M. Hargittai, I. Hargittai - Symmetry through the Eyes of a Chemist (793765), страница 54
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According to the latest results, this prototype Dields–Alder reaction follows the concerted mechanism, for which the barrierheight of the transition-state is about 13 kJ/mol lower than that of thestepwise mechanism [78].7.3.2. Intramolecular Cyclization(a) Orbital Correlation for the Butadiene/Cyclobutene Interconversion. The electrocyclic interconversion between an open-chainconjugated polyene and a cyclic olefin is another example for theapplication of the symmetry rules.
The simplest case is the interconversion of butadiene and cyclobutene:3447 Chemical ReactionsThis process can occur in principle in two ways. In one the two endsof the open chain turn in the opposite direction into the transition state.This is called a disrotatory reaction.The other possibility is a conrotatory process in which the two endsof the open chain turn in the same direction.The ring opening of substituted cyclobutenes proceeds at relativelylow temperatures and in conrotatory fashion [79], as illustrated by theisomerization of cis- and trans-3,4-dimethylcyclobutene [80]:This stereospecificity is well accounted for by the correlationdiagrams constructed for the unsubstituted butadiene/cyclobuteneisomerization in Figs. 7-18 and 7-19.
Since two double bonds in butadiene are broken and a new double bond and a single bond are formedduring the cyclization, two bonding and two antibonding orbitals mustbe considered on both sides. The persisting symmetry element is aplane of symmetry in the disrotatory process. The correlation diagram(Figure 7-18) shows a bonding electron pair moving to an antibonding7.3. Examples345Figure 7-18. Correlation diagram for the disrotatory closure of butadiene.
Adaptation of Figure 10.14 from reference [81] with permission.level in the product, and, thus, the right-hand side corresponds toan excited-state configuration. The disrotatory ring opening is thusa thermally forbidden process.Figure 7-19 shows the same reaction with conrotatory ring closure.Here, the symmetry element maintained throughout the reaction isthe C2 rotation axis. After connecting orbitals of like symmetry, it is3467 Chemical ReactionsFigure 7-19. Correlation diagram for the conrotatory ring closure in the butadienecyclobutene isomerization. Adaptation of Figure 10.12 from reference [82] withpermission.seen that all ground-state reactant orbitals correlate with ground-stateproduct orbitals, so the process is thermally allowed.(b) Symmetry of the Reaction Coordinate–Cyclobutene Ring Opening.It is interesting to consider the butadiene–cyclobutene reaction froma somewhat different viewpoint, viz., to determine whether thesymmetry of the reaction coordinate does indeed predict the properreaction.
Let us look at the reaction from the opposite direction, i.e.,7.3. Examples347the cyclobutene ring opening process. From the symmetry point ofview, this change of direction is irrelevant.The symmetry group of both cyclobutene and butadiene is C2v butthe transition state is of C2 symmetry in the conrotatory and Cs inthe disrotatory mode. Pearson [83] suggested that this reaction mightbe visualized in the following way. In the cyclobutene–butadienetransition, two bonds of cyclobutene are destroyed, to wit the ringclosing and the opposite bonds. Hence, four orbitals are involvedin the change, the filled and empty and ∗ orbitals and the filled andempty and ∗ orbitals.
These orbitals are indicated in Figure 7-20.Their symmetry is also given for the three point groups involved.Figure 7-21 demonstrates the nuclear movements involved in theconrotatory and disrotatory ring opening. These movements define thereaction coordinate, and they belong to the A2 and B1 representationof the C2v point group, respectively.The two bonds of cyclobutene can be broken either by removingelectrons from a bonding orbital or by putting electrons into an antibonding orbital.
Consider the → ∗ and the → ∗ transitions.Figure 7-20. The molecular orbitals participating in the cyclobutene ring opening.3487 Chemical ReactionsFigure 7-21. The symmetry of the reaction coordinate in the conrotatory and disrotatory ring opening of cyclobutene.According to Pearson [84], the direct product of the two representations must contain the reaction coordinate: → ∗ : a1 · a2 = a2 → ∗ : b1 · b2 = a2A2 is the irreducible representation of the conrotatory ring openingmotion, so this type of ring opening seems to be possible. We can testthe rules further.
During a conrotatory process, the symmetry of thesystem decreases to C2 . The symmetry of the relevant orbitals alsochanges in this point group (see Figure 7-20). Both a1 and a2 becomea, and both b1 and b2 become b. Therefore, these orbitals are ableto mix. Also, the symmetry of the reaction coordinate becomes A.This is consistent with the rule saying that the reaction coordinate,except at maxima and minima, must belong to the totally symmetricrepresentation of the point group.The next step is to test whether the disrotatory ring opening ispossible.
The → ∗ and → ∗ transitions obviously cannot beused here, since they correspond to the conrotatory ring opening of A2symmetry. Let us consider the → ∗ and the → ∗ transitions: → ∗ : a1 · b2 = b2 → ∗ : b1 · a2 = b2Both direct products contain the B2 irreducible representation. Itcorresponds to an in-phase asymmetric distortion of the molecule,7.3. Examples349which cannot lead to ring opening.
The symmetry of the disrotatoryreaction coordinate is B1 (Figure 7-21). Moreover, if we considerthe symmetry of the orbitals in the Cs symmetry point group ofthe disrotatory transition, it appears that and ∗ as well as and ∗ belong to different irreducible representations. Hence, theirmixing would not be possible anyway. The prediction from thismethod is the same as the prediction from the orbital correlationdiagrams. While examination of the reaction coordinate gives moreinsight into what is actually happening during a chemical reaction, it is somewhat more complicated than using orbital correlationdiagrams.An ab initio calculation of the cyclobutene to butadiene ringopening [85] led to the following observation.
In the conrotatoryprocess, first the C–C carbon single bond lengthens followed bytwisting of the methylene groups. The C–C bond lengthening is asymmetric stretching mode with A1 symmetry and the methylene twistis an A2 symmetry process which was earlier supposed to be the reaction coordinate. This apparent controversy was resolved by Pearson[86], who emphasized the special role of the totally symmetric reaction coordinate. The effect of the C–C stretch is shown in Figure 7-22.The energies of the and ∗ orbitals increase and decrease, respectively, as a consequence of the bond lengthening. The A1 symmetryvibrational mode does not change the molecular symmetry.
Thecrucial → ∗ and →∗ transitions, which are symmetry related toFigure 7-22. The effect of C–C stretching on the energies of the critical orbitals inthe cyclobutene ring opening.3507 Chemical Reactionsthe A2 twisting mode, occur more easily. Apparently, the large energydifference between these orbitals is the determining factor in theactual process. The transition structure for this electrocyclic reactionhas been studied extensively by means of quantum-chemical calculations [87]. Their results fully support the conclusions of the abovereasoning.We have to stress again that there might be special reasons thatmake a disrotatory process or a stepwise mechanism favored over theconrotatory process; such as ring-strains and steric effects [88].7.3.3. Generalized Woodward–Hoffmann RulesThe selection rules for chemical reactions derived by using symmetryarguments show a definite pattern.
Woodward and Hoffmann generalized the selection rules on the basis of orbital symmetry considerationsapplied to a large number of systems [89]. Two important observations are summarized here; we refer to the literature for further details[90, 91].(a) Cycloaddition. The reaction between two molecules is thermallyallowed if the total number of electrons in the system is 4n + 2 (n is aninteger), and both components are either suprafacial or antarafacial. Ifone component is suprafacial and the other is antarafacial, the reactionwill be thermally allowed if the total number of electrons is 4n.(b) Electrocyclic reactions. The rules are similar to those given above.A disrotatory process is thermally allowed if the total number of electrons is 4n + 2, and a conrotatory process is allowed thermally if thenumber of delocalized electrons is 4n. For a photochemical reaction,both sets of rules are reversed.7.4.
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