D6h point group

However, for the D6h point group the metal 4 s and 4 p levels once more transform as alg and a2u + elu respectively, and the calculations of Shustorovich and Dyatkina (27)... 

Note 4 The structure of a smectic B mesophase is characterised by a D6h point group symmetry, in the Schoenflies notation, by virtue of the bond orientational order. 

Benzene is another molecule where molecular symmetry can be useful for construction of the ground and covalent excited states (5,6,16,17,24). The molecule possesses five covalent VB Rumer structures, two are the Kekule structures, and the three Dewar types, shown in Fig. 7.4a. It is seen that the Kekule structures are mutually transformable by the D6h point group operations i, C2, and av. Consequently, we can make two linear combinations the positive one is the totally symmetric Aig state, which gives rise to the ground state, while the negative one is the B2U state, which corresponds to the excited state. This is shown in the VB mixing diagram in Fig. 7.4b. 

The next example is the hexagonal planar molecule of type A6 or A6B6 (benzene) shown in Fig. 1-24. The molecule is not of a special symmetry. It has a center of symmetry and a C6 axis of symmetry. No S2 axis exists. Since six C2 axes perpendicular to the C6 axis are found, this molecule also falls into the D classification. Since it has a horizontal plane of symmetry perpendicular to the C6 axis, the molecule belongs to the D6h point group. 

In polyatomic molecules, the geometric symmetry of the molecule also plays a very important role. For example, the benzene molecule, which is the example we discuss in this book (Figure 6.1) has the point group symmetry D6h. 

Consider planar molecules, such as 1,2-dichlorobenzene (C2v), glyoxal (Fig. 1, structure 6 point group C2A), orthoboric acid [B(OH)3 structure 7 point group C3h), naphthalene (D2h), or benzene (D6h). Such a molecule will have all its atoms in one principal axes plane, say the yz plane, so that x, = 0 for all i. 

In the case of benzene (point group D6h) excimer states arise from configuration interaction of the 8-fold degenerate CR states and exciton states of both 1La and 1Lb origin. Owing to the very large separation of 1La and 1Lb states in this molecule, the lowest exciton state is of 1Lb character and contributes to the lowest excimer state after configuration interaction.68... 

A chemist isolated an unknown transition metal complex with a formula of ABe. Five potential structures were considered, belonging to point groups C, Dih, D6h, Dlh, and Djj. Spectroscopic studies led to the conclusion that the p orbitals originating on A in the complex were completely nondegenerate. Sketch a structural formula that is consistent with each of the five point group assignments and decide which structures can be eliminated on the basis of the experimental results. 

For point group invariant systems, the intrinsic group is G = Point group. The construction of the basis for these systems is a standard group theoretical problem. For the groups D4h, D6h and 0 it was done by Hamermesh many years ago [13]. I report here only the case of G D4i,. For positive parity one has Table 3. For negative parity one has Table 4. 

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. 

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... 

The next step is to determine how these group orbitals transform in the D(,h point group. The D6h character table is given in Table 6-7. Since most of the AOs in the suggested group orbitals are transformed into another AO by most of the symmetry operations, the representations will be quite simple, though still reducible ... 

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