M. Hargittai, I. Hargittai - Symmetry through the Eyes of a Chemist (793765), страница 53
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Examples335Reference [63]). In these two approaches only the designation of theorbitals and states is different; the outcome, i.e., the state correlationdiagram, is the same.In determining the symmetries of the states (see Chapter 6), wemust remember that states with completely filled orbitals are alwaystotally symmetric. In other cases, the symmetry of the state is determined by the direct product of the incompletely filled orbitals.2The ground-state configuration of the two-ethylene system is ag2 b1u(see Table 7-1). This state is totally symmetric, Ag . The excitationof an electron from the HOMO to the LUMO will give an electronconfiguration: ag2 b1u b3u .
The direct product is:b1u · b3u = b2gThis yields a state of B2g symmetry. The electronic configuration of2the product is ag2 b3u, again with Ag symmetry. This electron configuration corresponds to a doubly excited state of the reactants. Finally,the state correlation diagram can be drawn (Figure 7-13).An obvious connection between states that possess the same electronic configuration would be the one indicated by dashed lines inFigure 7-13.
This does not occur, however, because states of the samesymmetry cannot cross. This is, again, a realization of the noncrossingrule, which applies to electronic states as well as to orbitals. Insteadof crossing, when two states are coming too close to each other theywill turn away, and so the two ground states, both of Ag symmetry andalso two Ag symmetry excited states will each mutually correlate.Figure 7-13. State correlation diagram for the ethylene dimerization.3367 Chemical ReactionsThe solid line connecting the two ground states in Figure 7-13indicates that there is a substantial energy barrier to the groundstate-to-ground-state process; this reaction is said to be “thermallyforbidden”.Consider now one electron in the reactant system excited photochemically to the B2g state.
Since this state correlates directly with theB2g state of the product, this reaction does not have any energy barrierand may occur directly. It is said that the reaction is “photochemicallyallowed.” Indeed, it is an experimental fact that olefin dimerizationoccurs smoothly under irradiation.This observation can be generalized. If a concerted reaction is thermally forbidden, it is photochemically allowed and vice versa; if it isthermally allowed then it is photochemically forbidden.Although the state correlation diagram is physically more meaningful than the orbital correlation diagram, usually the latter is usedbecause of its simplicity. This is similar to the kind of approximationmade when the electronic wave function is replaced by the productsof one-electron wave functions in MO theory.
The physical basis forthe rule that only orbitals of the same symmetry can correlate is thatonly in this case can constructive overlap occur. This again has itsanalogy in the construction of molecular orbitals. The physical basisfor the noncrossing rule is electron repulsion. It is important that thisapplies to orbitals—or states—of the same symmetry only. Orbitals ofdifferent symmetry cannot interact anyway, so their correlation linesare allowed to cross.(d) Parallel Approach, Orbital Correspondence Analysis.
It is worthwhile to see what additional information can be learned from orbitalcorrespondence analysis [64, 65]. The correspondence diagram of theethylene dimerization reaction is drawn after Halevi in Figure 7-14.It is essentially the same as the correlation diagram in Figure 7-12with the following difference: Here the maximum symmetry of thesystem, D2h , is taken into consideration, and the irreducible representation of each MO in this point group is shown. The solid lines ofthe diagram connect molecular orbitals of the same symmetry. Thisis the same as the correlation diagram derived from consideration ofthe crucial symmetries.
In addition, we can see that the required transition toward producing a stable ground-state cyclobutane would befrom an MO of b1u symmetry to another MO of b3u symmetry. The7.3. Examples337Figure 7-14. Correspondence diagram of the face-to-face dimerization of ethylene.After Reference [65] reproduced with permission.symmetry of the necessary vibration is given by the direct product ofthese MOs:b1u · b3u = b2gThe B2g symmetry motion of a rectangle of D2h symmetry would bean in-plane vibration that shortens one of the diagonals and lengthensthe other:3387 Chemical ReactionsThis result suggests a stepwise mechanism—and also it shows thevalue of the additional information yielded by the orbital correspondence approach.
In the suggested stepwise mechanism the first step isthe formation of a transoid tetramethylene biradical. Then, this intermediate rotates, thereby permitting closure of the cyclobutane ringin a second step. The nature of this reaction has been studied extensively. The reverse of ethylene dimerization, the pyrolysis of cyclobutane, was experimentally observed long ago [66]. Soon after, quantumchemical calculations and thermochemical considerations suggestedthat the pyrolysis proceeds through a 1,4-biradical intermediate [67].As to ethylene dimerization, it is subject to continuing interest.
Thereactive intermediate tetramethylene radical was identified by experiment using femtosecond laser techniques. Quantum chemical calculations still do not completely agree on the nature of the reaction and ofthe intermediate [68], for recent literature, see, e.g., Reference [69].(e) Orthogonal Approach. Let us consider ethylene dimerization in yetanother approach. Assume that the orientation of the two molecules isorthogonal:There is one symmetry element that is maintained in this arrangement, i.e., the C2 rotation. Considering the behavior of the reactant MOs and the product MOs under the C2 operation, the correlation diagram shown in Figure 7-15 can be drawn. It shows that bothbonding MOs of the reactant side correlate with a bonding MO onthe product side.
There is a net energy gain in the reaction, and theprocess is “thermally allowed”.One of the ethylene molecules enters the above reaction antarafacially; this means that the two new bonds are formed on opposite sidesof this molecule:7.3. Examples339Figure 7-15. Correlation diagram for the orthogonal orientation of two ethylenemolecules in the dimerization reaction. Adaptation of Figure 10.22 from reference[70] with permission.The other ethylene molecule enters the reaction suprafacially; thismeans that the two new bonds are formed on the same side of thissecond molecule:Thus, in the orthogonal approach the two molecules enter the reaction differently: one of them antarafacially and the other suprafacially.3407 Chemical ReactionsOn the other hand, in the parallel approach of two ethylenes, bothmolecules enter the reaction suprafacially:The following abbreviation is often used in the literature: 2s + 2smeans that both ethylene molecules are approaching in a suprafacialmanner, while 2s + 2a indicates that the same molecules are reactingin a process which is suprafacial for one component and antarafacialfor the other.
The number 2 indicates that two electrons arecontributed by each ethylene molecule.Just for the sake of completeness it is worthwhile mentioningthat, according to the orbital correspondence analysis, this 2s + 2acycloaddition of ethylene is also thermally forbidden [71]. Quantumchemical calculations [72] reported a transition structure for this thermally allowed concerted reaction, but due to steric repulsions betweensome of the hydrogens, this transition structure is very high in energy.Indeed, the reaction is not observed experimentally.7.3.1.2. Diels–Alder Reaction(a) HOMO–LUMO Interaction.
Another famous example that demonstrates the applicability of symmetry rules in determining the courseof chemical reactions is the Diels–Alder reaction. It was discussed inFukui’s seminal paper [73] on the frontier orbital method. Figure 7-16illustrates the HOMOs and LUMOs of ethylene (dienophile) and butadiene (diene). The only symmetry element common to both the dieneand dienophile is the reflection plane that passes through the central2,3-bond of the diene and the double bond of the dienophile. Thesymmetry behavior of the MOs with respect to this symmetry elementis also shown.There are two favorable interactions here.
One is between theHOMO of ethylene and the LUMO of butadiene, and the other isbetween the HOMO of butadiene and the LUMO of ethylene. Thesetwo interactions occur simultaneously. There is, however, a difference in the role of these two interactions because of their differentsymmetry behavior. The HOMO of ethylene and the LUMO ofbutadiene are symmetric with respect to the symmetry element that7.3. Examples341Figure 7-16. HOMO–LUMO interaction in the Diels–Alder reaction.is maintained throughout the reaction.
There is no nodal plane atthis symmetry element, so the electrons can be delocalized over thewhole new bond. Thus, both carbon atoms of ethylene are boundsynchronously to both terminal atoms of butadiene.The situation is different with the other HOMO–LUMO interaction. These orbitals are antisymmetric with respect to the symmetryelement, and the two ends of the new linkage are separated by anodal plane.
Therefore, two separate chemical bonds will form, eachconnecting an ethylene carbon atom with a terminal butadiene carbonatom. From this consideration, it follows that the first symmetric interaction is the dominant one. Also, the symmetric pair (HOMO of ethylene and LUMO of butadiene) are closer in energy and thus give astronger interaction.(b) Orbital Correlation Diagram. The ethylene and butadienemolecules must approach each other in the manner indicated at thetop of Figure 7-17 in order to participate in a concerted reaction.There is only one persisting symmetry element in this arrangement,viz.
the plane which bisects the 2,3-bond of the diene and the doublebond of the dienophile. The orbitals affected by the reaction are the orbitals of the reactants which will be broken; two new bonds andone new bond are formed in the product. The orbitals and their3427 Chemical ReactionsFigure 7-17. Orbital correlation diagram for the ethylene-butadiene cycloaddition.Adaptation of Figure 10.20 from reference [74] with permission.7.3. Examples343antibonding pairs for the reactants are shown on the left-hand side ofFigure 7-17. The new and orbitals, both bonding and antibonding,of the product cyclohexene are on the right-hand side of this figure.These are the orbitals that are affected by the reaction. The behaviorof these orbitals with respect to the vertical symmetry plane is alsoindicated. The correlation diagram shows that all the filled bondingorbitals of the reactants correlate with filled ground-state bondingorbitals of the product.
The reaction, therefore, is symmetry allowed.The predictions that arise by application of the correlation method andby application of the HOMO–LUMO treatment are identical.The ethylene–butadiene cycloaddition is a good example to illustrate that symmetry allowedness does not necessarily mean that thereaction occurs easily. This reaction has a comparatively high activation energy, around 120–150 kJ/mol, depending on the method ofdetermination. A large number of quantum chemical calculations hasbeen devoted to this reaction with conflicting results and it has beenthe subject of heated debates (for references, see, References [75]and [76]). The difficulty is that, apparently, the stepwise reaction hasan activation energy very similar to that of the concerted reaction.The opposite reaction, the breaking of cyclohexene into butadieneand ethylene, was also studied by femtosecond-resolved mass spectrometry [77].
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