Identifying point groups

To help students to determine the symmetry point group of a molecule, various flow charts have been devised. One such flow chart is shown in Table 6.2.3. However, experience indicates that, once we are familiar with the various operations and with visualizing objects from different orientations, we will dispense with this kind of device. 

Compound Perspective diagram Projection diagram Point group 

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Particular care should be taken to check for two-fold axes perpendicular to the principal axis. Overlooking these is probably the commonest error made in identifying point groups. Note also that the group that results from the product of a centre of inversion with Dn is Dnh when n is even but Dnd when n is odd. 

FIGURE 6.7 Flow chart for identifying point groups. Only the most common cubic point groups are listed. 

In a second example, the three CH bonds, three CH antibonds, CO bond and antibond, and three 0-atom non-bonding orbitals of the methoxy radical H3C-O also cluster into ai and e orbitals as shown below. In these cases, point group symmetry allows one to identify degeneracies that may not have been apparent from the structure of the orbital interactions alone. 

A convenient scheme for identifying the point group symmetry of any given species is set out in the flow chart. Starting at the top of the chart... 

IR absorption spectra of oxypentafluoroniobates are discussed in several publications [115, 157, 167, 185, 186], but only Surandra et al. [187] performed a complete assignment of the spectra. Force constants were defined in the modified Urey-Bradley field using Wilson s FG matrix method. Based on data by Gorbunova et al. [188], the point group of the NbOF52 ion was defined as C4V. Fifteen normal modes are identified for this group, as follows ... 

The free Sy molecule is of Cs symmetry but in its various solid allotropes it occupies sites of Ci symmetry [154]. In any case, in these point groups all fundamental modes are infrared and Raman active and no degeneracies occur. Four allotropes of Sy (a, p, y, S) have been identified by Raman spec-... 

The structure factor itself is expressed as the sum of energy diffracted, over one unit-cell, of the individual scattering factors, fi, for atoms located at X, y and z. Having done this, we can then identify the exact locations of the atoms (ions) within the unit-cell, its point-group sjmimetiy, and crystal system. This then completes our picture of the structure of the material. 

If you have arrived at this point, you have found no improper axis but more than one proper axis of order n Or, you have identified at least one other axis of order n in addition to that collinear with Sin- Now, look for n binary axes perpendicular to C . If you do not find any, the point group is one of the t -type. Otherwise, there are n binary axes and the group is one of type 0. 

Make sketches of the following showing approximately correct geometry and all valence shell electrons. Identify all symmetry elements present and determine the point group for the species. 

In a famous paper by Shechtman et al. (1984) electron diffraction patterns were shown of rapidly quenched and solidified aluminium-manganese alloys. Sharp diffraction peaks, suggesting long-range translational order, were observed with the presence however of five-fold symmetry (that is of a non-crystallographic symmetry see 3.6.1.1). By different orientation of the specimen five-fold axes (in 6 directions), three-fold axes (in 10 directions) and two-fold axes (in 15 directions) were identified with the subsequent observation of the existence also of an inver-sion centre the assignment of this phase to the icosahedral point group, m36, was defined. 

In an opposite way, if we are able to identify the diffraction group from experimental diffraction patterns, then, we can obtain the point group. This is the basis of the point group determination. To reach this aim, two experimental methods are available a method proposed by Buxton et al. [3] and a multi-beam method proposed by Tanaka et. al. [4]. 

The connection between the diffraction group and the point group is obtained from Table II. High symmetry diffraction groups are very useful. One or a few Zone-Axis Patterns are required to identify the point group. 

Does the molecule belong to one of the special point groups, T d, Oh or /A If it does, the point group has been identified. 

The procedure described will identify the point groups of the majority... 

The groundwork for the application of MO theory to the water molecule has been carried out to a large extent in Section 2.2.1. The procedure is to identify the point group to which the molecule belongs. To demonstrate the power of MO theory, both of the extreme geometries of the molecule, the bent (bond angle, 90°) and linear (bond angle, 180°) forms, are treated. 

Identify the point group to which the molecule belongs. 

Classify the valency orbitals of the ligand atoms with respect to the point group of the molecule and identify their group orbitals. 

By far the most powerful tool for analysis of fullerene compounds is solution 13C NMR spectroscopy, as the number, positions, and relative intensities of resonances often provide unambiguous evidence for a particular structure. The molecular point group of about 300 fullerene compounds has been identified using 13C NMR spectroscopy. 

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-... 

A number of relationships exist between the elements of symmetry of a point group which are a consequence of the closure property of groups. They may be used to identify difficult-to-locate symmetry elements. 

The snoutene skeleton is shown below. Locate all of the elements of symmetry (state the point group if you know it), and identify the stereochemical relationship between the specified pairs of groups or faces. 

Determine the distinct symmetry operations which take it into itself construct the group multiplication table for these operations, and identify the point group to which this figure belongs. 

Read the section on point groups in Chapter 3 again, and identify the symmelry elemeni.s and operaitons in the molecules and ions shown in the figures listed below. Determine the appropriate point group for each molecule and ton. 

Look at Uie drawings accompanying Problem 3.6. Is it possible to superimpose the cube on the dodecahedron Castieman and coworfcers have recently detected a cation with mje = 28, identified as TigC. It b bebeved that the titanium atoms form a cube with the addition of twelve carbon atoms to complete a pentagonal dodecahedron. Draw the proposed structure. What e its point group symmetry ... 

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