Orbitals of 1,3-Butadiene

Highest Energy Occupied Molecular Orbital (HOMO) 

Lowest Energy Unoccupied Molecular Orbital (LUMO) 

The unequal sizes of the 2p atomic orbitals from which the n MOs are made to show the degree to which they contribute to the molecular orbital. A bonding interaction results from constructive overlap of 2p orbitals of the same sign. Nodal planes are shown between carbon atoms as vertical lines this is where destructive overlap occurs. The energy of the orbitals increases as the number of nodal planes increases. The sign of the orbital inverts going from one side of a nodal plane to the other. Note that is the highest occupied MO (HOMO) and that Ti is the lowest unoccupied MO (LUMO). 

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

What is the symmetry of the highest energy molecular orbital containing electrons in 1,3,5,7-octa-tetraene  

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For this curriputtir prujoct, obtain the. orbitals of butadiene and prediet whether the eyelization of butadiene to eyelobutene is eonrotatory or disrotatory. 

The cyclobutene-butadiene interconversion can serve as an example of the reasoning employed in construction of an orbital correlation diagram. For this reaction, the four n orbitals of butadiene are converted smoothly into the two n and two a orbitals of the ground state of cyclobutene. The analysis is done as shown in Fig. 11.3. The n orbitals of butadiene are ip2, 3, and ij/. For cyclobutene, the four orbitals are a, iz, a, and n. Each of the orbitals is classified with respect to the symmetiy elements that are maintained in the course of the transformation. The relevant symmetry features depend on the structure of the reacting system. The most common elements of symmetiy to be considered are planes of symmetiy and rotation axes. An orbital is classified as symmetric (5) if it is unchanged by reflection in a plane of symmetiy or by rotation about an axis of symmetiy. If the orbital changes sign (phase) at each lobe as a result of the symmetry operation, it is called antisymmetric (A). Proper MOs must be either symmetric or antisymmetric. If an orbital is not sufficiently symmetric to be either S or A, it must be adapted by eombination with other orbitals to meet this requirement. 

FIGURE 2.3 The four tc orbitals of butadiene, formed by overlap of four p orbitals. 

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 Tz orbitals of butadiene (Scheme 18) qualitatively obtained from the orbitals of ethylenes are also supported by the electronic spectra of polyenes. The HOMO of butadiene is higher that the HOMO of ethylene since the former is the out-of-phase combination of the latter. The LUMO of butadiene is the in-phase combination of the LUMOs of ethylene and lies lower than the LUMO of ethylene. The energy gap between the HOMO and the LUMO is smaller in butadiene. In fact, the wavelength ( m ) is longer for butadiene (217 nm) than for ethylene (165 nm). The wavelength increases with the chain length of the polyenes. 

In the above example although the ground state orbital of cyclobutene, o, correlates with the ground state orbitals of butadiene /b the n orbital of the former does not correlate the /2 orbital of the latter, but rather it correlates with the /3 which is an excited state. So in such a case the thermal transformation by disrotatory processes will be a symmetry forbidden reaction. 

On the other hand in a photochemical transformation by a disrotatory process, one electron is promoted from jt to n orbital and so the o, n and it orbitals of cyclobutene would correlate with /. /2 and /3 orbitals of butadiene. Thus the first excited state of cyclobutene, since it correlates with the first excited state of butadiene, therefore, the process would be a photochemically symmetry allowed process. 

Drawn diagram for the relative energies of the various types ofp orbitals of butadiene (which has two bonding and two antibonding p orbitals) to illustrate the ground state and the Sp Tj, S2 and T2 excited states. 

Sometimes reaction coordinates are studied that involve substantial changes in bonding. In such an instance, it is critical that a consistent choice of orbitals be made. For instance, consider the electrocyclization of 1,3-butadiene to cyclobutene (Figure 7.2). The frontier orbitals of butadiene are those associated with the tt system, so, as just discussed, a (4,4) approach seems logical. However, the electrocyclization reaction transforms the two jt bonds into one different jr bond and one new a bond. Thus, a consistent (4,4) choice in cyclobutene would involve the jr and jt orbitals and the a and <7 orbitals of the new single bond. 

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 10.20 Construction of the 7r orbitals of butadiene by end-to-end interaction of two ethylenes.

Figure 11.2 The it orbitals of butadiene. At the top are shown the symmetry elements of the molecule, two mirror planes and a C2 axis, and the basis orbitals to be used in constructing the 7r molecular orbitals. Below are the four molecular orbitals in an energy-level diagram, with their symmetry behavior under each of the symmetry operations listed at the right.

Let us suppose, for example, that we wish to know about the interaction of the 7r orbitals of butadiene with orbitals of some other molecule. If the butadiene is unsubstituted (Figure 11.2), the molecular symmetry and the symmetry needed for the orbital model are the same. The symmetry elements of the mole-... 

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. 

LUMO of a simple carbonyl group. The nearest thing you have met so far (in Chapter 7) are the orbitals of butadiene (C=C conjugated with C=C), which we can compare with the a,(3-unsaturated aldehyde acrolein (C=C conjugated with C=0). The orbitals in the 7t systems of butadiene and acrolein are shown here. They are different because acrolein s orbitals are perturbed (distorted) by the oxygen atom (Chapter 4). You need not be concerned with exactly how the sizes of the orbitals are worked out, but for the moment just concentrate on the shape of the LUMO, the orbital that will accept electrons when a nucleophile attacks. 

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