CHAPTER 6: Question 2

Consider first the conformation of ferrocene in which the two aromatic rings are neither staggered nor eclipsed. The only symmetry elements present in this conformation are the identity element E and a C₅ axis which passes through the iron atom and the centre of both aromatic rings as shown below. The point group can be determined as C₅ either from the set of symmetry elements and Table 6.2, or by using the flow chart in Figure 6.11. The appropriate part of the flow chart is reproduced below. Note that all conformations of ferrocene will contain a C₅ axis since the effect of the corresponding symmetry operations C₅ⁿ are to rotate the atoms in each of two rings by 72^o, to a position where another identical atom will always be found.

 
In addition to the E and C₅ elements, the eclipsed conformation contains a horizontal plane of symmetry (s_h) through the iron atom and parallel to the two aromatic rings as shown below. Since a horizontal plane is present, the C₅ axis is also an S₅ axis. There are five vertical planes of symmetry (s_v), each perpendicular to the
plane of the aromatic rings and located along two of the C-H bonds (one C-H bond on each aromatic ring) and five C₂ axes each paralled to two of the C-H bonds and passing through the iron atom as shown below. The point group can be determined as D_5h either from the set of symmetry elements and Table 6.2, or by using the flow chart in Figure 6.11. The appropriate part of the flow chart is reproduced below.

The staggered conformation contains the E and C₅ elements, and also contains five vertical planes of symmetry (s_d) and five C₂ axes as shown below. Note, that whilst the planes are located along two of the C-H bonds (one C-H bond on each aromatic ring) as for the eclipsed conformation, the C₂ axis are now at 90^o to the  C-H bonds. There is a centre of inversion (located at the iron atom) in the staggered conformation, and the C₅ axis is also an S₁₀ axis since rotation of either aromatic ring by 36^o follwed by reflection in a plane perpendicular to the C₅ / S₁₀ axis moves the atoms to the positions of identical atoms in the other aromatic ring.  The point group can be determined as D_5d either from the set of symmetry elements and Table 6.2, or by using the flow chart in Figure 6.11. The appropriate part of the flow chart is reproduced below.

Consider first the conformation in which the two aromatic rings are neither staggered nor eclipsed. The only symmetry elements present in this conformation are the identity element E and a C₆ axis which passes through the chromium atom and the centre of both aromatic rings as shown below. The point group can be determined as C₆ either from the set of symmetry elements and Table 6.2, or by using the flow chart in Figure 6.11. Note that all conformations of this compound will contain a C₆ axis since the effect of the corresponding symmetry operations C₆ⁿ are to rotate the atoms in each of two rings by 60^o, to a position where another identical atom will always be found.

 In addition to the E and C₆ elements, the eclipsed conformation contains a horizontal plane of symmetry (s_h) through the chromium atom and parallel to the two aromatic rings as shown below. Since a horizontal plane is present, the C₆ axis is also an S₆ axis. There are three vertical planes of symmetry (s_v), each perpendicular to the plane of the aromatic rings and located along the C-H bonds; three dihedral planes of symmetry (s_d), each bisecting the H-C-C-H torsional angles; and six C₂ axis, three paralled to the C-H bonds and three bisecting the H-C-C-H torsional angles and all passing through the chromium atom as shown below. Finally, there is a centre of inversion located at the chromium atom. The point group can be determined as D_6h either from the set of symmetry elements and Table 6.2, or by using the flow chart in Figure 6.11. 

The staggered conformation contains the E and C₆ elements, and also contains six vertical planes of symmetry (s_d) and six C₂ axes as shown below. The C₆ axis is also an S₁₂ axis since rotation of either aromatic ring by 30^o follwed by reflection in a plane perpendicular to the C₆ / S₁₂ axis moves the atoms to the positions
of identical atoms in the other aromatic ring. The point group can be determined as D_6d either from the set of symmetry elements and Table 6.2, or by using the flow chart in Figure 6.11. 

Note that whilst for ferrocene, it is the staggered conformation which contains a centre of inversion, for bis(benzene)chromium it is the eclipsed conformation which contains this symmetry element.

 
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