designations to each of the isomers. 6.id The Structure for AliBr (Fig. 6. Ih) is assumed by both Al2Br6and ALCUin the gas phase. In the solid, however, the structures can best be described as closest packed arrays of halogen atoms (or ions) with aluminum atoms (or ions) in tetrahedral or octahedral holes. In solid aluminum bromide the aluminum atoms arc found in pairs in adjacent tetrahedral holes. In solid aluminum chloride, atoms are found in one-lhird of the octahedral holes... 

Consider the molecule CIFjOn (with chlorine the central atom). How many isomers are possible Which is the most stable Assign point group designations to each of the isomers. 

In order to give the point group designation of this crystal, it is necessary to identify all of the symmetry elements in the crystal and to understand the relationship of these elements to the crystallographic axes. 

In most of the other crystal systems, the axis with the highest order rotational symmetry is designated the z-axis, which is more commonly called the c-axis. The order of this axis is given first in the point group designation. In the monoclinic systan, the -axis is taken as the two-fold axis or as perpendicular to the mirror plane. 

Examine the crystal in Figure 28 and give the point group designation. 

If we compare the point group designations for the NaCl structure and the sphalerite structure (4/m32/m vs 43m), we immediately notice the greater symmetry of the NaCl structure. For example, the perpendicular mirror planes present in the NaCl structure are not present in the sphalerite structure. 

Can you determine the point group designation from these three views ... 

Based upon your identification of symmetry elements, give the crystal system and the point group designation. 

Point group designations facilitate discussions of chirality. We usually think first of molecules that show enantiomerism as being asymmetric (without symmetry) due to the presence of a carbon atom with four different substituents, as illustrated by the 1-bromo-l-chloro-l-fluoroethane isomer 13. More generally, asymmetric structures have three or more nonequivalent substituents bonded to a central atom in such a way that the central atom and the substituents do not all lie in the same plane. Such structures are said to exhibit enantiomerism due to asymmetry about a point and belong to point group Cj. ... 

A very powerful mathematical tool, namely group theory, has been developed which allows the exploitation of symmetry in an exact manner. Most problems in molecular chemistry use symmetry point group theory. The nuclei of a molecule are represented by a set of points, which are interchanged or permuted by the symmetry operations. Each molecule belongs to one of the point groups, designated by symbols such as Tj, C y, Oh, etc. Each point group is defined by the number and kind of symmetry elements that it possesses. 

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