Orbital Symmetry Diagrams

The product is cyclobutane. We only draw the MOs relevant to the bonds being formed. These bonds are drawn as C-C a bond group orbitals of the sort we have seen before in Chapter 1. Each individual bond is created from combinations of hybrid orbitals on the carbons where bonding changes have occurred. The molecular orbitals are created by combining the a bond group orbitals. In-phase combinations of the ct bonds are lower in energy than out-of-phase combinations. 

After reading Chapter 14, you might be wondering why we can represent the a bonds in such a simple manner, because fully delocalized MOs without carbon hybridization are the results obtained from sophisticated electronic structure theory. Experience has shown that in pericyclic reactions there is no need to include spectator bonds , bonds that remain intact throughout the reaction, in the analysis. Remember that orbitals and our notions of bonding are just models. Any model that explains experimental results and can predict them is useful, and the simplest is always the best. Here we show the simplest model that works. We could complicate our model by including the spectator bonds, but the results would be the same. 

The two examples just discussed illustrate the conservation of orbital symmetry approach. Orbitals of reactants correlate with product orbitals of like symmetry. Whether a reaction is allowed or forbidden in the geometry assumed is determined by whether the ground state of the starting material correlates to the ground state or an excited state of the products. The key to the method is to recognize symmetry elements that persist throughout the reaction and to correlate molecular orbitals of like symmetry. In subsequent sections we 

Symmetry with respect to the single mirror plane - 

The orbital correlation diagram for the prototype ]4+2] cycloaddition. Energy levels for the various orbitals are only qualitatively meaningful. 

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In connection with a-ir exchanges of equations (94) and (96), we noted that certain additions or eliminations were forbidden. A typical orbital symmetry diagram for the forbidden four-center bromine addition to an alkene is given in Fig. 22. Apparently similar concerted additions are allowed, e.g. hydrogen halides in equation (97), because favorable orbital overlap is available. 

The addition of to a >C=C< system is thermodynamically favorable but generally difficult to achieve. In the laboratory, chemists use catalysts such as platinum black and Rainey nickel to make the reaction proceed at a reasonable rate. The kinetic barrier for this reaction can be understood in terms of simple orbital symmetry diagrams, shown in Figure 5.2. The basic principle is that in the activated state the electrons must flow in such a way as to make and break the appropriate bonds. In the case of hydrogenation, the electron flow must break the H—H o and C—C n bonds and make two C—H bonds. The electrons must flow from an occupied orbital on one molecule to an unoccupied orbital on the other, that is, from the highest occupied molecular orbital, HOMO, on one species to the lowest unoccupied molecular orbital, LUMO, on the other. 

Connecting the energy-ordered orbitals of reactants to those ofproducts according to symmetry elements that are preserved throughout the reaction produces an orbital correlation diagram. 

Determine the symmetries of the resultant moleeular orbitals in the D3h point group. Draw a qualitative orbital energy diagram using the HMO energies you have ealeulated. 

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. 

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

Correlation diagrams can be constructed in an analogous fashion for the disrotatory and conrotatory modes for interconversion of hexatriene and cyclohexadiene. They lead to the prediction that the disrotatory mode is an allowed process whereas the conrotatory reaction is forbidden. This is in agreement with the experimental results on this reaction. Other electrocyclizations can be analyzed by the same method. Substituted derivatives of polyenes obey the orbital symmetry rules, even in cases in which the substitution pattern does not correspond in symmetiy to the orbital system. It is the symmetry of the participating orbitals, not of the molecule as a whole, that is crucial to the analysis. 

We have now considered three viewpoints from which thermal electrocyclic processes can be analyzed symmetry characteristics of the frontier orbitals, orbital correlation diagrams, and transition-state aromaticity. All arrive at the same conclusions about stereochemistiy of electrocyclic reactions. Reactions involving 4n + 2 electrons will be disrotatory and involve a Hiickel-type transition state, whereas those involving 4n electrons will be conrotatory and the orbital array will be of the Mobius type. These general principles serve to explain and correlate many specific experimental observations made both before and after the orbital symmetry mles were formulated. We will discuss a few representative examples in the following paragraphs. 

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... 

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. 

The complementary relationship between thermal and photochemical reactions can be illustrated by considering some of the same reaction types discussed in Chapter 11 and applying orbital symmetry considerations to the photochemical mode of reaction. The case of [2ti + 2ti] cycloaddition of two alkenes can serve as an example. This reaction was classified as a forbidden thermal reaction (Section 11.3) The correlation diagram for cycloaddition of two ethylene molecules (Fig. 13.2) shows that the ground-state molecules would lead to an excited state of cyclobutane and that the cycloaddition would therefore involve a prohibitive thermal activation energy. 

Fig. 13.3. Orbital correlation diagram for one ground-state ethene and one excited-state ethene. The symmetry designations apply, respectively, to the horizontal and vertical planes for two ethene molecules approaching one another in parallel planes.

The methylene group carries an empty p orbital. Howr will the methyl group interact w ith this empty orbital Clearly the 7r-type orbitals of the methyl group (ttu in E, tt. in B) have the appropriate symmetry to mix with the p orbital. A typical orbital interaction diagram (for E) is shown in Fig. 37. Several conclusions emerge immediately from this diagram ... 

We will conclude this section on theory with such a case. In Section 8.3 it was shown that the influence of substituents on the rate of dediazoniation of arenediazonium ions can be treated by dual substituent parameter (DSP) methods, and that kinetic evidence is consistent with a side-on addition of N2. We will now discuss these experimental conclusion with the help of schematic orbital correlation diagrams for the diazonium ion, the aryl cation, and the side-on ion-molecule pair (Fig. 8-5, from Zollinger, 1990). We use the same orbital classification as Vincent and Radom (1978) (C2v symmetry). 

This crossing is, in turn, an orbital symmetry requirement for the fragmentation to follow the allowed process through path [1 ], as shown by the level diagram of Fig. 12b. 

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