Symmetry approaching ethylene molecules

Figure 6.3. D2/1 symmetry coordinates of two approaching ethylene molecules...

Frontier orbital theory also provides the basic framework for analysis of the effect that the symmetiy of orbitals has upon reactivity. One of the basic tenets of MO theory is that the symmetries of two orbitals must match to permit a strong interaction between them. This symmetry requirement, when used in the context of frontier orbital theory, can be a very powerful tool for predicting reactivity. As an example, let us examine the approach of an allyl cation and an ethylene molecule and ask whether the following reaction is likely to occur. 

Let us consider two ethylene molecules approaching each other in such a way that the top of one n system interacts with the bottom of the other. The HOMO of one n system must be matched with the LUMO of the other as shown. In both the cases the phase relationships at one end of the system are wrong for bond formation. So a concerted process in which both new G bonds are formed simultaneously is not possible and the reaction will be termed a symmetry-forbidden reaction. 

Figure 11.14 Symmetry elements for the suprafacial approach of two ethylene molecules.

Consider first the frontier orbital interactions between two ethylene molecules that approach one another in parallel planes ( face to face ). Their HOMOs and LUMOs are indicated in Figure 7-8 on the left and right, respectively. Also shown is the behavior of these orbitals with respect to the symmetry plane bisecting the two... 

Figure 7-8. Frontier orbital interactions in the face-to-face approach of two ethylene molecules. S indicates symmetric and A indicates antisymmetric behavior with respect to the a" symmetry plane.

Inspection of this correlation diagram immediately reveals that there is a problem. One of the bonding orbitals at the left correlates with an antibonding orbital on the product side. Consequently, if orbital symmetry is to be conserved, two ground state ethylene molecules cannot combine via face-to-face approach to give a ground-state cyclobutane, or vice versa. This concerted reaction is symmetry forbidden. ... 

In the present work, the interaction of the ethylene molecule with the (100) surfaces of platinum, palladium and nickel is studied using the cluster model approach. All these metals have a face centered cubic crystal structure. The three metal surfaces are modelled by a two-layer M9(5,4) cluster of C4V symmetry, as shown in Fig. 6, where the numbers inside brackets indicate the number of metal atoms in the first and second layer respectively. In the three metal clusters, all the metal atoms are described by the large LANL2DZ basis set. This basis set treats the outer 18 electrons of platinum, palladium and nickel atoms with a double zeta basis set and treats all the remainder electrons with the effective core potential of Hay and Wadt... 

Fig. 8. The approach of two ethylene molecules to form cydobutane. The symmetry planes oi and og are also shown...

Consider first the frontier orbital interactions between two ethylene molecules that approach one another in parallel planes ( face to face ). Their HOMOs and LUMOs are indicated in Figure 7-8 on the left and right, respectively. Also shown is the behavior of these orbitals with respect to the symmetry plane bisecting the two breaking ir bonds. Since the HOMOs are symmetric and the LUMOs are antisymmetric with respect to this operation, there is a symmetry mismatch between the HOMO of one molecule and the LUMO of the other. The symmetry-allowed combination is between the two filled HOMOs. Since the interaction of two filled molecular orbitals of the same energy is destabilizing, the reaction will not occur thermally. 

Since the LUMO has the symmetry as just shown, another molecule approaching the ethylene molecule would need to have the same symmetry for a reaction to occur. In that case, the reaction would be considered as symmetry allowed. If the symmetry does not match that of the LUMO of ethylene, the reaction would be symmetry forbidden. In other words, for overlap to be positive (S > 0), the HOMO on one of the reacting molecules must have the same symmetry as the LUMO on the other. 

Fig. 13.2. Orbital correlation diagram for two ground state ethylenes and cyclobutane. The symmetry designations apply, respectively, to the horizontal and vertical planes for two ethylene molecules approaching one another in parallel planes.

The principal component of the reaction coordinate is the approach of the two ethylene molecules towards one another with retention of the full symmetry assumed in the construction of the correspondence diagram as Fig. 6.2 Wcts set up in D2/1, this least motion approach has the irrep ag. The diagram then tells us that the reaction coordinate for concerted conversion of the two tt bonds into the two (T bonds of cyclobutane also has to include a 625 component. Several symmetry coordinates, and the subgroups of D2/1 to which they desymmetrize the reaction path, are shown in Fig. 6.3. If the correspondence diagram had called for an displacement, the relatively facile formation of cyclobutane in its stable puckered D2 conformation would have been expected. If a b u component were required to induce the neccesary correspondence, the favored pathway would generate a cisoid biradical, which would immediately collapse to cyclobutane. The nominally stepwise reaction would then be kinetically indistinguishable from one in which the formation of both bonds is synchronous. 

A few words have to be said here about the concerted [ 2 + 2a] pathway [2, p. 69ff.] in the approach depicted on the right-hand side of Fig. 1.11. It was pointed out in Section 1.4.2 that this pathway is formally allowed only if one of the reacting ethylene molecules is singled out beforehand to react suprafa-cially and the other to react antarafacially. The various ways in which two free ethylene molecules, initially oriented in D2/1, can approach one another were broken down to their component symmetry coordinates (see Section 6.1.2.1) in the primary publication on OCAMS. [9] It was shown that this particular... 

Let us mention some very basic problems to illustrate this point. Consider two ethylene molecules approaching each other for a [2 -F 2] reaction. The answer to the question of whether that reaction is allowed thermally or photo-chemically, or whether a suprafacial or antarafacial process will take place, or whether the reaction will take place at all, is very much dependent on the symmetry of alignment of the two reacting molecules or moieties. The extremes are D2h for a parallel approach and C2 for an orthogonal approach, and it has been predicted successfully that the former is needed for a suprafacial photochemical formation of cyclobutane. Most of the time, however, the two ethylenes are not in an ideal Djh arrangement. This may be due to an intramolecular frozen conformation of the two double bonds, to non-symmetric sterical hindrance caused by substituents on the double bond, and to the dynamical nature of the system (rotations and translations, especially in viscous media). 

The symmetry (a) is shown at top center. At left are the butadiene 7r MO s, classified according to their symmetry with respect to o at right are the ethylene w MO s, also classified according to a. The HOMO of each molecule can interact with the LUMO of the other, and a stabilization occurs as they approach one another. 

Ethylene has the well-known classical >2/1 structure with a barrier to rotation. The next in complexity of the simple hydrides is the methyl radical CH3. The obvious (sp2) planar arrangement can only accommodate six of the seven valence electrons. The electronic configuration of this molecule can therefore not be described in terms of either atomic wave functions or hybrid orbitals. An alternative approach is to view the structure of the methyl radical as a reduced-symmetry form, derived from the structure of methane, to be considered next. 

Now, consider a thermal [2 4 2] cyclization, dimerization of ethylene. This would involve overlap of the HOMO, tt, of one molecule with the LUMO, tt, of the other. But w and n are of opposite symmetry, and, as Fig. 29.21 shows, lobes of opposite phase would approach each other. Interaction is antibonding and repulsive, and concerted reaction does not occur. 

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