1,3-Butadiene molecular orbitals, theory

Serrano-Andres, L., Merchan, M., Nebot-Gil, I., Lindh, R., Roos, B. O., 1993, Towards an Accurate Molecular Orbital Theory for Excited States Ethene, Butadiene, and Hexatriene , J. Chem. Phys., 98, 3151. 

Hiickel molecular orbital theory and its application to ethylene and butadiene... 

Hiickel molecular orbital theory benzene, 174 butadiene, 171-173 computational resources, 174 ethylene, 173... 

Pentadiene, like 1,3-butadiene, has four tt electrons. However, unlike the delocalized TT electrons in 1,3-butadiene, the tt electrons in 1,4-pentadiene are completely separate from one another. In other words, the electrons are localized. The molecular orbitals of 1,4-pentadiene have the same energy as those of ethene—a compound with one pair of localized tt electrons. Thus, molecular orbital theory and contributing resonance structures are two different ways to show that the tt electrons in 1,3-butadiene are delocalized and that electron delocalization stabilizes a molecule. 

Solutiorn Electrocyclic reactions are concerted, therefore they are completely stereospecific. The exact stereochemistry of the product depends upon the number of double bonds in the polyene molecular orbital theory allows us to predict this stereochemistry. Let us look at the electron configuration of butadiene, a four-ir-electron system, in the ground state and in the first excited state (achieved by the absorption of radiation) ... 

Opposite page) Molecular orbital picture diagrams rationalizing the Diels-Alder reaction between 1,3-butadiene and ethylene (top) using A) the conservation of orbital symmetry (Woodward and Hoffmann) B) frontier molecular orbital theory (Fukui). 

Use Huckel molecular orbital theory to construct molecular orbitals for conjugated hydrocarbon molecules such as butadiene and benzene... 

Clearly, the reaction of 2 and butadiene is much faster than the reaction of ethene because it does not require high temperatures and high pressure the reaction with 5 is slower. According to frontier molecular orbital theory, a mechanistic explanation of these experimental observations must include a discussion of the molecular orbitals of 1,3-butadiene and ethene (see Figure 24.2) compared with the molecular orbitals of 2 and 5. Figure 24.2 shows the energy level of the molecular orbitals but does not show the actual orbitals. Indeed, only the energy value is required once it is known that the HOMO of the diene reacts with the LUMO of each alkene. 

An approximate treatment of tt electron systems was introduced in 1931 by Erich Huckel (Figure 15.17) and is called the Huckel approximation of tt orbitals. The first step in a Huckel approximation is to treat the sigma bonds separately from the pi bonds. Therefore, in a Huckel approximation of a molecule, only the tt bonds are considered. The usual assumption is that the <7 bonds are understood in terms of regular molecular orbital theory. The <7 bonds form the overall structure of the molecule, and the tt bonds spread out over, or span, the available carbon atoms. Such 77 bonds are formed from the side-on overlap of the carbon 2p orbitals. If we are assuming that the tt bonds are independent of the cr bonds, then we can assume that the 77 molecular orbitals are linear combinations of only the 2p orbitals of the various carbon atoms. [This is a natural consequence of our earlier linear combination of atomic orbitals—molecular orbitals (LCAO-MO) discussion.] Consider the molecule 1,3-butadiene (Figure 15.18). The tt orbitals are assumed to be combinations of the 2p atomic orbitals of the four carbon atoms involved in the conjugated double bonds ... 

Frontier molecular orbital theory considers only the signs of the wave functions at the terminal carbon atoms of the HOMO and LUMO. The HOMO of 1,3-butadiene is 712- It is antisymmetric. As we noted earher, this means that the signs of the wave functions of the contributing terminal 2p atomic orbitals are reversed on opposite sides of the reference vertical plane. In all cases, MOs are either symmetric or antisymmetric with respect to this plane. The LUMO of 1,3-butadiene is 713. It is antisymmetric. 

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). 

Problem 8.25 Apply the MO theory to 1,3-butadiene and compare the relative energies of its molecular orbitals with those of ethene (Problem 8.24). 

This equivalence of the valence bond and molecular orbital descriptions of the bonding in these complexes arises from the alternant1 properties of the metal-butadiene bonding network. A similar equivalence between the two theories occurs for benzene and other polyenes that have alternant 7r-systems (73, 140). 

According to the frontier orbital theory,525 electron-withdrawing substituents lower the energies of the lowest unoccupied molecular orbital (LUMO) of the di-enophile thereby decreasing the highets occupied molecular orbital (HOMO)-LUMO energy difference and the activation energy of the reaction. 1,3-Butadiene itself is sufficiently electron-rich to participate in cycloaddition. Other frequently used dienes are methyl-substituted butadienes, cyclopentadiene, 1,3-cyclohexa-diene, and 1,2-dimethylenecyclohexane. 

To treat the 7r-electron system of 1,3-butadiene by simple MO theory, we combine the four p carbon orbitals of an atomic-orbital model, such as 17, to obtain four molecular orbitals ... 

These theories assert that the pathway of a chemical reaction accessible to a compound is controlled by its highest occupied molecular orbital (HOMO). For the thermal reaction of butadiene, which is commonly called ground-state chemistry, the HOMO is 2 and lowest unoccupied molecular orbital (LUMO) is photochemical reaction of butadiene, which is known to be excited-state chemistry, the HOMO is 1//3 (Fig. 3.5.6). 

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