Cn point groups

A Cn point group contains a Cn axis of symmetry. By implication it does not contain a, i or Sn elements. However, it must contain C, C, ..., C" 1. 

This is the point group to which all regular octahedral molecules, such as SFe (Figure 4.12b) and [Fe(CN)6], belong. 

Molecules that belong to Cn or Dn point groups are also chiral. For instance, tra i-2,5-dimethylpyrrolidine (Fig. 1-9), containing a twofold rotation axis, belongs to the point group C2 and is chiral.5 7... 

The fourth question applies only to Cn groups is there a ch present If there is, the molecule belongs to the point group Cnh. There are very few examples of such molecules, and Figure 2.14 shows the planar form of B(OH)3 which has a C3 major axis perpendicular to the molecular plane, but there are no other planes of symmetry. It belongs, therefore, to the point group Cw... 

A There is a Cm axis passing through the ball along its largest dimension and an infinite number of vertical planes containing that axis. There are also an infinite number of C2 axes that are perpendicular to the major axis and which are contained by the horizontal plane. This passes the nC2 JL Cn test with n = so the ball belongs to the point group. 

Type 2. Only one axis of rotation point groups Cn,Sn, Cnv, C h. 

Enantiomers The same in all scalar properties and distinguishable only under chiral conditions. Only molecules of which the point groups are Cn (n> 1), Dn (n> 1), T, O, or / are chiral and can exist in enantiomeric forms. 

Take, for example, the bent triatomic molecule B—A—B (say, HsO). Following Table 3-7.1, it is not linear, it does not have two or more Cn with n 3, it does have a Ct axis hut there are not n Ct axes perpendicular to this axis, it does possess two [Pg.48]

As noted earlier, point groups with no threefold or higher proper or improper axis have only one-dimensional representations hence a necessary condition for a molecule to have degenerate vibrational modes is that it possess a Cn or an S axis with n> 3. Asymmetric tops have no degenerate vibrational modes. 

The point group of dodecahedral Mo(CN)t is D2d. List the symmetry operators of this point group and determine which atomic orbitals of Mo4+ form hybrid a bonds in Mo(CN)4. ... 

Distortions along non-totally symmetric modes may occur in certain excited states. These distortions are non-symmetry preserving the point group of the molecule changes in the excited state. The specific examples in this paper are the linear to bent geometry changes of metal nitrosyls (e.g., from Ci(V to C3 in [Fe(CN)5N0]2+.)... 

This group has symmetry element E, a principal Cn axis, n secondary C2 axes perpendicular to Cn, and a ah also perpendicular to C . The necessary consequences of such combination of elements are a S axis coincident with the Cn axis and a set of n ctv s containing the C2 axes. Also, when n is even, symmetry center i is necessarily present. The BrF molecule has point group symmetry D4h, as shown in Fig. 6.1.8. Examples of other molecules belonging to point groups >2h, D3h, Z>5h and D6h are given in Fig. 6.2.6. 

A Cnv point group contains a Cn axis of symmetry and n a planes of symmetry, all of which contain the Cn axis. It also contains other elements which may be generated from these. 

In the C, Cs, Cn and Cnv point groups the totally symmetric symmetry species is A, A, A and A i (or X1), respectively. For example, CHFCIBr (Figure 4.7) belongs to the Cl point group therefore ju 0 and, since all three translations are totally symmetric, the dipole... 

If Cn axes exist, select the one of highest order. If the molecule also has an S2n axis, with or without an inversion center, the point group is S . 

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