1,3-Butadiene symmetry

Figure 2.13 (a) symmetry of p, orbital on oxygen atom in H 0 symmetry group C, . (b Symmetry of 2/m bonding MO of s-trans-butadiene symmetry Cjj. 

Electi ocyclic reactions are examples of cases where ic-electiDn bonds transform to sigma ones [32,49,55]. A prototype is the cyclization of butadiene to cyclobutene (Fig. 8, lower panel). In this four electron system, phase inversion occurs if no new nodes are fomred along the reaction coordinate. Therefore, when the ring closure is disrotatory, the system is Hiickel type, and the reaction a phase-inverting one. If, however, the motion is conrotatory, a new node is formed along the reaction coordinate just as in the HCl + H system. The reaction is now Mdbius type, and phase preserving. This result, which is in line with the Woodward-Hoffmann rules and with Zimmerman s Mdbius-Huckel model [20], was obtained without consideration of nuclear symmetry. This conclusion was previously reached by Goddard [22,39]. 

FIGURE 10 11 The HOMO of 1 3 butadiene and the LUMO of ethylene have the proper symmetry to allow cr bond formation to occur at both ends of the diene chain in the same tran sition state... 

Let us now examine the Diels-Alder cycloaddition from a molecular orbital perspective Chemical experience such as the observation that the substituents that increase the reac tivity of a dienophile tend to be those that attract electrons suggests that electrons flow from the diene to the dienophile during the reaction Thus the orbitals to be considered are the HOMO of the diene and the LUMO of the dienophile As shown m Figure 10 11 for the case of ethylene and 1 3 butadiene the symmetry properties of the HOMO of the diene and the LUMO of the dienophile permit bond formation between the ends of the diene system and the two carbons of the dienophile double bond because the necessary orbitals overlap m phase with each other Cycloaddition of a diene and an alkene is said to be a symmetry allowed reaction... 

Symmetry allowed reaction (Section 10 14) Concerted reac tion in which the orbitals involved overlap in phase at all stages of the process The conrotatory ring opening of cy clobutene to 1 3 butadiene is a symmetry allowed reaction... 

There are several general classes of pericyclic reactions for which orbital symmetry factors determine both the stereochemistry and relative reactivity. The first class that we will consider are electrocyclic reactions. An electrocyclic reaction is defined as the formation of a single bond between the ends of a linear conjugated system of n electrons and the reverse process. An example is the thermal ring opening of cyclobutenes to butadienes ... 

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. 

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 11.3 illustrates the classification of the MOs of butadiene and cyclobutene. There are two elements of symmetry that are common to both s-cw-butadiene and cyclobutene. These are a plane of symmetry and a twofold axis of rotation. The plane of symmetry is maintained during a disrotatory transformation of butadiene to cyclobutene. In the conrotatory transformation, the axis of rotation is maintained throughout the process. Therefore, to analyze the disrotatory process, the orbitals must be classified with respect to the plane of symmetry, and to analyze the conrotatory process, they must be classified with respect to the axis of rotation. 

Fig. 11.3. Symmetry properties of cyclobutene (top) and butadiene (bottom) orbitals.

Fig. 11.4. Correlation diagram for cyclobutene and butadiene orbitals (symmetry-forbidden disrotatory reaction).

Cycloaddition involves the combination of two molecules in such a way that a new ring is formed. The principles of conservation of orbital symmetry also apply to concerted cycloaddition reactions and to the reverse, concerted fragmentation of one molecule into two or more smaller components (cycloreversion). The most important cycloaddition reaction from the point of view of synthesis is the Diels-Alder reaction. This reaction has been the object of extensive theoretical and mechanistic study, as well as synthetic application. The Diels-Alder reaction is the addition of an alkene to a diene to form a cyclohexene. It is called a [47t + 27c]-cycloaddition reaction because four tc electrons from the diene and the two n electrons from the alkene (which is called the dienophile) are directly involved in the bonding change. For most systems, the reactivity pattern, regioselectivity, and stereoselectivity are consistent with describing the reaction as a concerted process. In particular, the reaction is a stereospecific syn (suprafacial) addition with respect to both the alkene and the diene. This stereospecificity has been demonstrated with many substituted dienes and alkenes and also holds for the simplest possible example of the reaction, that of ethylene with butadiene ... 

How do orbital symmetry requirements relate to [4tc - - 2tc] and other cycloaddition reactions Let us constmct a correlation diagram for the addition of butadiene and ethylene to give cyclohexene. For concerted addition to occur, the diene must adopt an s-cis conformation. Because the electrons that are involved are the n electrons in both the diene and dienophile, it is expected that the reaction must occur via a face-to-face rather than edge-to-edge orientation. When this orientation of the reacting complex and transition state is adopted, it can be seen that a plane of symmetry perpendicular to the planes of the... 

An orbital correlation diagram can be constructed by examining the symmetry of the reactant and product orbitals with respect to this plane. The orbitals are classified by symmetry with respect to this plane in Fig. 11.9. For the reactants ethylene and butadiene, the classifications are the same as for the consideration of electrocyclic reactions on p. 610. An additional feature must be taken into account in the case of cyclohexene. The cyclohexene orbitals tr, t72. < i> and are called symmetry-adapted orbitals. We might be inclined to think of the a and a orbitals as localized between specific pairs of carbon... 

Fig. 11.9. Symmetry properties of ethylene, butadiene, and cyclohexene orbitals with respect to cycloaddition.

When the orbitals have been classified with respect to symmetry, they can be arranged according to energy and the correlation lines can be drawn as in Fig. 11.10. From the orbital correlation diagram, it can be concluded that the thermal concerted cycloadditon reaction between butadiene and ethylene is allowed. All bonding levels of the reactants correlate with product ground-state orbitals. Extension of orbital correlation analysis to cycloaddition reactions involving other numbers of n electrons leads to the conclusion that the suprafacial-suprafacial addition is allowed for systems with 4n + 2 n electrons but forbidden for systems with 4n 7t electrons. 

Figure 15.16 Reaction of butadiene and ethylene to form cyclohexene under Cj symmetry...

Let us finally consider two Z-matrices for optimization to transition structures, the Diels-Alder reaction of butadiene and ethylene, and the [l,5]-hydrogen shift in Z-1,3-pentadiene. To enforce the symmetries of the TSs (Cj in both cases) it is again advantageous to use dummy atoms. 

Symmetry considerations have also been advanced to explain predominant endo addition. In the case of 2 + 4 addition of butadiene to itself, the approach can be exo or endo. It can be seen (Fig. 15.10) that whether the HOMO of the diene overlaps with the LUMO of the alkene or vice versa, the... 

Although the orbital-symmetry rules predict the stereochemical results in almost all cases, it is necessary to recall (p. 1070) that they only say what is allowed and what is forbidden, but the fact that a reaction is allowed does not necessarily mean that the reaction takes place, and if an allowed reaction does take place, it does not necessarily follow that a concerted pathway is involved, since other pathways of lower energy may be available.Furthermore, a forbidden reaction might still be made to go, if a method of achieving its high activation energy can be found. This was, in fact, done for the cyclobutene butadiene interconversion (cis-3,4-dichloro-cyclobutene gave the forbidden cis.cis- and rran.y, ra i -l,4-dichloro-1,3-butadienes,... 

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. 

Diels-Alder reactions are allowed by orbital symmetry in the delocalization band and so expected to occur on the surface. In fact, [4-1-2] cycloaddition reaction occurs on the clean diamond (100)-2 x 1 surface, where the surface dimer acts as a dienophile. The surface product was found to be stable up to approximately 1,000 K [59, 60], 1,3-Butadiene attains high coverage as well as forms a thermally stable adlayer on reconstructed diamond (100)-2 x 1 surface due to its ability to undergo [4h-2] cycloaddition [61],... 

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