Naphthalene point group

The chemist perceives no fewer than seven nontrivial symmetry operations in naphthalene (point group D2h or mmm), the corresponding symmetry elements are three mutually perpendicular mirror planes, three mutually perpendicular twofold rotation axes, and the center of inversion. In addition, the trivial symmetry operation, onefold rotation, is always present. Each of these, however, yields one of the above four permutations. The notion of point group of a molecule will be introduced later. 

The point group is the same as 2 - Ethylene (Figure 4.1a) and naphthalene (Figure 4.3c) belong to the >2 point group in which, because of the equivalence of the three mutually perpendicular C2 axes, no subscripts are used for the planes of symmetry. 

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. 

Consider the naphthalene molecule (point group D2/ ). Each carbon atom has a p. orbital to contribute to the n MOs of the molecule. Take these 10 pz orbitals as a basis set and answer the following questions ... 

The naphthalene molecule belongs to the point group Dlh. The set of 10 pn orbitals may be used as the basis for a representation, Tn, of this group. 

The naphthalene molecule, as mentioned previously, belongs to the point group D. A set of coordinate axes and a numbering scheme for the atoms have already been shown in Figure 7.2. The pn orbitals j, form three subsets the members of each are symmetry equivalent to each other but not to those in other sets. These sets and the irreducible representations for which they form bases are as follows ... 

The three classical Kekule structures (already alluded to in section III.E) of naphthalene are shown in Scheme 36a. Two of them are designated as Ki and K2 and represent the annulenic resonance along the perimeter of the naphthalene, while the third one, Kc, has a double bond in the center and transforms as the totally symmetric irreducible representation, Ag of the Dzh group. The Ki and K2 structures are mutually interchangeable by the i, C2, and ov symmetry operations of the point group, much as in the case of benzene. An in-phase combination transforms, therefore, as Ag, whereas an out-of-phase one transforms as B2u. These symmetry adapted wave func-... 

Naphthalene and anthracene are archetypes of the even and odd members of the polyacene series. In each subseries, one can start by classifying the classical Kekule structures by using the symmetry operations i, C2, and point group. Then one can form symmetry-adapted linear combinations of the mutually transformable Kekule structures and deduce their bonding characteristics. Finally, these 1 Ag and 1 B2u symmetry-adapted combinations are allowed to mix and form the states of interest, the ground and first covalent excited states (16). 

As an example of the use of two-photon spectroscopy in assigning excited states that are not observed in one-photon UV spectroscopy, the two-photon absorption spectrum of naphthalene is shown in Figure 1.17. Since for the point group all Bg states have a theoretical polarization degree of H = 3/2, the polarization measurement reveals immediately a Bg state near 42,000 cm . In the two-photon absorption spectrum this shows up only as a shoulder, whereas the maximum at 44,500 cm" can be assigned to an Ag state. Neither state is prominent in the one-photon spectrum. 

As an example we consider the case of the naphthalene crystal, G ft being its space group. The point group C-2h (see Table 2.1) has only one-dimensional representations. Since any subgroup of the group C h can also have only onedimensional representations, it is clear that in crystals of naphthalene type the compulsory degeneracy for excitonic states inside the first Brillouin zone is not possible. 

Naphthalene is a molecule with the point group D2h- It has a centre of inversion i, three twofold axes of rotational symmetry l(J z), 2(J y) and 3(J ), and three mirror planes perpendicular to the axes of rotational symmetry, xy, xz, and yz. The secular determinant for the calculation of the energy eigenvalues of the electronic system of the naphthalene molecule contains 10 x 10 coefficients cp- (see Problem PI.3 and Fig. PI.3). The first row and first column of the determinant are shown in the following fragment ... 

Now consider the HMO treatment of naphthalene. For butadiene and benzene, we set up the secular equation without bothering with the intermediate step of constructing symmetry orbitals from the Ipir AOs. For these molecules, the secular equation was easy enough to solve without the simplifications introduced by symmetry orbitals. For naphthalene the 10 X 10 secular determinant is difficult to deal with, and we first find symmetry orbitals. The point group of naphthalene (Fig. 17.6) is 2h-... 

A clear dependence on the position of the methyl group in the naphthalene ring may be recognized this is directly connected with the electron distribution in naphthalene. It is known that the 1-position of naphthalene is the point of greatest electron density (cf. Pullmann and Pullmann, 1952 Coulson, 1961). Substituting a methyl group into the... 

---