Ih point group

3 Although an atom with partially filled orbitals may not be spherically symmetrical, the electronic wave function is classified according to the Kh point group. 

Molecules belonging to the Ih point group are very highly symmetrical, having 15 C2 axes, 10 C3 axes, 6 C5 axes, 15c planes, 10. S6 axes, 6 510 axes and a centre of inversion i. In addition to these symmetry elements are other elements which can be generated from them. 

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Buckminsterfullerence (C6o) has attracted considerable attention in recent years. As expected from its extremely high symmetry (Ih point group), this molecule exhibits very small numbers of vibrations in IR and Raman spectra (see Section 4.2.7). 

The naked C60 cluster (a fullerene) was briefly mentioned at the end of Chapter 2 as an example of a three-connect bare cluster with a delocalized system containing the external cluster electrons. Here we will discuss some properties of fullerene-derived solids (there is C60, but also C70, Cg4, etc.). At room temperature, solid C60 adopts an fee structure with weak van der Waals interactions between the C60 molecules. Look more closely at the structure of C60 itself. It has the highest symmetry possible for a molecule, Ih point group, and consists of a polyhedron with 20 hexagonal... 

Selecting the Character Table button on the main command bar of the GT Calculator files activates the main display window as shown, again, for the case of the Ih point group, in Figure 1.4. 

For the standard test case of the Ih point group and the GT Calculator file Ih.xls, Figure 1.23a displays the input needed to carry out the powers calculations for 1 x Hg. The symmetric square is calculated according to the character relation (see equation 4.9),... 

Table 3.20 Central polynomials of Ag irreducible symmetry for tbe Ih point group.

The shapes of the three complexes in Figure 7 have important consequences in their use as sensitizers in multi-component assemblies. The tris-bpy and tris-phen complexes have three-fold symmetry (Ih point group) while the bis-terpy complex... 

At higher frequencies (above 200 cm ) the vibrational spectra for fullerenes and their cry.stalline solids are dominated by the intramolecular modes. Because of the high symmetry of the Cgo molecule (icosahedral point group Ih), there are only 46 distinct molecular mode frequencies corresponding to the 180 6 = 174 degrees of freedom for the isolated Cgo molecule, and of these only 4 are infrared-active (all with Ti symmetry) and 10 are Raman-active (2 with Ag symmetry and 8 with Hg symmetry). The remaining 32 eigcnfrequencies correspond to silent modes, i.e., they are not optically active in first order. 

Td, possesses 32 symmetry, and requires a minimum of 12 asymmetric units the cube and octahedron, which belong to the point group Oh, possess 432 symmetry, and require a minimum of 24 asymmetric units and the dodecahedron and icosahedron, which belong to the point group Ih, possess 532 symmetry, and require a minimum of 60 asymmetric units. The number of asymmetric units required to generate each shell doubles if mirror planes are present in these structures. 

The first two of the shapes are extremely common in chemistry, while the third shape is important in boron chemistry and many other cluster molecules (a cluster is defined as a molecule in which three or more identical atoms are bonded to each other) and ions. The three special shapes are associated with point groups and their character tables and are labelled, Td, Oh and Ih, respectively. The point group to which a molecule belongs may be decided by the answers to four main questions ... 

By observing the number and relative intensity of 13C resonances it is possible to identify to which point group an adduct belongs. For C60, with Ih symmetry, all 60 carbon atoms are equivalent, giving rise to a single sharp line at 143.3 ppm in C6D6. Complex formation causes a reduction in symmetry, and the fullerene carbon atoms become in-... 

As a second example, let us consider a molecule with the formula AB6 having the symmetry of a trigonal bipyramid Ih. The vector system is shown in Fig. 11-3.2. The set of five hybrid orbitals (or vectors) on A form a basis for a reducible representation of the point group, with the following character ... 

B3.2 There are three relatively common types of dodecahedron. In addition to the pentagonal dodecahedron (point group Ih) there are the trigonal dodecahedron (a) and the rhomboidal dodecahedron (b). To what point group does each of these belong ... 

Croups with Ih, Oh, Tt, Clt C and C, symmetries were assigned in the text by inspection Take the molecules given as illustrations of these symmetries (Figs. 3.10 and 3.11) and run them through the flowchart (Fig. 3.16) to assign their proper point groups. 

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... 

Figure 3. Polymorphism of deltahedral surface lattices. The T = 4 icosadeltahedron at the left (A80, point group Ih) is transformed to a A80 with Dbh symmetry (middle). At the right, the half-icosahedral cap defined by the h,k = 10,0 circumferential vector has been extended by adding rings of 10 V6 connectors. The bottom of this tube could be capped symmetrically (as for the A80 models) or asymmetrically using the h,k = 10,0 cap shown in figure 4 or the two other h,k = 10,0 caps listed in table 1.

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