Symmetry point group determination

The MO (molecular orbitals) of a polyatomic system are one-electron wave-function k which can be used as a (more or less successful) result for constructing the many-electron k as an anti-symmetrized Slater determinant. However, at the same time the k (usually) forms a preponderant configuration, and it is an important fact67 that the relevant symmetry for the MO may not always be the point-group determined by the equilibrium nuclear positions but may be a higher symmetry. For many years, it was felt that the mathematical result (that a closed-shell Slater determinant contains k which can be arranged in fairly arbitrary new linear combinations by a unitary transformation without modifying k) removed the individual subsistence... 

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. 

Determine the symmetry point groups of the following compounds. In each case show the symmetry elements in the structural formula. Use the flow chart in the appendix to assist you. 

Deduce whether enniatin B (a compound with antiretroviral activity) is chiral and determine its symmetry point group. 

Determine the symmetry elements present in the following boranes and hence assign their symmetry point groups. The numbered circles in the polyhedra represent the boron atoms with the corresponding number of attached hydrogen atoms. 

Show that [CoCl2(en)2] (en = ethane-1,2-diamine) can be racemic. Determine the symmetry point groups of each isomer and assign suitable stereodescriptors. 

Determine unequivocally the configuration of l,6-dibromo-3,6-dichloro-adamantane. How many stereoisomers of this compound exist and to which symmetry point groups do they belong ... 

Simplifications can be brought about whenever the surface structure has symmetries. Point-group symmetries help moderately to reduce the matrix dimensions. On the other hand, two-dimensional periodicity can help drastically by reducing the number N to the number of atoms within a single two-dimensional unit cell with a depth perpendicular to the surface of a few times the electron mean free path. For surface crystallography this is, however, not yet sufficient, because surface structural determination requires repeating such calculations for hundreds of different geometrical models of the surface structure. 

The combination of point group determination and identification of translation symmetry allows the unique identification of space groups. Both CBED and LACBED techniques can be used for this purpose. 

Many molecular orbital programs determine the symmetry point group of a molecule before using this information to simplify the calculations, but some require you to state the point group in the information that you give the computer. 

Use your flow chart or Figure 6.17 to determine the symmetry point groups of the following molecules (a) S02 (V-shaped) (b) carbon monoxide, CO ... 

Figure 2.10 shows a classical diagram that allows determination of the symmetry point group and distinguishes between achiral and chiral molecules. 

A set of symmetry elements (or of symmetry operations) enables us to define a symmetry point group which is represented by a symbol. There is a simple method to determine the point group, and it is not necessary to establish a complete list of all the symmetry operations in the molecule under consideration. 

To assign a molecule to a specific point group outside of these high and low symmetry point groups, you need to either follow this list of steps or go through the point group flow chart of Figure 7-8. Both methods determine the same result. 

Then, one is able to determine the symmetry point group of the molecule adsorbed on the surface. For a chemisorbed molecule, there is likely to be lower symmetry compared to the molecule in the bulk phase. In particular, for a strongly chemisorbed molecule, its geometry may be changed significantly by the interaction with the surface. 

After obtaining the symmetry point group of the metal-adsorbate system, one can determine which symmetry representations of the vibrations of the molecule will be Raman active using group character tables for the given point group. Raman-active modes are those that possess nonzero components of the Raman polarizability tensor. 

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