Benzene orbital energies

The pattern of orbital energies is different for benzene than it would be if the six tt electrons were confined to three noninteracting double bonds The delocalization provided by cyclic conjugation in benzene causes its tt electrons to be held more strongly than they would be in the absence of cyclic conjugation Stronger binding of its tt electrons is the factor most responsible for the special stability—the aromaticity—of benzene... 

One of molecular orbital theories early successes came m 1931 when Erich Huckel dis covered an interesting pattern m the tt orbital energy levels of benzene cyclobutadiene and cyclooctatetraene By limiting his analysis to monocyclic conjugated polyenes and restricting the structures to planar geometries Huckel found that whether a hydrocarbon of this type was aromatic depended on its number of tt electrons He set forth what we now call Huckel s rule... 

Fig. 10.3. Orbital coefficients for HOMO and next highest n orbital for some substituted benzenes. (From CNDO/2 ealculations. Ortho and meta eoefficients have been averaged in the case of the unsymmetrical methoxy and formyl substituents. Orbital energies are given in atomic units.)...

The pattern of orbital energies in Figure 11.13 provides a convincing explanation for why benzene is aromatic while square cyclobutadiene and planar- cyclooctatetraene are not. We start by counting tt electrons cyclobutadiene has four, benzene six, and cyclooctatetraene has eight. These tt electrons are assigned to MOs in accordance with the usual rules—lowest energy orbitals first, a maximum of two electrons per orbital. 

Consider now the rr-system in benzene. The MO approach will generate linear combinations of the atomic p-orbitals, producing six rr-orbitals delocalized over the whole molecule with four different orbital energies (two sets of degenerate orbitals). Figure 7.3. The stability of benzene can be attributed to the large gap between the HOMO and LUMO orbitals. 

FIGURE 3.39 The molecular orbital energy-level diagram for the ir-orbitals of benzene. In the ground state of the molecule, only the net bonding orbitals are occupied. 

Fig. 11. Top molecular orbital energies for precursor, structure C (broken lines) and for bridged intermediate, structure D (full lines). Bottom bridging energy (AE) for N =0 (full line) and N = 1 (broken line), where N is the number of electrons transferred from the carbon residue to the platinum. The energies are plotted as functions of the 7rC3-to-platinum overlap integral (S). The energy unit 0 [ is the absolute value of the exchange integral between a pair of p1 orbitals in benzene. For structures C and D, cf. reaction (7). After J. R. Anderson and N. R. Avery, J. Calal. 7, 315 (1967).

In the cyclophane 1, although the overlap between the n-system (2p) and the bridging cr-bonds (2s2p) is most effective, these orbital energy levels match worst, the first ionization potentials being 9.25 eV for benzene and 12.1 eV for ethane. As a result, the HOMOs are the almost pure it MOs with the b2g and b3g combinations. Both the PE spectrum and theoretical calculation demonstrate the degeneracy of the two HOMO levels. The absorption bands are attributed to the 17-17 transitions associated with the HOMOs. 

The LCAO-MO expressions corresponding to the HMO orbital energies (3.141) for the pi MOs symmetry properties of the cyclic C topology.66 For benzene, for example, the results are (renumbered in... 

Figure 3.48 The Frost-Musulin circle mnemonic (Eq. (3.141)) for HMO orbital energies ej of benzene, n = 6.

Figure 5.3. SHMO orbitals for cyclopropenyl, cyclobutadiene, cyclopentadienyl, and benzene. The energies are in units of f relative to a. Two alternative but equivalent representations are shown for the degenerate n orbitals of cyclobutadiene. Sizes of the 2p orbitals are shown proportional to the magnitudes of the coefficients whose numerical values are given. Coefficients not specified may be obtained by symmetry.

The (An + 2) n electron standard follows from the pattern of orbital energies in monocyclic, completely conjugated polyenes. The tt energy levels were shown for benzene earlier in Figure 11.4 and are repeated in Figure 11.13b. Figure 11.13a and 11.13c show the T7 energy levels for square cyclobutadiene and planar cyclooctatetraene, respectively. 

If you compare the orbital energies of the Hiickel and Mobius cyclic 7r systems (Figures 21-13 and 21-16), you will see that the Hiickel systems have only one lowest-energy MO, whereas the Mobius systems have two. Hiickel systems have an odd number of bonding orbitals (which, when full, accommodate 2, 6, 10, 14, or An + 2 electrons) and the Mobius systems have an even number of bonding orbitals (which, when full, accommodate 4, 8, 12, or An electrons). The Hiickel molecular orbitals have zero or an even number of nodes (see, for example, the benzene MOs, Figure 21-5) the Mobius molecular orbitals are not shown, but they have one or an odd number of nodes. 

Ag+ has a low-lying LUMO, so it interacts strongly with one of the relatively high-energy benzene HOMOs. o (I2) lies at much higher energy, so it overlaps better with the VP1 benzene orbital. 

The 7r energy levels, along with the molecular orbital wavefunctions, are pic-torially displayed in Fig. 7.1.12. Since there are six n electrons in benzene, orbitals a2u and e % are filled, giving rise to a 1 /V ig ground state with the total n energy... 

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