Molecular orbitals 1.3- butadiene, antibonding

Having just seen a resonance description of benzene, let s now look at the alternative molecular orbital description. We can construct -tt molecular orbitals for benzene just as we did for 1,3-butadiene in Section 14.1. If six p atomic orbitals combine in a cyclic manner, six benzene molecular orbitals result, as shown in Figure 15.3. The three low-energy molecular orbitals, denoted bonding combinations, and the three high-energy orbitals are antibonding. 

Butadiene has two n bonds. The interaction between the two n bonds is one of the simplest models to derive molecular orbitals from bond orbitals. A n bond in butadiene is similar to that in ethylene. The n bond is represented by the bonding and antibonding orbitals. The interactions occur between the n bonds in butadiene. The bond interactions are represented by the bond orbital interactions. 

All the atoms of butadiene lie in a plane defined by the s p hybrid orbitals. Each carbon atom has one remaining p orbital that points perpendicular to the plane, in perfect position for side-by-side overlap. Figure 10-42 shows that all four p orbitals interact to form four delocalized molecular orbitals two are bonding MOs and two are antibonding. The four remaining valence electrons fill the orbitals, leaving the two p orbitals empty. 

We concentrate our attention on just four molecular orbitals. In the reactants these are the bonding (tt) and antibonding (tt ) orbitals of the double bond and the bonding (u) and antibonding (o ) orbitals of the bond that is being broken. In the product we have the four tt molecular orbitals of cis butadiene, which in order of increasing energy we label ttj, ttj, tTj, 714. 

Butadiene contains two double bonds, i.e. four carbon atoms which contribute one p orbital each there are then four delocalized molecular orbitals which are shown in Figure 3.17 as having no node (t/>i), one node two nodes (t/>3) and finally three nodes (t/>4). The bonding or antibonding character of an orbital is obtained by counting the number of bonds and... 

As with ethylene, the second molecular orbital (172) of butadiene (Figure 15-5) has one vertical node in the center of the molecule. This MO represents the classic picture of a diene. There are bonding interactions at the Cl—C2 and C3—C4 bonds, and a (weaker) antibonding interaction between C2 and C3. 

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. 

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). 

The orbital in ethylene that receives these electrons is the lowest-energy orbital available, the Lowest Unoccupied Molecular Orbital (LUMO). In ethylene, the LUMO is the tt antibonding orbital. If the electrons in the HOMO of butadiene can flow smoothly into the LUMO of ethylene, a concerted reaction can take place. 

Butadiene has two Jt bonds and so four electrons in the n system. Which molecular orbitals are these electrons in Since each molecular orbital can hold two electrons, only the two molecular orbitals lowest in energy are filled. Let s have a closer look at these orbitals. In, the lowest-energy bonding orbital, the electrons are spread out over all four carbon atoms (above and below the plane) in one continuous orbital. There is bonding between all the atoms. The other two electrons are in 2. This orbital has bonding interactions between carbon atoms 1 and 2, and also between 3 and 4 but an antibonding interaction between carbons 2 and 3. Overall, in both the occupied Jt orbitals there are... 

On irradiation with ultraviolet light ihp), 1,3-butadiene absorbs energy and a tt 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 it molecular orbital, we call this a tt —> tt excitation (read as pi to pi star ). The energy gap between the HOMO and the LUMO... 

TT molecular orbitals whose energies depend on the number of nodes they have between nuclei. Those molecular orbitals with few er nodes are lower in energ than the isolated p atomic orbitals and are bomiingMOs those molecular orbitals wnth more nodes are higher in energy than the isolated p orbitals and are antibonding MOs. Pi molecular orbitals of ethylene and l,v- -butadiene are shown in Figure 30.1. 

Under photochemical conditions, the electrocyclic ring closing of butadienes always proceeds by the disrotatory pathway, which is the opposite of the result under thermal conditions. The FMOs make the stereochemical result easy to understand. Under photochemical conditions, an electron is promoted from the HOMO i]ii to the LUMO 1//7, so i//i becomes the HOMO. Molecular orbital i//i has an antibonding interaction between the termini of the 77 system in the conrotatory TS but a bonding interaction between the termini of the 77 system in the disrotatory TS, so the reaction proceeds in a disrotatory fashion. 

The forbidden nature of the disrotatory process rests in the crossing of the 7t( 3) and 7t (02) molecular orbitals. The n electrons in cyclobutene occupy an orbital correlated with an antibonding orbital ( 3) of butadiene. To construct butadiene from cyclobutene, electron pairs must flow into the two bonding orbitals, tfii and 2. Similar to cyclobutanation, then, this process could conceivably be rendered allowed if an electron pair were removed from the 1/13) orbital and an electron pair added to the 7r ifiz) orbital as the disrotatory process proceeded. A transition metal could effect these operations through properly ordered dyz and dzx orbitals. This process is illustrated in Fig. 9. 

Let us consider again the cyclobutene-butadiene reaction. The molecular orbitals of cyclobutene that undergo a radical change in the course of reaction are a and a, the bonding and antibonding orbitals of the bond that is broken, and n and n the bonding and antibonding orbitals of the double bond. 

Butadiene. The tt molecular orbitals of 1,3-butadiene are shown in Figure 10.9. The four rp -hybridized carbons contribute four 2p atomic orbitals, and their overlap leads to four tt molecular orbitals. Two are bonding (tti and TT2) and two are antibonding (ttI and tt ). Each tt molecular orbital encompasses all four carbons of the diene. There are four tt electrons, and these are distributed in pairs between the two orbitals of lowest energy (tti and TT2). Both bonding orbitals are occupied tt2 is the HOMO. Both antibonding orbitals are vacant tt is the LUMO. 

---