Point groups assignment method

FIGURE 4-7 Diagram of the Point Group Assignment Method. 

We have only one example in our list that falls into the S2 groups, as seen in Figure 4.12. A flowchart that summarizes this point group assignment method is given in Figure 4.7, and more examples are given in Table 4.4. 

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 ... 

A method of assigning molecules to particular point groups was outlined. 

We illustrate the application of Figure 3.10 with reference to four worked examples, with an additional example in Section 3.8. Before assigning a point group to a molecule, its structure must be determined by, for example, microwave spectroscopy, or X-ray, electron or neutron diffraction methods. 

From the above discussion when dpjdq, or more rigorously, VqPy is zero or has a slope discontinuity, there are likely to be slope discontinuities in the combined density of states, as revealed by infrared and Raman spectra of two-phonon processes. Points in the Brillouin zone where each of the components of VqP = 0 are known as critical points. The intensity of infrared absorption or Raman scattering depends upon quantum mechanical matrix elements which are, in general, not simple to evaluate. However, by using symmetry considerations and group theoretical methods, the various modes can be assigned as infrared or Raman active. 

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. 

The distribution of the iN — 6 vibrational symmetry coordinates of a nonlinear polyatomic molecule among the irreducible representations of its symmetry point group can be determined by standard methods. [7] Ordinarily, not all of the symmetry species will be represented and several of them will include more than one coordinate. If the molecule belongs to a commutative symmetry point group, all of them will be assigned to one-dimensional symmetry species. If its group is non-commutative, and therefore has representations that are two-or three-dimensional, some of its vibrations may be degenerate these are best discussed separately. 

The SALC for an irreducible representation can be determined using the projection operator method (Section 6.6). This builds the linear combination by considering the effect of each operation in the group on a generating vector with a coefficient assigned from the character of the irreducible representation. This process requires all symmetry operations for the point group to be considered, i.e. operations within the same class must be considered separately. 

Table 7.12 The projection operator method applied to the C=C orbital set for ethene. The rotational subgroup D2 is used to simplify the process and u and g labels required for the full D2h point group are assigned in the text. The generating functions are the 2s and 2p orbitals of atom 1.

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