Pi Molecular Orbitals of Benzene

Now let us look at the experimental data. Although benzene is hydrogenated only with difficulty (Section 14-7), special catalysts carry out this reaction, so the heat of hydrogenation of benzene can be measured LH° = -49.3 kcal mol , much less than the -78.9 kcal mol predicted. 

We have just examined the atomic orbital picture of benzene. Now let us look at the molecular orbital picture, comparing the six tt molecular orbitals of benzene with those of 1,3,5-hexatriene, the open-chain analog. Both sets are the result of the contiguous overlap of six p orbitals, yet the cyclic system differs considerably from the acyclic one. A comparison of the energies of the bonding orbitals in these two compounds shows that cyclic conjugation of three double bonds is better than acyclic conjugation. 

Recall Mixing six p orbitals generates six new molecular orbitals. 

Cyclic overlap modifies the energy of benzene s molecular orbitals 

Some reactions have aromatic transition states 

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Figure 12.8 The pi molecular orbitals of benzene. The view is from the side. The nodes are planes that go through the center and cut both sides of the loop.

Figure 15-4 Pi molecular orbitals of benzene compared with those of 1,3,5-hexatriene. The orbitals are shown at equal size for simplicity. Favorable overlap (bonding) takes place between orbital lobes of equal sign. A sign change is indicated by a nodal plane (dashed line). As the number of such planes increases, so does the energy of the orbitals. Note that benzene has two sets of degenerate (equal energy) orbitals, the lower energy set occupied (i/fj, ifrs), the other not ( / 4. lAs). as shown in Figure 15-5.

STO-3G One-Electron Energies for Pi-Molecular Orbitals of Benzene (Hartrees)... 

Because of their similar shape and orientation, each 2p orbital overlaps two others, one on each adjacent carbon atom. According to the rules listed on p. 398, the interaction of six 2p orbitals leads to the formation of six pi molecular orbitals, of which three are bonding and three antibonding. A benzene molecule in the ground state therefore has six electrons in the three pi bonding molecular orbitals, two electrons with paired spins in each orbital (Figure 10.28). 

Energy diagram of the molecular orbitals of benzene. Benzene s six pi electrons fill the three bonding orbitals, leaving the antibonding orbitals vacant. 

The behavior of pyridine in substitution reactions can be understood on the basis of its resonance structures (la-d) and on the basis of the electron-density distribution at the various ring positions as derived from molecular-orbital-theoretical calculations, An example of the published pi-electron density distribution is shown in II, The resonance energy of pyridine is 35 kcal/mole (versus 39 kcal/mole for benzene). 

We start with some biographical notes on Erich Huckel, in the context of which we also mention the merits of Otto Schmidt, the inventor of the free-electron model. The basic assumptions behind the HMO (Huckel Molecular Orbital) model are discussed, and those aspects of this model are reviewed that make it still a powerful tool in Theoretical Chemistry. We ask whether HMO should be regarded as semiempirical or parameter-free. We present closed solutions for special classes of molecules, review the important concept of alternant hydrocarbons and point out how useful perturbation theory within the HMO model is. We then come to bond alternation and the question whether the pi or the sigma bonds are responsible for bond delocalization in benzene and related molecules. Mobius hydrocarbons and diamagnetic ring currents are other topics. We come to optimistic conclusions as to the further role of the HMO model, not as an approximation for the solution of the Schrodinger equation, but as a way towards the understanding of some aspects of the Chemical Bond. 

Recall from Section 3.6 that molecules such as benzene that have a series of conjugated p orbitals cannot be described very well by localized molecular orbitals that extend over only two atoms at a time. Instead, delocalized pi MOs that extend over the entire group of conjugated p orbitals must be employed. For benzene, all six of the p atomic orbitals combine to form six delocalized MOs. The number of MOs equals the number of AOs that overlap to form them. 

Unlike the pi bonding molecular orbitals in ethylene, those in benzene form delocalized molecular orbitals, which are not confined between two adjacent bonding atoms, but actually extend over three or more atoms. Therefore, electrons residing in any of these orbitals are free to move around the benzene ring. For this reason, the structure of benzene is sometimes represented as... 

FIGURE 10.28 (a) The six 2p orbitals on the carbon atoms in benzene, (bj The delocalized molecular orbital formed by the overlap of the 2p orbitals. The delocalized molecular orbital possesses pi symmetry and lies above and below the plane of the benzene ring. Actually, these 2p orbitals can combine in six different ways to yield three bonding molecular orbitals and three antibonding molecular orbitals. The one shown here is the most stable. 

We can now state that each carbon-to-carbon linkage in benzene contains a sigma bond and a partial pi bond. The bond order between any two adjacent carbon atoms is therefore between 1 and 2. Thus molecular orbital theory offers an alternative to the resonance approach, which is based on valence bond theory. (The resonance structures of benzene are shown on p. 349.)... 

Fig. 8.28. The benzene molecule. The hybridization concept allows us to link the actual geometry of a molecule with its electronic structure (a). The sj - hybrids of the six carbon atoms form the six cr CC bonds and the structure is planar. Each carbon atom thus uses two out of its three hybrids, the third one lying in the same plane protrudes towards a hydrogen atom and forms the cr CH bond. In this way, each carbon atom uses its three valence electrons. The fourth one resides on the 2p orbital that is perpendicular to the molecular plane. The six 2p orbitals form six it molecular orbitals, out of which three are doubly cKcupied and three are empty. The doubly txxupied ones are shown in Fig. (b). The 3 orbital that apparently completes all combinations of single-ntxle molecular orbitals is redundant (that is why it is in parentheses), because the orbital represents a linear combination of the tpi and tp2-...

Molecules with delocalized molecular orbitals are generally more stable than those containing molecular orbitals locahzed on only two atoms. The benzene molecule, for example, which contains delocalized molecular orbitals, is chanically less reactive (and hence more stable) than molecules containing localized C=C bonds, such as ethylene. Benzene is so stable because the energy of the pi electrons is lower when the electrons are delocalized over the entire molecule than when they are localized in individual bonds, much as the energy of the particle in a one-dimensional box is lowered when the length of the box is increased (see Section 1.3). 

Ionization of benzene undoubtedly also involves loss of an electron from the highest occupied v-molecular orbital. The relatively high energy required (PI I = 9.245 e.v.) (Table VIII) compared to that for hexatriene (UV / = 8.26 e.v.) (Table VII) demonstrates clearly the additional v-electronic stability of the aromatic ring. The more extensive x-network in naphthalene results in a lower ionization potential, 8.12 e.v. 

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