M. Hargittai, I. Hargittai - Symmetry through the Eyes of a Chemist (793765), страница 55
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Hückel–Möbius ConceptThere are a number of other methods used to predict and interpretchemical reactions without relying upon symmetry arguments. It isworthwhile to compare at least some of them with symmetry-basedapproaches.7.4. Hückel–Möbius Concept351The so-called “aromaticity rules” are chosen for comparison, asthey provide a beautiful correspondence with the symmetry-basedWoodward–Hoffmann rules. A detailed analysis [92] showed theequivalence of the generalized Woodward–Hoffmann selection rulesand the aromaticity-based selection rules for pericyclic reactions.Zimmermann [93] and Dewar [94] have made especially importantcontributions in this field.The word “aromaticity” usually implies that a given molecule isstable, compared to the corresponding open chain hydrocarbon. Fora detailed account on aromaticity, see, e.g., Reference [95]. Thearomaticity rules are based on the Hückel–Möbius concept.
A cyclicpolyene is called a Hückel system if its constituent p orbitals overlapeverywhere in phase, i.e., the p orbitals all have the same sign aboveand below the nodal plane (Figure 7-23). According to Hückel’s rule[96], if such a system has 4n + 2 electrons, the molecule will bearomatic and stable. On the other hand, a Hückel ring with 4n electrons will be antiaromatic.Based on simple Hückel molecular orbital calculations,Heilbronner predicted that if the Hückel ring is twisted once,as shown in Figure 7-24a, the situation is reversed [97].
Dewar[98] referred to this twisted ring as an “anti-Hückel system.” It isalso called a “Möbius system” [99], an appropriate name indeed.The Möbius strip is a—somewhat against common-sense—twodimensional surface with only one side. It is formed by twisting thestrip by 180◦ around its own axis and then attaching its two ends.There is a phase inversion at the point where the two ends meet,as seen in Figure 7-24a and b.
The Möbius strip was discoveredsimultaneously and independently by two German mathematicians,August Ferdinand Möbius (1790–1868) and Johann Benedict Listing(1808–1882). It fascinates mathematicians and artists as well asFigure 7-23. Illustration of a Hückel ring.3527 Chemical Reactions(a)(b)(c)(d)(e)(f)Figure 7-24. (a) Illustration of a Möbius ring; (b) Möbius strip. Drawing by the lateGyorgy Doczi; (c) Möbius strip-sculpture, Evanston, IL; (d) Möbius strip-sculpture,Cambridge, Massachussetts; (e) Möbius strip-sculpture at Fermilab in Batavia, Illinois; (f) Möbius strip on the facade of a Moscow scientific institute. Photographs bythe authors.7.4.
Hückel–Möbius Concept353chemists [100]. Figure 7-24c–f depict Möbius strips from differentparts of the world.According to Zimmermann [101] and Dewar [102], the allowednessof a concerted pericyclic reaction can be predicted in the followingway: A cyclic array of orbitals belongs to the Hückel system if ithas zero or an even-number phase inversions. For such a system, atransition state with 4n + 2 electrons will be thermally allowed due toaromaticity, while the transition state with 4n electrons will be thermally forbidden due to antiaromaticity.A cyclic array of orbitals is a Möbius system if it has an oddnumber of phase inversions.
For a Möbius system, a transitionstate with 4n electrons will be aromatic and thermally allowed,while that with 4n + 2 electrons will be antiaromatic and thermally forbidden. For a concerted photochemical reaction, the rulesare exactly the opposite to those for the corresponding thermalprocess.Even though the stability of Möbius systems was predictedover 40 years ago [103], for a long time no such systems weresynthesized.
One possible reason for this is the expected strainin the twisted structure. Based on quantum chemical calculations,different groups suggested the stability of [4n]annulenes [(CH)n ,with n = 3–5], but it was also shown that there are many possibleisomers of this system that are close in energy and thus theMöbius system might easily flip back to the less strained Hückelstructures [104].The first real Möbius systems ([16]annulenes) were only synthesized a few years ago [105]. In these systems the authors achievedenough rigidity for the molecules so that they would not flip back toa Hückel system.
It was also determined that these Möbius-twistedannulenes are more aromatic in their character than the Hückelsystems [106].The rules based on the Hückel–Möbius concept have their counterpart among the Woodward–Hoffmann selection rules. There was amarked difference between the suprafacial and antarafacial arrangements in the application of the Woodward–Hoffmann treatment ofcycloadditions. The disrotatory and conrotatory processes in electrocyclic reactions presented similar differences.
The suprafacialarrangement in both of the reacting molecules in the cycloadditionas well as the disrotatory ring closure in Figure 7-25 correspond to3547 Chemical ReactionsFigure 7-25. Comparison of the disrotatory ring closure and the 2s + 2s reactionwith the Hückel ring.the Hückel system.
On the other hand, the suprafacial–antarafacialarrangement as well as the conrotatory cyclization have a phaseinversion (Figure 7-26), and they can be regarded as Möbius systems.All the selection rules mentioned above are summarized in Table 7-3;their mutual correspondence is evident.Both the Woodward–Hoffmann approach and the Hückel–Möbiusconcept are useful for predicting the course of concerted reactions. They both have their limitations as well.
The application of the Hückel–Möbius concept is probably preferable forsystems with low symmetry. On the other hand, this concept canonly be applied when there is a cyclic array of orbitals. Theconservation of orbital symmetry approach does not have thislimitation.7.4. Hückel–Möbius Concept355Figure 7-26. Comparison of the conrotatory ring closure and the 2s + 2a reactionwith the Möbius ring.Table 7-3.
Selection Rules for Chemical Reactions from Different ApproachesApproachaReactionThermallyThermallyAllowedForbidden1s+sa+as+a4n + 24n + 24n4n4n4n + 22DisrotatoryConrotatory4n + 24n4n4n + 23Hückel system: sign inversion4n + 24neven or 0Möbius system: sign4n4n + 2inversion odda1: Woodward–Hoffmann cycloaddition; 2: Woodward–Hoffmann electrocyclicreaction; 3: Hückel–Möbius concept.3567 Chemical Reactions7.5. Isolobal AnalogySo far, our discussion of reactions has been restricted to organicmolecules.
However, all the main ideas are applicable to inorganic systems as well. Thus, for example, the formation ofinorganic donor–acceptor complexes may be conveniently describedby the HOMO–LUMO concept. A case in point is the formationof the aluminum trichloride–ammonia complex (cf. Figure 3-15).This complex can be considered to result from interaction betweenthe LUMO of the acceptor (AlCl3 ) and the HOMO of thedonor (NH3 ).The potential of a unified treatment of organic and inorganicsystems has been expressed eloquently in Roald Hoffmann’s Nobellecture [107] entitled “Building Bridges between Inorganic andOrganic Chemistry.”The main idea is to examine the similarities between the structures of relatively complicated inorganic complexes and relativelysimple and well-understood organic molecules.
Then the structure andpossible reactions of the former can be understood and even predictedby the considerations working so well for the latter. Two importantpoints were stressed by Hoffmann:1. “It is the resemblance of the frontier orbitals of inorganic andorganic moieties that will provide the bridge that we seek betweenthe subfields of our science.”2.
Many aspects of the electronic structure of the moleculesdiscussed and compared are heavily simplified, but “the timenow, here, is for building conceptual frameworks, and so similarity and unity take temporary precedence over difference anddiversity.”One of the fastest growing areas of inorganic chemistry is transition metal organometallic chemistry. In a general way, the structure of transition metal organometallic complexes can be thought ofas containing a transition metal–ligand fragment, such as M(CO)5 ,M(PF3 )5 , M(allyl) and MCp (Cp = cyclopentadienyl), or in general,MLn . All these fragments may be derived from an octahedralarrangement:7.5.
Isolobal Analogy357In describing the bonding in these fragments, first the six octahedralhybrid orbitals on the metal atom are constructed. Hybridization is notdiscussed here, but symmetry considerations are used in constructinghybrid orbitals just as in constructing molecular orbitals [108]. In anoctahedral complex, the six hybrid orbitals point towards the ligands,and together they can be used as a basis for a representation of thepoint group.
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