Molecular Orbital Picture of a Conjugated System

Relative energies of conjugated, isolated, and cumulated dienes compared with alkynes, based on heats of hydrogenation (kJ/mol). 

In a strongly acidic solution, 1,4-cyclohexadiene tautomerizes to 1,3-cyclohexadiene. Propose a mechanism for this rearrangement, and explain why it is energetically favorable. 

The heat of hydrogenation of 1,3-butadiene is about 17 kJ/mol (4.0 kcal/mol) less than twice that of 1-butene, showing that 1,3-butadiene has a resonance energy of 17 kJ/mol. 

Structure of 1,3-butadiene in its most stable conformation. The 1.48 A central carbon-carbon single bond is shorter than the 1.54 A bonds typical of alkanes because of its partial double-bond character. 

Lewis structures are not adequate to represent delocalized molecules such as 1,3-butadiene. To represent the bonding in conjugated systems accurately, we must consider molecular orbitals that represent the entire conjugated pi system, and not just one toid at a time. 

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Conjugated compounds undergo a variety of reactions, many of which involve intermediates that retain some of the resonance stabilization of the conjugated system. Common intermediates include allylic systems, particularly allylic cations and radicals. Allylic cations and radicals are stabilized by delocalization. First, we consider some reactions involving allylic cations and radicals, then (Section 15-8) we derive the molecular orbital picture of their bonding. 

This separation of the cr framework and the re bond is the essence of Hiickel theory. Because the re bond in ethylene in this treatment is self-contained, we may treat the electrons in it in the same way as we do for the fundamental quantum mechanical picture of an electron in a box. We look at each molecular wave function as one of a series of sine waves, with the limits of the box one bond length out from the atoms at the end of the conjugated system, and then inscribe sine waves so that a node always comes at the edge of the box. With two orbitals to consider for the re bond of ethylene, we only need the 180° sine curve for re and the 360° sine curve for re. These curves can be inscribed over the orbitals as they are on the left of Fig. 1.23, and we can see on the right how the vertical lines above and below the atoms duplicate the pattern of the coefficients, with both c and c2 positive in the re orbital, and c positive and c2 negative in re. ... 

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. 

The energies of the molecular orbitals can be deduced by inscribing the conjugated system inside a circle of radius 2(3. There is no need for dummy atoms, since the sine curves go right round the ring, and the picture is therefore... 

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