1,3,5-Cyclohexatriene

Our experience has been that some 125 kJ/mol (30 kcal/mol) is given off when ever a double bond is hydrogenated When benzene combines with three molecules of hydrogen the reaction is far less exothermic than we would expect it to be on the basis of a 1 3 5 cyclohexatriene structure for benzene... 

The precise value of the resonance energy of benzene depends, as comparisons with 1,3,5-cyclohexatriene and (Z)-l,3,5-hexatriene illustrate, on the compound chosen as the reference. What is important is that the resonance energy of benzene is quite large, six to ten times that of a conjugated triene. It is this very large increment of resonance energy that places benzene and related compounds in a separate category that we call aromatic. 

Does this mean that benzene is in fact an equilibrium mixture of two 1,3,5-cyclohexatriene molecules Or, does this mean that benzene is a single molecule with some intermediate type of bonding ... 

Cyclohexatriene to benzene displays a sequence of structures from 1,3,5-cyclohexatriene (withCC single and double bonds initially set to 1.5 and 1.3 A, respectively) to benzene (witb all CC bonds set to 1.4 A) and back to cyclohexatriene. Plot energy (vertical axis) vs. CC bond length (horizontal axis). How many energy minima are there Do the minima look more like 1,3,5-cyclohexatriene or benzene What is the correct interpretation of the resonance picture ... 

Problem 10.1 Benzene is a planar molecule with bond angles of 120°. All six C-to-C bonds have the identical length, O.I39nm. Is benzene the same as 1,3,5-cyclohexatriene <... 

No. The bond lengths in 1,3,5-cyclohexatriene would alternate between 0,153nm for the single bond and 0.132nm for the double bond. The C-to-C bonds in benzene are intermediate between single and double bonds. 

When there are two or more substituents on a benzene ring, position isomerism arises. Thus there are three possible isomeric disubstituted benzene derivatives according to whether the substituents have the 1,2, 1,3, or 1,4 relationship. The isomers commonly are designated as ortho, meta, and para (or o, m, and p) for the 1,2-, 1,3-, and 1,4-isomers, respectively. The actual symmetry of the benzene ring is such that only one 1,2-disubstitution product is found, despite the fact that two would be predicted if benzene had the 1,3,5-cyclohexatriene structure ... 

The 1,3,5-cyclohexatriene structure, 6, proposed for benzene in 1866 by Kekule, has alternating single and double bonds around the ring, which would be predicted to have bond lengths of 1.48 A and 1.34 A, respectively (see Table 2-1) ... 

Benzene also is more stable by about 36-38 kcal mole-1 than anticipated for the 1,3,5-cyclohexatriene structure. You will recall from earlier discussions that the heat of combustion of one mole of benzene is 38 kcal less than calculated for cyclohexatriene (see Section 6-5 A). Also, the heat of hydrogenation of benzene is only 49.8 kcal mole-1, which is 36 kcal less than expected for 1,3,5-cyclohexatriene this estimate is based on the assumption that the heat of hydrogenation of 1,3,5-cyclohexatriene (with three double bonds) would be three times that of cyclohexene (28.5 kcal mole-1, for one double bond), or 3 X 28.5 = 85.5 kcal mole-1. 

The extra stability of benzene relative to the hypothetical 1,3,5-cyclohexatriene can be called its stabilization energy. Most (but not all) of this stabilization may be ascribed to resonance or electron delocalization. 

As mentioned in Section 21-2B, delocalization of the electrons over all six centers in benzene should give a more stable electron distribution than any structure in which the electrons are localized in pairs between adjacent carbons (as in the classical 1,3,5-cyclohexatriene structure). 

What happens if we use the MO method to calculate the 77-electron energy of classical 1,3,5-cyclohexatriene The procedure is exactly as for benzene, except that we decree that each carbon p orbital forms a 77 bond with... 

Figure 21-6 Energies and schematic representations of the -u molecular orbitals of localized 1,3.5-cyclohexatriene. The molecular orbitals are the w orbitals of three localized ethene bonds and the total r-electron energy is 6(a + 0) = (6a + 6/3).

It was shown in Section 21-3 that benzene is 36-38 kcal more stable than the hypothetical molecule 1,3,5-cyclohexatriene on the basis of the differences between experimental heats of combustion, or hydrogenation, and heats calculated from bond energies. We call this energy difference the stabilization energy (SE) of benzene. We have associated most of this energy difference with 7r-electron delocalization, which is the delocalization energy (DE). The difference between SE and DE will be small only if our bond-energy tables are reliable and steric and strain effects are small. 

A. 1,3,5-cyclohexatriene is a higher energy molecule than benzene. 

Because of resonance, the benzene molecule is more stable than its 1,3,5-cyclohexatriene structure suggests. This extra stability (36 kcal/mole) is referred to as its resonance energy. 

The dotted lines in the transition states represent delocalized MO s formed by interaction either of six AO s on six adjacent atoms or of four AO s on four adjacent atoms. The situation is qualitatively similar to that in benzene or cyclobutadiene. Now the it energy of benzene is lower than that of 1,3,5-cyclohexatriene, whereas that of cyclobutadiene is probably higher than that of... 

Delocalization energy denotes the energy by which a molecule is stabilized or destabilized compared to a hypothetical reference compound in which electrons (usually ji electrons) are not as mobile. The canonical example is the energy of benzene compared to the hypothetical 1,3,5-cyclohexatriene in which there are three distinct double and three distinct triple bonds. With caveats, one measure of this energy is the heat of hydrogenation of benzene compared to three times the heat of hydrogenation of cyclohexene. As an electronic phenomenon, this lies outside the purview of MM. 

---