Butadiene frontier orbitals

The LCAO Model of tt-MOs of Ethene, Acetylene, and Butadiene Frontier Orbitals... 

Btamp/e Another example of frontier orbital theory uses the reaction of phenyl-butadiene with phenylethylene. This reaction is a [4 + 2] pericyclic addition to form a six-membered ring. It could proceed with the two phenyl rings close to each other (head to head) or further away from each other (head to tail). 

A complete mechanistic description of these reactions must explain not only their high degree of stereospecificity, but also why four-ir-electron systems undergo conrotatory reactions whereas six-Ji-electron systems undergo disrotatory reactions. Woodward and Hoifinann proposed that the stereochemistry of the reactions is controlled by the symmetry properties of the HOMO of the reacting system. The idea that the HOMO should control the course of the reaction is an example of frontier orbital theory, which holds that it is the electrons of highest energy, i.e., those in the HOMO, that are of prime importance. The symmetry characteristics of the occupied orbitals of 1,3-butadiene are shown in Fig. 11.1. 

In certain cases, multiple frontier orbital interactions must be considered. This is particularly true of cycloaddition reactions, such as the Diels-Alder reaction between 1,3-butadiene and ethene. 

The chemical reactions through cyclic transition states are controlled by the symmetry of the frontier orbitals [11]. At the symmetrical (Cs) six-membered ring transition state of Diels-Alder reaction between butadiene and ethylene, the HOMO of butadiene and the LUMO of ethylene (Scheme 18) are antisymmetric with respect to the reflection in the mirror plane (Scheme 24). The symmetry allows the frontier orbitals to have the same signs of the overlap integrals between the p-or-bital components at both reaction sites. The simultaneous interactions at the both sites promotes the frontier orbital interaction more than the interaction at one site of an acyclic transition state. This is also the case with interaction between the HOMO of ethylene and the LUMO of butadiene. The Diels-Alder reactions occur through the cyclic transition states in a concerted and stereospecific manner with retention of configuration of the reactants. 

The frontier orbital interactions at other than reaction sites can determine the selectivity [14]. The interaction between the HOMO of cyclopentadiene and the LUMO of maleic anhydride is illustrated in Scheme 26. The HOMO of cyclopentadiene has the same phase property as butadiene (Scheme 18). The LUMO of maleic anhydride is an in-phase combined orbital of and transition state for the... 

Theoretical calculations have also permitted one to understand the simultaneous increase of reactivity and selectivity in Lewis acid catalyzed Diels-Alder reactions101-130. This has been traditionally interpreted by frontier orbital considerations through the destabilization of the dienophile s LUMO and the increase in the asymmetry of molecular orbital coefficients produced by the catalyst. Birney and Houk101 have correctly reproduced, at the RHF/3-21G level, the lowering of the energy barrier and the increase in the endo selectivity for the reaction between acrolein and butadiene catalyzed by BH3. They have shown that the catalytic effect leads to a more asynchronous mechanism, in which the transition state structure presents a large zwitterionic character. Similar results have been recently obtained, at several ab initio levels, for the reaction between sulfur dioxide and isoprene1. ... 

Thus we find that the reaction is a syn (suprafacial) addition with respect to both the diene and dienophile. The frontier orbitals involved shows that the reaction occurs by interaction of HOMO and LUMO. So there is no possibility of substituents to change their position. Substituents which are on the same side of the diene or dienophile will be cis on the newly formed ring as is seen between the reaction of dimethyl maleate (a cis dienophile) with 1,3 butadiene. The product formed is cis 4,5 dicarbomethoxy cyclohexane. 

The SC descriptions of the electronic mechanisms of the three six-electron pericyclic gas-phase reactions discussed in this paper (namely, the Diels-Alder reaction between butadiene and ethene [11], the 1,3-dipolar cycloaddition offulminic acid to ethyne [12], and the disrotatory electrocyclic ring-opening of cyclohexadiene) take the theory much beyond the HMO and RHF levels employed in the formulation of the most popular MO-based treatments of pericyclic reactions, including the Woodward-Hoffmarm mles [1,2], Fukui s frontier orbital theory [3] and the Dewar-Zimmerman model [4—6]. The SC wavefunction maintains near-CASSCF quality throughout the range of reaction coordinate studied for each reaction but, in contrast to its CASSCF counterpart, it is very much easier to interpret and to visualize directly. 

It was Woodward and Hoffmann who first introduced organic chemists to the idea that so-called frontier orbitals (the HOMO and LUMO) often provide the key to understanding why some chemical reactions proceed easily whereas others do not. For example, the fact that the HOMO in cw-1,3-butadiene is able to interact favorably with the LUMO in ethylene, suggests that the two molecules should readily combine in a concerted manner to form cyclohexene, i.e., Diels-Alder cycloaddition. 

For radical cations of norcaradiene and derivatives, the interaction of the cyclopropane in-plane e orbitals with the butadiene frontier MO favors the type B structure. The assignments are based on ab-initio calculations, CIDNP results, and the ET photochemistry. The norcaradiene radical cation (lla ) has a electronic ground state (Cj symmetry). The Cl—C6 bond is shortened on ionization (—3.4 pm) while the lateral bonds are lengthened (+2.8 pm). The delocalization of spin density to C7 (py = 0.246 py 5 = 0.359) and the hyperfine coupling constants of the cyclopropane moiety a e = 1.36 mT oysyn = —0.057 mT flvanti = —0.063 mT) support a type B structure. 

An additional point of interest concerns the behaviour of homo and lumo orbitals of reactants in allowed reactions. Fukui (1970, 1975) has pointed out that the frontier-orbital gap actually narrows as the reaction proceeds. This has been confirmed computationally for the cycloaddition of ethylene and butadiene (Townshend et al., 1976), and contrasts with what one might expect based on a static homo-lumo interaction. Such an interaction causes the energy gap between resultant orbitals to widen, as indicated in Fig. 29. 

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. 

Figure 7.2 The frontier orbitals of s-cis- 1,3-butadiene are the four tt orbitals (jtt is the specilic example shown). If these orbitals are followed in a diabatic sense along the elechocychzation reaction coordinate, they correlate with the indicated orbitals of cyclobutadiene...

Fig. 9. Frontier orbital mixing for the thermal addition of 1,3-butadiene to V-methyl-quinolinium-3-olate (467 -> 468).

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. 

Use frontier orbital analysis to decide whether the dimeriza-tion of 1,3-butadiene shown here is symmetry allowed or forbidden. 

Formulate fulvene as a combination of ethylene and butadiene and uses a perturbation approach to calculate its frontier orbitals. 

As FO theory applies normally to bimolecular reactions, it is easier to study the reverse reaction butadiene + N2 —> 32. The MOs of butadiene are shown p. 50 and those of N2 in Figure 4.10. A priori, four stereochemistries are possible the butadiene component can react in a conrotatory or disrotatory mode and N2 in a linear or nonlinear mode. Depending on the stereochemistry, the butadiene FOs VP2 and can overlap with the <5Z, nx, nf, ny or ny orbitals. Therefore, to treat all these cases, a set of seven frontier orbitals must be taken into account. 

Figure 15.2 (Section 15.2.1) showed the stereostructures of the transition states of the [4+2]-cycloadditions between ethene or acetylene, respectively, and butadiene. The HOMOs and LUMOs of all substrates involved are shown in Figure 15.4. Figures 15.8 and 15.9 depict the corresponding HOMO/LUMO pairs in the transition states of the respective [4+2]-cycloaddi-tions. Evaluation of Equation 15.2 reveals two new bonding HOMO/LUMO interactions of comparable size in both transition states. Therefore, the transition states of both cycloadditions benefit from a stabilization that is attenuated by a large energy difference between the frontier orbitals involved. That is why fairly drastic conditions are require for these specific processes.

Fig. 15.8. Frontier orbital interactions in the transition state of the one-step [4+21-cycloaddition of ethene and butadiene.

In contrast to the [4+2]-additions of butadiene to ethene or acetylene (Figures 15.8 and 15.9), the two HOMO/LUMO interactions stabilize the transition state of the [2+2]- addition of ketenes to alkenes to a very different extent. Equation 15.2 reveals that the larger part of the stabilization is due to the LUMOketene/HOMOethene interaction. This circumstance greatly affects the geometry of the transition state. If there were only this one frontier orbital interaction in the transition state, the carbonyl carbon of the ketene would occupy a position in the transition state that would be perpendicular above the midpoint of the ethene double bond. The Newman projection of the transition state (Figure 15.11) shows that this is almost the case but... 

Butadienes with alkyl substituents in the 2-position favor the formation of the so-called para-products (Figure 15.25, X = H) in their reactions with acceptor-substituted dienophiles. The so-called mefa-product is formed in smaller amounts. This regioselectivity increases if the dienophile carries two geminal acceptors (Figure 15.25, X = CN). 2-Phenyl-1,3-butadiene exhibits a higher para -selectivity in its reactions with every unsymmetrical dienophile than any 2-alkyl-1,3-butadiene does. This is even more true for 2-methoxy- 1,3-butadiene and 2-(trimethylsilyloxy)-l,3-butadiene. Equation 15.2, which describes the stabilization of the transition states of Diels-Alder reactions in terms of the frontier orbitals, also explains the para "/"meta "-orientation. The numerators of both fractions assume different values depending on the orientation, while the denominators are independent of the orientation. 

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