M. Hargittai, I. Hargittai - Symmetry through the Eyes of a Chemist (793765), страница 52
Текст из файла (страница 52)
Of course, its high degree of rigor mayrender its application more complicated as compared with themethods which focus only upon changes in the electronic structure.The approaches introduced by Fukui and Woodward and Hoffmannseem to have received more widespread acceptance and utilization.7.3. Examples7.3.1. Cycloaddition7.3.1.1. Ethylene DimerizationThe interaction of two ethylene molecules will be considered intwo geometrical arrangements.
The two molecules adopt a mutuallyparallel approach in one arrangement and a mutually perpendicularapproach in the other. Applications of various methods will be considered briefly.(a) Parallel Approach, HOMO-LUMO. According to the frontierorbital method only the HOMOs and the LUMOs of the twoethylene molecules need to be considered. A further simplificationis introduced in the pictorial description of the interactions. Althoughthe molecular orbitals of the reactants are used to construct the MOsof the products, the former are usually drawn schematically as atomicorbitals from which they are built. The reason is that the form of theatomic orbitals is better defined and better understood than is the formof the molecular orbitals without resorting to actual calculations.The MOs of ethylene can be constructed according to the principles given in the preceding chapter.
The HOMO of ethylene is thebonding MO, and the LUMO is the antibonding MO composed of thetwo pz orbitals of carbon. These MOs are of b1u and b2g symmetry,respectively in the D2h point group. Figure 7-7 shows them both in asimplified way along with the corresponding contour diagrams.Consider first the frontier orbital interactions between two ethylene molecules that approach one another in parallel planes (“faceto face”). Their HOMOs and LUMOs are indicated in Figure 7-8on the left and right, respectively.
Also shown is the behavior ofthese orbitals with respect to the symmetry plane bisecting the two7.3. Examples329Figure 7-7. The HOMO and LUMO of ethylene.breaking bonds. Since the HOMOs are symmetric and the LUMOsare antisymmetric with respect to this operation, there is a symmetrymismatch between the HOMO of one molecule and the LUMO of theother. The symmetry-allowed combination is between the two filledHOMOs. Since the interaction of two filled molecular orbitals of thesame energy is destabilizing, the reaction will not occur thermally.(b) Parallel Approach, Correlation Diagram.
Now consider the ethylene dimerization using the Woodward–Hoffmann approach. Thereis again the important condition mentioned before which must befulfilled: for the whole reacting system at least one symmetry elementFigure 7-8. Frontier orbital interactions in the face-to-face approach of two ethylene molecules. S indicates symmetric and A indicates antisymmetric behavior withrespect to the symmetry plane.3307 Chemical Reactionsmust persist throughout the entire process.
Let us consider the reactionin this respect. Each separate ethylene molecule has D2h symmetry.When two of these molecules approach one another with their molecular planes parallel as shown in Figure 7-9, the whole system retainsthis symmetry. Finally, the product cyclobutane is of D4h symmetry.Since D2h is a subgroup of D4h , the symmetry elements of D2h persist.One of the symmetry elements in the D2h point group is thesymmetry plane (Figure 7-9).
All of the MOs considered in thisreaction, that is, those associated with the broken bonds of the twoethylene molecules and the two new bonds of cyclobutane lie inthe plane of this symmetry element. All of them will be symmetricto reflection in this plane. There will be no change in their behaviorwith respect to this symmetry operation during the reaction.
Thisbrings us back to a very important point in the construction ofcorrelation diagrams: the symmetry element chosen to follow the reaction must bisect bonds broken or made during the process. Addingextra symmetry elements, like above, will not change the result.It is not wrong to include them; it is just not necessary.
Considering,however, only such symmetry elements could lead to the erroneousconclusion that every reaction is symmetry allowed.As was found to be the case when constructing MOs from AOs, thesymmetry of the reacting system as a whole must be considered ratherthan just the symmetry of the individual molecules alone. Figure 7-10illustrates this point with respect to one of the reflection planes.
Theplane transforms the MO drawn as the two pz orbitals of the twoFigure 7-9. The symmetry of reactants, transition structure, and product in theface-to-face dimerization of ethylene.7.3. Examples331Figure 7-10. The MO of one ethylene molecule alone does not belong to any irreducible representation of the point group of the system of two ethylene molecules.carbon atoms of one ethylene molecule into the molecular orbital ofthe other ethylene molecule. Thus, each MO of the reacting systemhas a contribution from each pz orbital.The possible combinations of the and ∗ orbitals of the two ethylene molecules are presented on the left side of Figure 7-11 in order ofincreasing energy.
Consideration of these MOs shows that 1 + 2 and1∗ + 2∗ are in proper phase to form a bonding MO (that is, closingthe ring). The right side of Figure 7-11 illustrates this, together withthe formation of the antibonding orbitals of cyclobutane.The construction of the correlation diagram is shown inFigure 7-12. The two crucial symmetry elements are indicated in theupper part of the figure.
The molecular orbitals of the reactants andtheir behavior with respect to these symmetry elements are indicatedin order of increasing energy at the left side of the diagram; the corresponding product MOs are shown at the right in this same figure.Since and are maintained throughout the reaction, there mustbe a continuous correlation of orbitals of the same symmetry type.Therefore, orbitals of like symmetry correlate with one another andthey can be connected. This, the crucial idea of the WoodwardHoffmann method, is shown in the central part of the diagram.Inspection of this correlation diagram immediately reveals thatthere 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 ethylenemolecules cannot combine via face-to-face approach to give a groundstate cyclobutane, or vice versa. This concerted reaction is symmetryforbidden.∗∗Note that considerations of either one of the crucial symmetry elements, and ,alone would give the same result.3327 Chemical ReactionsFigure 7-11. Molecular orbitals of the ethylene–ethylene system and the construction of molecular orbitals of cyclobutane.
(The energy scale refers to the reactantorbitals only.)(c) State Correlation. The correlation diagram in Figure 7-12 refersto molecular orbitals. The molecular orbitals and the correspondingelectronic configurations are, however, only substitutes for the realwave functions which describe the actual electronic states. It is theelectronic states that have definite energy and not the electronic7.3. Examples333Figure 7-12. Construction of the correlation diagram for ethylene dimerization withparallel approach.
Adaptation of Figure 10.19 from Reference [61] with permission.3347 Chemical ReactionsTable 7-1. The Symmetry of Molecular Orbitals in the Face-to-Face Dimerizationof EthyleneaEthylene + EthyleneCyclobutaneCharacter under(xz) (xy) (yz)Orbital occupationD2hCharacter under(xz) (xy) (yz)D2h1–1–1b2g——— ———b2g——— ———b1u11–1b3u—|—|— —|—|—b3u1–11b1u—|—|— —|—|—ag111agaThe orientation of the coordinate axes is given in Figure 7-9.1111–1–111–11–11configurations (cf.
Chapter 6). Since electronic transitions occur physically between electronic states, the correlation of these states is ofinterest. It was Longuet-Higgins and Abrahamson who drew attentionto the importance of state-correlation diagrams [62].The rules for the state correlation diagrams are the same as forthe orbital correlation diagrams; only states that possess the samesymmetry can be connected.
In order to determine the symmetriesof the states, first the symmetries of the MOs must be determined.These are given for the face-to-face dimerization of ethylene inTable 7-1. The D2h character table (Table 7-2) shows that the twocrucial symmetry elements are the symmetry planes (xy) and (yz).The MOs are all symmetric with respect to the third plane, (xz) (videsupra). The corresponding three symmetry operations will unambiguously determine the symmetry of the MOs. Another possibilityis to take the simplest subgroup of D2h which already contains thetwo crucial symmetry operations, that is, the C2v point group (cf.,D2hEC2 (z)Table 7-2. The D2h Character TableC2 (y) C2 (x)i(xy) (xz) (yz)AgB1gB2gB3gAuB1uB2uB3u1111111111–1–111–1–11–11–11–11–11–1–111–1–111111–1–1–1–111–1–1–1–1111–11–1–11–111–1–11–111–1RzRyRxzyxx2 , y2 , z2xyxzyz7.3.
![](https://s.studizba.com/z.php?f=/templates/si/i/noavatar.png&w=100&h=100&t=1"){kind=avatar}
