Butadiene orbital diagram

Refer to the molecular orbital diagrams of allyl cation (Figure 10 13) and those presented earlier in this chapter for ethylene and 1 3 butadiene (Figures 10 9 and 10 10) to decide which of the following cycloaddition reactions are allowed and which are forbidden according to the Woodward-Floffmann rules... 

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

The butadiene orbitals are denoted F and the orbital representing the donor substituent D. The MO diagram (c) below shows that the HOMO of the 1-substituted... 

We have drawn the molecular orbital diagram for the n molecular orbitals of butadiene as a result of combining the Jt molecular orbitals of two ethene molecules. There are some important points to notice here. 

Since the HMO Fock matrix is not dependent on the orbital coefficients, no SCF procedure as for ab initio methods (Sec. 2) has to be performed. In the present example withiVc = 4, the four orbital energies are x = 1.618/1, x2 = 0.618/1, x3 = —0.618/1, and x4 = —1.618/1. Since the parameter /I is chosen to be negative, the first energy xq has the lowest value, and the fourth x4 has the highest value. This corresponds to the usual convention in quantum chemistry. From these values, the orbital diagram of butadiene can be drawn. 

Electron delocalization also causes a conjugated diene to be more stable than an isolated diene. The tt electrons in each of the double bonds of an isolated diene are localized between two carbons. In contrast, the rr electrons in a conjugated diene are delocalized. As you discovered in Section 7.6, electron delocalization stabilizes a molecule. Both the resonance hybrid and the molecular orbital diagram of 1,3-butadiene in Figure 7.9 show that the single bond in 1,3-butadiene is not a pure single bond, but has partial double-bond character as a result of electron delocalization. 

The molecular orbital diagram also helps us explain some aspects of the reactivity of butadiene. Notice that we have marked on for you the HOMO ( /2) and the LUMO ( /3). On either side you can see the equivalent HOMO (re orbital) and LUMO (re orbital) for the isolated alk-ene (i.e. ethene). Some relevant features to note ... 

The symmetry properties of the cyclobutene and butadiene orbitals with respect to this twofold axis are shown in Fig. 10.5 and the derived correlation diagram, in Fig. 10.6. This reaction is symmetry-allowed, since the bonding orbitals of cyclobutene correlate with the bonding orbitals of butadiene, and vice versa. 

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. 

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. 11.10. Orbital correlation diagram for ethylene, butadiene, and cyclohexene orbitals.

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 15.21 Orbital correlation diagram for the disrotatoric ring closure of butadiene...

In a concerted reaction, orbital and state symmetry is conserved throughout the course of the reaction. Thus a symmetric orbital in butadiene must transform into a symmetric orbital in cyclobutene and an antisymmetric orbital must transform into an antisymmetric orbital. In drawing the correlation diagram, molecular orbitals of one symmetry on one side of the diagram are connected to orbitals of the same symmetry on the other side, while observing the noncrossing rule. 

FIGURE 10. Correlation diagram showing the influence of non-bonded through-space (n.bd.th.sp) interaction between the pseudo w-orbitals. t(( IU ) (circles) and the double-bond tr-orbitals tra and (ovals) on the 7r-orbital energies of the butadiene w-system. Aa is the basis energy of tra and 7Tb and SA the inductive and hyperconjugative destabilization (see equation 34)... 

FIGURE 22. Top Labels of the four localized basis w-orbitals of [4.4]spirononatetraene 247 and Newman projection defining their relative phases. Middle Newman projections of the four linear combinations ld2(tr), b <7T) and 1 c(jt). defined in equation 59. Bottom Correlation diagram showing the splitting due to spiroconjugation between the butadiene moieties in 247... 

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