Molecular orbitals in benzene

The energy level diagram and the wavefunctions of the six n molecular orbitals in benzene. 

This project to extend the GMS method to anthracene proved to be too hard for the times. The starting point was to get the basis molecular orbitals. In benzene they are fully determined by the hexagonal symmetry, but in anthracene have to be found by calculation. For the full computation many integrals were needed including the repulsion integrals (2.1) that now seem easy,... 

Top) The a hybrids of the carbon atoms of benzene. The n atomic orbitals in benzene (a), and the Kekule pairing schemes (b, c). (Bottom) The n molecular orbitals in benzene (double streamers). 

In molecular orbital theory, the tt molecular orbitals in benzene are formed from a linear combination of the six carbon 2p orbitals and are delocahzed over the entire molecule. The lowest energy tt bonding molecular orbital is shown here. 

Figure 15-5 Energy levels of the 7T molecular orbitals In benzene and 1,3,5-hexatriene. In both, the six TT electrons fill the three bonding molecular orbitals. In benzene, two of them are lower in energy and one is higher than the corresponding orbitals in 1,3,5-hexatriene. Overall, energy is reduced and stability increased in going from the acyclic to the cyclic system.

Three-dimensional plots of the n molecular orbitals in benzene. The MOs are displayed at a value of 0.05 e. where the black and gray surfaces correspond to positive and negative, respectively, values of the wavefunction. These are ab initio calculations with a 3-21 G basis set. 

FIGURE 114 The TT molecular orbitals of benzene arranged in order of increasing energy and showing nodal surfaces The six tt electrons of benzene occupy the three lowest energy or bitals all of which are bonding... 

Having just seen a resonance description of benzene, let s now look at the alternative molecular orbital description. We can construct -tt molecular orbitals for benzene just as we did for 1,3-butadiene in Section 14.1. If six p atomic orbitals combine in a cyclic manner, six benzene molecular orbitals result, as shown in Figure 15.3. The three low-energy molecular orbitals, denoted bonding combinations, and the three high-energy orbitals are antibonding. 

Another example which illustrates beautifully the mixing of a group orbitals to form delocalized molecular orbitals is benzene. First of all the six crcc bond orbitals interact to give six linear combinations which are delocalized over the entire carbon skeleton. The amplitudes of the various bond orbitals in each [Pg.23]

The operation of (d) is seen in cyclopentadiene (14) which is found to have a pKa value of 16 compared with 37 for a simple alkene. This is due to the resultant carbanion, the cyclopentadienyl anion (15), being a 6n electron delocalised system, i.e. a 4n + 2 Hiickel system where n = 1 (cf. p. 18). The 6 electrons can be accommodated in three stabilised n molecular orbitals, like benzene, and the anion thus shows quasi-aromatic stabilisation it is stabilised by aromatisation ... 

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).

The orbitals of the second row can be hypothetically obtained from those of the first row by deforming the orbital around the benzene ring in a clockwise direction. If the orbital is moved even further in that direction, one can pass from the second row to the third row, and eventually from the third row to the fourth row. In fact, this transition from the first row to the last row is a continuous process, and there exist infinitely many sets of localized orbitals of intermediate character, only two of which have been indicated in the second and the third rows.s7) Again the first column contains the superimposed fifth strongest contours for each set of molecular orbitals (in the case of the orbitals of the third row the fifth strongest contour happens to divide up into two disconnected parts). 

Benzene is unusually stable and it is the delocalised electrons that account for this stability. The presence of the delocalised electrons also explains why benzene does not undergo addition reactions. Addition reactions would disrupt the electron delocalisation and so reduce the stability of the ring. Substitution reactions, on the other hand, can occur without any such disruption and the stability of the benzene ring is maintained. The delocalised electrons in the % molecular orbital make benzene susceptible to attack by electrophiles (electron pair acceptors). As a result, benzene undergoes electrophilic substitution reactions and some of these are outlined at the top of the next page. Note that the electrophiles are shown in red, the reagents in blue and the reaction names in green. 

The electronegativity of Nitrogen is greater than that of Carbon therefore a molecular orbital that includes the Nitrogen p orbital is lower in energy than the analogous orbital in benzene. 

In general, a molecular-centered basis set is not suitable for constructing a function which does not approach spherical symmetry and have most of its structure close to the origin. For example, an extensive linear combination of molecule-centered atomiclike orbitals would be needed to construct the nodes in a b2g molecular orbital of benzene. Also, because the interference effects are specifically characteristic of the interplay between electron wavelength and the set of internuclear spacings, a molecule-centered basis set will not adequately describe interference effects. 

Esr spectra are subject to exchange effects in the same way as nmr spectra. A specific example is provided by electron exchange between sodium naphthalenide and naphthalene. Naphthalene has a set of ten 77-molecular orbitals, similar to the six 7r-molecular orbitals of benzene (Figure 21-5). The ten naphthalene it electrons fill the lower five of these orbitals. In a solvent such as 1,2-dimethoxyethane, which solvates small metal ions well, naphthalene accepts an electron from a sodium atom and forms sodium naphthalenide, a radical anion ... 

Example 6.2-1 This example discusses the molecular orbitals of benzene.The numbering system used for the atoms is shown in Figure 6.3. The point group of benzene is... 

Figure 6.4. Energy-level diagram for the molecular orbitals of benzene evaluated in the Huckel approximation.

The molecular orbitals of benzene are schematically represented in Fig. 3. The first excited state of benzene cannot be described by one electron configuration, due to the degeneracy of the highest occupied molecular orbitals (HOMOs) and the lowest unoccupied molecular orbitals (LUMOs). The Si state of benzene (B2u) can be represented as 4>24>4 - 4>35 and the S2 or state (Biu) as 4>24>5 - 4)3(t,4-... 

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