Buta-1,3-diene molecular orbitals

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

All four carbon atoms of buta-1,3-diene are sp2 hybridized, and (in the planar conformation) they all have overlapping p orbitals. Let s review how we constructed the pi molecular orbitals (MOs) of ethylene from the p atomic orbitals of the two carbon atoms (Figurel5-3). Each p orbital consists of two lobes, with opposite phases of the wave function in the two lobes. The plus and minus signs used in drawing these orbitals indicate the phase of the wave function, not electrical charges. To minimize confusion, we will... 

Now we are ready to construct the molecular orbitals of buta-1,3-diene. The p orbitals on Cl through C4 overlap, giving an extended system of four p orbitals that form four pi molecular orbitals. Two MOs are bonding, and two are antibonding. To represent the four p orbitals, we draw four p orbitals in a line. Although buta-1,3-diene is not linear, this simple straight-line representation makes it easier to draw and visualize the molecular orbitals. 

The 77 antibonding molecular orbital of buta-1,3-diene. The highest-energy MO has three nodes and three antibonding interactions. It is strongly antibonding, and it is vacant in the ground state. 

Just as the four p orbitals of buta-1,3-diene overlap to form four molecular orbitals, the three atomic p orbitals of the allyl system overlap to form three molecular orbitals, shown in Figure 15-11. These three MOs share several important features with the MOs of the butadiene system. The first MO is entirely bonding, the second has one node, and the third has two nodes and (because it is the highest-energy MO) is entirely antibonding. 

The six overlapping p orbitals create a cyclic system of molecular orbitals. Cyclic systems of molecular orbitals differ from linear systems such as buta-1,3-diene and the allyl system. A two-dimensional cyclic system requires two-dimensional MOs, with the possibility of two distinct MOs having the same energy. We can still follow the same principles in developing a molecular orbital representation for benzene, however. 

The regiochemistry of Diels-Alder reactions with 3.3.3-trifluoropropene (1) shows that the inductive effect of a trifluoromethyl group increases the magnitude of the molecular orbital coefficient of the unsubstituted terminus, but the effect is not great enough to achieve high regioselectivity with dienes other than l-methoxy-3-(trimethylsiloxy)buta-l,3-diene (Danishefsky s diene, 4) compare the reaction of 1 with 2, 3, and 4. ... 

Figure 7.5 Molecular orbitals of ethene and buta-1,3-diene...

Excitation from the HOMO (i/zi), the highest occupied molecular orbital, to the LUMO ( j/ i), the lowest unoccupied molecular orbital, of buta-1,3-diene (Figure 4.5) requires — 1.236/3 (/3 is a negative energy). We can use this result to obtain a first calibration of /3. The absorption maximum of the first 7t,7t transition of buta-1,3-diene lies at vnrdx = 4.6 jam hence /3/he 3.7 pm ... 

In the molecule of buta-1,3-diene, there are four p-orbitals located on four adjacent carbon atoms and hence this generates four new tt -molecular orbitals on overlapping. The way to get these new 7r-molecular orbitals is the linear combination of two ir-molecular orbitals of ethene according to the perturbation molecular orbital (PMO) theory. Like the combination of atomic orbitals, overlapping of the bonding (ct or tu) or antibonding molecular orbitals (a or TT ) of the reactants (here, ethene) results in the formation of the new molecular orbitals that are designated as Wi, W2, etc. in the product (here, buta-1,3-diene). 

On the basis of molecular orbital diagrams of ethene, buta-1,3-diene, and hexa-l,3,5-triene, the following points should be considered while constructing the molecular orbitals of the conjugated polyenes ... 

The lowest energy molecular orbital (for example, Wi in the case of buta-1,3-diene) always has no node, however, the next higher has one node and the second higher has two nodes and so on. Thus, the nth molecular orbital will have n — 1 nodes. 

It is important to note that the nodes are found at the most symmetric points in a molecular orbital. For example, in the case of W2 of buta-1,3-diene, a node is present at the center of C2—C3 bond, however, it will be incorrect if the node is present at the center of a Ci—C2 bond or C3—C4 bond. 

FIGURE 8.13 Four IT molecular orbitals in buta-i,3-diene. Note that the number of nodes between nuclei increases as the energy level of the orbital increases. 

Having just seen a resonance description of benzene, let s now look at the alternative molecular orbital description. We can construct v molecular orbitals for benzene just as we did for buta-1,3-diene in Section 8.12. If six p atomic orbitals combine in a cyclic manner, six benzene molecular orbitals result, as shown in Figure 9.2. The three lower-energy molecular orbitals, denoted lAi, tl>2, and ip3, are bonding combinations, and the three higher-energy orbitals are antibonding. 

On irradiation with ultraviolet light [hv], buta-1,3-diene absorbs energy and a v electron is promoted from the highest occupied molecular orbital, or HOMO, to the lowest unoccupied molecular orbital, or LUMO. Since the electron is promoted from a bonding tt molecular orbital to an antibonding... 

T molecular orbital, we call this a tt tt excitation (read as pi to pi star ). The energy gap between the HOMO and the LUMO of buta-1,3-diene is such that UV light of 217 nm wavelength is required to accomplish the tt tt electronic transition (Figure 10.19). 

FIGURE 10.19 Ultraviolet irradiation of buta-i,3-diene results in promotion of an electron from ip2, the highest occupied molecular orbital (HOMO), to 1//3, the lowest unoccupied molecular orbital (LUMO). 

FICURE17.10 The IT bonding molecular orbitals of a conjugated enone (propenal) and a conjugated diene (buta-i,3-diene) are similar in shape and are spread overthe entire tt system. 

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