Molecular orbitals of 1,3-butadiene

Scheme 18 The Jt molecular orbitals of butadiene from the bond orbitals...

The energies, the phases and the amplitudes of the tz molecular orbitals of butadiene are shown in Scheme 19. The, n, and orbitals corresponds to half, one,... 

The molecular orbitals of butadiene can be represented by the free electron (FE) model. The 4-C atoms give rise to 4 MOs (Sec. 2.10.1) lshown in Figure S.5. 

Figure 11.8 Classification of the reacting molecular orbitals of butadiene and cyclobutene for the conrotatory process. Symmetry classifications are with respect to the C2 axis, S indicating symmetric and A antisymmetric orbitals. The correlation lines are obtained by connecting orbitals of the same symmetry.

Use Coulson s equations to derive the n molecular orbitals of butadiene. 

Table 3 5 1. The Hiickel energies and wavefunction of the jt molecular orbitals of butadiene...

The molecular orbitals of butadiene, shown in Fig. 3.5.6, can be used to predict, or at least to rationalize, the course of concerted reactions (those which take place in a single step without involvement of intermediates) it would undergo. For instance, experimentally it is known that different cyclization products are obtained from butadiene by heating and upon light irradiation. 

Q Explain how to construct the molecular orbitals of butadiene and other conjugated systems. 

We will not develop all of the Woodward-Hoffmann rules, but we will show how the molecular orbitals can indicate whether a cycloaddition will take place. The simple Diels-Alder reaction of butadiene with ethylene serves as our first example. The molecular orbitals of butadiene and ethylene are represented in Figure 15-18. Butadiene, with four atomic p orbitals, has four molecular orbitals two bonding MOs (filled) and two antibonding MOs (vacant). Ethylene, with two atomic p orbitals, has two MOs a bonding MO (filled) and an antibonding MO (vacant). 

We have drawn the molecular orbital diagram for the n molecular orbitals of butadiene as a result of combining the Jt molecular orbitals of two ethene molecules. There are some important points to notice here. 

Figure 19. Structures of norcaradiene, 16, and two derivatives, 17,18, and schematic illustration of homoconjugation between the frontier molecular orbitals of butadiene (bottom left) and styrene (bottom right), respectively, with the anti-symmetrical cyclopropane HOMO.

C-Substituted Olefins. First let us consider the effect of merely adding conjugation (C-), as we do in going from ethylene to butadiene. This is easy, because we know how the molecular orbitals of butadiene lie in relation to those of ethylene (Fig. 2-12) the HOMO is raised in energy and the LUMO lowered. 

A second system is essentially the same, but with two more electrons—the enediolate ion 2.33 has the re molecular orbitals of butadiene, lowered by the presence of the two electronegative atoms, but with two electrons in ip3. However one thinks of it, it is a re system higher in energy than the separated components. We have seen therefore that both the diketone and the enediolate are destabilised systems, but that the... 

Figure 8.27 Formation of the 0 Huckel molecular orbital of butadiene from the 2p atomic orbitals. The black dots represent the carbon nuclei...

A similar consideration leads to the following symmetry properties for the four Tc-molecular orbitals of butadiene and six Tt-molecular orbitals of hexa-triene and are summarized in Figure 1.11. 

The Diels—Alder reaction may also be analyzed by a similar consideration of the molecular orbitals of butadiene and ethene. In this case, there are two possible HOMO—LUMO interactions. Since the phases of the 1,4-lobes of the HOMO of butadiene match with those in the LUMO of ethene, the [7r" s + TT s] cycloaddition is thermally allowed. We reach a similar conclusion by considering the symmetry of LUMO of butadiene and the HOMO of ethene (Figure 4.10). However, on energetic grounds the latter interaction will make a smaller contribution than the former. 

The same analysis is done for the molecular orbitals of butadiene, with the lowest energy orbital having zero nodes. Butadiene has four n-electrons, so there will be four n-molecular orbitals, each one capable of containing two electrons. Therefore, the two lower energy MOs will contain the four electrons—two each and spin paired. The lowest energy MO will have a + + + + array so that all four colored lobes overlap and there are zero nodes. It is important to understand that the four lobes shown for the + + + + array constitute one molecular orbital, not four. There are four carbon atoms and each is sp hybridized, so there are four lobes, but it is one of four molecular orbitals. 

To illustrate the molecular basis for this selectivity consider the molecular orbitals of butadiene and cyciobutene which are involved in the electronic rearrangement. These are illustrated in Fig. 6.7 their relative energies are tii < 7t2< ti < and a < n < n < a. Now consider disrotatory motion around the C—C bonds (rotation in the opposite direction) as shown in Fig. 6.8. The two orbitals and must correlate with two orbitals of cyciobutene. One of these is obviously n since both 7ti and TTg are in phase and therefore bonding between Cg and Cg the other is a since in both 7ti and Jig disrotatory motion creates a bonding (T-orbital between Cj and C4. Similar arguments can be used to establish the pair-... 

The molecular orbitals of butadiene can be used to predict, or at least rationalize, the course of reactions this compound undergoes. For instance, experimentally it is known that... 

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