Molecular orbitals of 1,3,5-hexatriene

Fig. 1.10. Graphic representation of K-molecular orbitals of 1,3,5-hexatriene as combinations of 2p AOs. The sizes of the orbitals are roughly proportional to the coefficients of the Hiickel wave functions.

Figure 30.2 The six n molecular orbitals of 1,3,5-hexatriene. In the ground state, the three bonding MOs are filled. In the excited state,

Answer the following questions for the tt molecular orbitals of 1,3,5-hexatriene ... 

Fig. 1.4 Molecular orbitals of 1,3,5-hexatriene and their wave functions and symmetry properties...

Problem 11.6 How many molecular orbitals of 1,3,5-hexatriene contain bonding k electrons Sketch each one, showing vertical nodal planes, and determine the symmetry of each wave function. 

Notice that as the MOs increase in energy, they alternate from being symmetric to being antisymmetric. Therefore, the ground-state HOMO and the excited-state HOMO always have opposite symmetries if one is symmetric, the other will be antisymmetric. A molecular orbital description of 1,3,5-hexatriene, a compound with three conjugated double bonds, is shown in Figure 28.3. As a review, examine the figure and note... 

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. 

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.

Figure 15-4 compares the tt molecular orbitals of benzene with those of 1,3,5-hexatriene. The acyclic triene follows a pattern similar to that of 1,3-butadiene (Figure 14-7), but with two more molecular orbitals The orbitals all have different energies, the number of nodes increasing in the procession from tti to tts. The picture for benzene is different in all respects different orbital energies, two sets of degenerate (equal energy) orbitals, and completely different nodal patterns. 

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.

Fig. 2.5. Representation of molecular orbitals and electron occupancy of 1, 3, 5-hexatriene.

To explain the pericychc reaction of 1,3,5-hexatriene by frontier molecular orbital theory, we need only consider the symmetry of 713 and 714. The HOMO is 713 it is symmetric. The LUMO is 714 it is antisymmetric. Note that this order of symmetry is opposite to that of 1,3-butadiene. The symmetry of the HOMO alternates with each additional double bond. The difference in the chemistry of polyenes noted earlier in this chapter for An 71 and 4 + 2 7t systems results from this difference in symmetry for the highest energy occupied molecular orbital involved in the reaction (Figure 25.3). 

Now let s compare the motions required for the HOMO and LUMO of 1,3,5- hexatriene with the corresponding molecular orbitals of 1,3-butadiene. The HOMO of 1,3,5-hexatriene is symmetric, and therefore a disrotatory motion is required to form a a bond (Figure 25.5a). This result is the opposite of that for 1,3-butadiene. The LUMO of 1,3,5-hexatriene is antisymmetric. Therefore, a conrotatory motion is required to form a O bond (Figure 25.5b). This result is again the opposite of that observed for 1,3-butadiene. 

A conjugated hydrocarbon has an alternation of double and single bonds. Draw the molecular orbitals of the TI system of 1,3,5-hexatriene. If the energy required to excite an electron from the HOMO to the LUMO corresponds to a wavelength of 256 nm, do... 

The Woodward-Hoffmann rules for pericyclic reactions require an analysis of all reactant and product molecular orbitals, but Kenichi Fukui at Kyoto Imperial University in Japan introduced a simplified version. According to Fukui, we need to consider only two molecular orbitals, called the frontier orbitals. These frontier orbitals are the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). In ground-state 1,3,5-hexa-triene, for example, 1//3 is the HOMO and excited-stale 1,3,5-hexatriene, however, 5 is the LUMO. 

Hexamethylphosphoramide, S -2 reaction and. 371 Hexane, 1R spectrum of. 424 mass spectrum of, 413 1,3,5-Hexatriene, molecular orbitals of, 1180... 

Electrocyclic reactions involve the cyclization of conjugated polyenes. For example, 1,3,5-hexatriene cyclizes to 1,3-cyclohexadiene on heating. Electrocyclic reactions can occur by either conrotatory or disrotatory paths, depending on the symmetry of the terminal lobes of the tt system. Conrotatory cyclization requires that both lobes rot lte in the same direction, whereas disrotatory cyclization requires that the lobes rotate in oj )posite directions. The reaction course in a specific case can be found by looking at the symmetry of the highest occupied molecular orbital (HOMO). 

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