Point groups molecular assignment

Individual molecular orbitals, which in symmetric systems may be expressed as symmetry-adapted combinations of atomic orbital basis functions, may be assigned to individual irreps. The many-electron wave function is an antisymmetrized product of these orbitals, and thus the assignment of the wave function to an irrep requires us to have defined mathematics for taking the product between two irreps, e.g., a 0 a" in the Q point group. These product relationships may be determined from so-called character tables found in standard textbooks on group theory. Tables B.l through B.5 list the product rules for the simple point groups G, C, C2, C2/, and C2 , respectively. 

Figure 2.32. Examples of symmetry group elements and molecular point group assignments.

The molecular structure is the nonplanar configuration from the electron diffraction study of Akishin et al. (8). A planar model (also point group < 2 ) was assumed by Hisatsune et al. (9) in their approximate normal coordinate analysis of the infrared and Raman spectra. The frequency assignments of these authors are listed above in the order for the planar model, although the vibrations for the nonplanar form will separate differently into the species 5A, 3A2, 3B and 4B2. Hisatsune et al. (9) estimated the N-O -N deformation frequency (8 cm ) from combination bands in the solid and gas phase spectra. The JANAF thermodynamic functions were obtained using these frequencies and assuming the two N0 groups to be hindered internal rotators. 

Typical infrared or Raman assignments of partial ionicity also depend on preserving the molecular point group symmetry The number and types of normal frequencies are then fixed and their q-dependence can be monitored, again assuming crystal perturbations to be small. However, the point group symmetry of phenazines changes with ionicity. While no systematic spectroscopic data is available, we would not expect studies to be nearly as successful as for TCNQ, TTF and other D21, donors or acceptors. 

Just as molecules have certain symmetry, molecular orbitals likewise have symmetry. Orbital labels such as rotational symmetry of the orbital, whereas the labels a, e, eg, t and so on met in complexes arise from considering orbital behaviour in the context of all symmetry operations of the point group of the molecule. A character table, which defines the symmetry types possible in a particular point group, provides a way of assigning these labels, but this will not be pursued here. 

Fig. 3.10 Scheme for assigning point groups of molecules and molecular ions. Apart from the cases of w = 1 or oo, most commonly has values of 2, 3, 4, 5 or 6. 

So far in this chapter, we have described the possible symmetry elements that a molecule might possess and, on the basis of these symmetry properties, we have illustrated how a molecular species can be assigned to a particular point group. Now we address some of the reasons why the recognition of symmetry elements in a molecule is important to the inorganic chemist. 

Using VSEPR theory to help you, draw the structures of CF4, XeF4 and SF4. Assign a point group to each molecule. Show that the numher of degrees of vihrational freedom is independent of the molecular symmetry. 

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