Benzene symmetry elements

Question. List the symmetry elements of each of the following molecules (a) 1,2,3-trifluorobenzene, (b) 1,2,4-trifluorobenzene, (c) 1,3,5-trifluorobenzene, (d) 1,2,4,5-tetrafluoro-benzene, (e) hexafluorobenzene, (f) l,4-dibromo-2,5-difluorobenzene. 

The coefficient of the symmetry element, in the top line, tells how many different equivalent operations of this type occur. However, not all symmetry elements of the same type are always equivalent. Thus, in the symmetry group of benzene, the thirteen C2 operations fall into three distinct classes the one dyad perpendicular to the molecular plane, the six that pass through opposite atoms in the ring, and the six that pass in between the atoms, through the centers of the bonds. Each of these operations is equivalent only to the others within the same class. 

The benzene molecule (Pauling and Brockway, 1934) has a sixfold axis of rotation, together with all the additional symmetry elements possessed by a crystal belonging to the holohedral hexagonal class 6/mmm. 

As other illustrations of equivalence and nonequivalence of symmetry elements, we may note that all three of the symmetry planes in BF3 that are perpendicular to the molecular plane are equivalent, as are the three in NH3, whereas the two planes in H20 are not equivalent. The six twofold axes lying in the plane of the benzene molecule can be divided into two sets of equivalent axes, one set containing those that transect opposite carbon atoms and the other set containing those that bisect opposite edges of the hexagon. 

Labeling of the 2p orbitals taking part in the jr bonding of benzene. Also shown are the locations of the symmetry elements Cj,, ov and od. 

Symmetry elements of the benzene molecule. The x axis is chosen to pass through a pair of carbon atoms, and the z axis points toward the reader. 

In the above reaction, the product benzene is of D6h symmetry, but only C2v symmetry elements are common for both Dewar benzene and benzene. We can perform therefore the symmetry analysis of the VB structures within the C2v point group framework. There are 6 essential valence electrons involved in the reaction, numbered from 1 to 6. These six valence electrons form three localized bonds (two ji bonds and one o bonds) in Dewar benzene, and a n delocalized bond in benzene, which can be described by five independent BTs within the OEO formalism (see Eq.(65)). Their corresponding BTs are... 

Example 4.3 (a) What symmetry elements can you discover for the planar molecule benzene, structure 4-5 (b) How many H and l3C NMR signals would you predict for benzene ... 

A symmetry operation is the actual event of converting one item into another apparently identical item. This symmetry operation can take place about a point, a line, or a plane of symmetry. Thus, an object is symmetrical when a symmetry operation applied to it gives an object indistinguishable from the original. The point, line or plane about which the symmetry operation is performed is defined as a symmetry element. For example, an axis of symmetry is a symmetry element that describes a line about which all parts of an object are symmetrically disposed. We are all familiar with the vertical reflection plane (or near reflection plane) in the human face. We are also familiar with the sixfold axis of symmetry that lies perpendicular to the plane of a benzene molecule and passes through the center of it (Figure 4.2). 

These ideas on symmetry are explained by A. Michael Glazer in the following way Many scientists tend to mix up the concepts of operation and element, although strictly speaking they are different ideas. In our example [benzene], there is one sixfold symmetry element (the axis of rotation), but six sixfold operations (six successive rotations of 60° to bring the object back to its initial state). ... 

The experimental results on valence isomerization of benzene can be rationalized by means of correlation diagrams that were first discussed for hexa-fluorobenzene by Haller (l%7). The orbital correlation diagram for the conversion of benzene to dewarbenzene (Figure 7.44a) has been constructed on the basis of a classification of the benzene Jt MOs according to C , symmetry. The full symmetry of benzene is D ,. The symmetry elements common to both point groups Cj, and are E, Cj, and o,(x,z) = o which is the plane through... 

EXAMPLE 9.7 List the symmetry elements of the benzene molecule. 

Figure 9.3 The benzene molecule with symmetry elements shown.

Two different values of REC for particular rings of benzene and phenanthrene result from different measurements of their molecular geometry. The different REC values for symmetrically equivalent rings in other benzenoid hydrocarbons result from the method of X-ray structure determination. If the symmetrical molecule does not lie at the symmetry element in the crystal lattice, each of the rings is measured independently and its geometry (and in turn its REC value) is biased by the another error of measurement. The differences in REC values for symmetrically equivalent... 

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