Benzene point groups

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... 

Cs subgroup which was used above in the allyl ease) has no degenerate representations. Moleeules with higher symmetry sueh as NH3, CH4, and benzene have energetieally degenerate orbitals beeause their moleeular point groups have degenerate representations. 

We will find an excitation which goes from a totally symmetric representation into a different one as a shortcut for determining the symmetry of each excited state. For benzene s point group, this totally symmetric representation is Ajg. We ll use the wavefunction coefficients section of the excited state output, along with the listing of the molecular orbitals from the population analysis ... 

Here /, are the three moments of inertia. The symmetry index a is the order of the rotational subgroup in the molecular point group (i.e. the number of proper symmetry operations), for H2O it is 2, for NH3 it is 3, for benzene it is 12 etc. The rotational partition function requires only information about the atomic masses and positions (eq. (12.14)), i.e. the molecular geometry. 

FIGURE 4. The molecular model of diphenyl sulfoxide (Cs point group) the benzene rings are nearly perpendicular to the CSC plane. 

The benzene molecule in its equilibrium configuration is planar. Its symmetry is described by the point group as shown in Fig. 8-l(c). The delocalized n system is represented there by dotted lines. The six pz orbitals contribute to tbe jt system, as simply described by the Htickel approximation. The reduction r, = B2g Hjg E2u can be found as in the previous examples. 

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. 

Figure 19 Ionization energies of the upper orbitals of benzene, pyridine and pyridazine. The assignments and correlations are tentative. The point group of pyrazine is D2h and that of pyridine is C2 (Reproduced with permission from (b-78mi204io ...

Benzene belongs to the point group and IPA transitions from the ground state (Ai symmetry) are dipole-allowed only to states of Ei and A2u symmetry [30]. 2PA transitions from the groimd state are allowed to Aj, Ei, and E2g states. Transitions to all other states are forbidden. 

Due to disorder in the cyclopentadienyl groups the exact bonding of the cyclopentadienyl group to zinc remained uncertain, but it has been suggested that the cyclopentadienyl group is /7 -bonded to one zinc atom and r -bonded to the other one. In solution, however, cryoscopic measurements in benzene pointed to the existence of discrete monomeric species. IR and H NMR studies of solutions of 57 are consistent with /j -binding of the cyclopentadienyl group to zinc in a symmetric Csy structure. 

In 1995, Maciel and co-workers (118) synthesized the trityl cation in the supercages of zeolite HY by a clever application of Friedel-Crafts chemistry—13CC14 was reacted with an excess of benzene (Fig. 15). Maciel and co-workers carried out a number of spectroscopic and chemical manipulations that unambiguously demonstrated that the product was the trityl cation and that the cation was in the zeolite. Ab initio calculations at various levels of theory predict that the point group of isolated 16 is D3 rather than Dih. It is interesting to speculate about the extent to which the zeolite environment might force the degree of twist away from the gas-phase equilibrium value. 

Character tables for many point groups are listed in Section 9.12 at the end of this chapter. As an example, consider the character table for 6D6/, the point group of benzene. This group is of order 24. The symmetry operations are found to be divided into the 12 classes (1) E (2) C6, C ... 

We begin by considering the most famous and important of such systems, benzene. This molecule belongs to the point group D6/l. When the set of six pn orbitals, one on each carbon atom, is taken as the basis for a representation of the group D6/ we obtain the result... 

If this molecule is assumed to consist of two benzene rings placed on either side of the chromium atom so that their planes are parallel and their Cb axes colinear, the molecular symmetry may be Z)w or depending on whether the rings are staggered or eclipsed. X-ray study of the crystalline compound shows that the chromium atom is at a center of inversion so that in the crystalline state at least the molecular point group is D<. There is evidence from infrared and Raman spectra that the molecule has D symmetry in solution. 

In this paper we will first review the manner in which spin-free permutation and point group symmetry arise. Some general concepts concerning time-dependent processes will be discussed. Spin-free processes in which spin is conserved will be studied, and spin-free spin conservation rules and examples will be given. Special attention will be given to processes in which spin apparently is not conserved, but is in actuality. In addition, we will treat processes in which spin is not conserved. The role of doublepoint group symmetry and of Franck-Condon factors will be developed. Special emphasis is given to spin-forbidden processes in methylene, benzene, and chromium(III) complexes. 

Prepared State. Here the Hamiltonian H is the time-independent molecular Hamiltonian. Both H0 and T are time independent. The initial prepared state is an eigenket to H0 and thus is nonstationary with respect to H = H0 + T. One example is provided by considering H0 as the spin-free Hamiltonian 77sp and the perturbation T as a spin interaction. A second example is provided by considering H0 as the spin-free Born-Oppenheimer Hamiltonian and T as a spin-free nonadiabatic perturbation. In the first example spin-free symmetry is not conserved but double-point group symmetry may be. In the second example point-group symmetry is not conserved, but spin-free symmetry is. The initial prepared state arises from some other time-dependent process as, for example, radiative absorption which occurs at a rate very much faster than the rate at which our prepared state evolves. Mechanisms for radiationless transitions in excited benzene may involve such prepared states, as is discussed in Section XI. 

Write down the electronic configurations for the ground states of the molecules water, carbon dioxide, formaldehyde, ethene, benzene, and the nitrogen dioxide radical. The occupied MO s shall be given using the full point group symmetry of the molecule. 

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