Reactions with Mobius transition states

Figure 1.4. Reactions with Mobius transition states...

Occasionally, though, you will run across a more exotic pericyclic process, and will want to decide if it is allowed. In a complex case, a reaction that is not a simple electrocyclic ringopening or cycloaddition, often the basic orbital symmetry rules or FMO analyses are not easily applied. In contrast, aromatic transition state theory and the generalized orbital symmetry rule are easy to apply to any reaction. With aromatic transition state theory, we simply draw the cyclic array of orbitals, establish whether we have a Mobius or Hiickel topology, and then count electrons. Also, the generalized orbital symmetry rule is easy to apply. We simply break the reaction into two or more components and analyze the number of electrons and the ability of the components to react in a suprafacial or antarafacial manner. 

The closed and open forms, 4 and 5, respectively, represent the formal starting and end points of an electrocyclic reaction. In terms of this pericyclic reaction, the transition state 6 can be analysed with respect to its configurational and electronic properties as either a stabilized or destabilized Huckel or Mobius transition state. Where 4 and 5 are linked by a thermally allowed disrotatory process, then 6 will have a Hiickel-type configuration. Where the process involves (4q + 2) electrons, the electrocyclic reaction is thermally allowed and 6 can be considered to be homoaromatic. In those instances where the 4/5 interconversion is a 4q process, then 6 is formally an homoantiaromatic molecule or ion. 

We have not given you much evidence to decide why it is that some thermal [2 + 2] cycloadditions occur but not others. What is special about fluoroalkenes, allenes, and ketenes in these reactions One possibility is that Mobius rather than the Hiickel transition states are involved, but the Mobius transition states are expected to suffer from steric hindrance (Section 21-10B). It is also possible that [2 + 2] cycloadditions, unlike the Diels-Alder additions, proceed by stepwise mechanisms. This possibility is strongly supported by the fact that these reactions generally are not stereospecific. Thus with tetrafluoroethene and trans,trans-2,5-bexadiene two products are formed, which differ in that the 1-propenyl group is trans to the methyl group in one adduct, 45, and cis in the other, 46 ... 

Mobius transition state (achieved by conrotation), whereas the photochemical reaction is most favorable with a Hiickel transition state (achieved by disrotation). 

Although Mobius molecules are rare. Mobius transition states, with one antarafacia component, are relatively common. For these systems, 4n electrons is the favourable number, giving a stabilized transition state and a taster reaction rate... 

In contrast, ring opening of the cyclohexadiene isomers 16 and 18 to give 17 and 19 are both disrotatory. For this reaction, with a Htickel transition state involved, 4 + 2 electrons is the favoured number, and for this number of electrons the conrotatory mode which would give a Mobius transition state is not favoured. 

The Woochvard-Huflimnn rules are a general expression of this. A pericyclic reaction which is entirely suprafacial is allowed thermally if 4n + 2 electrons are involved (Hiickel transition state), but forbidden for 4n electrons. If there is one antarafacial component, the reaction will be allowed thermally if 4n electrons are involved (Mobius transition state), but forbidden for 4n + 2 electrons. For photochemical reactions, these rules are reversed. Roald Hoffmann shared the Nobel prize for Chemistry with Kenichi Fukui in 1981 for his contribution to this concept Robert Burns Woodward had already won the prize in 1965. 

Figure 13.23 Ring current in the Mobius transition state of the electrocyclic reaction of octa-l,3,5,7-tetraene to cycloocta-1,3,5-triene. For details see Figure 13.21. Note that the basis orbitals (atomic orbitals that are involved in the reaction) can be written with arbitrary phase. The number of antibonding overlaps (sign inversion) will...

In the linear approach (a) the carbene orbitals are interacting in a supm-facial manner. The topology of the interaction with the polyene orbitals can be suprafacial, which therefore requires a disrotatory twisting about the terminal bond axes, or antarafacial which can result only if the canrotatoiy mode applies. The linear disrotatory process involves a Hiickel interaction, whereas the linear conrotatory reaction has a Mobius transition state. Hence if (m + 2), that is the total number of participant electrons, is equal to (4n+2) the Hiickel-type disrotatory closure will be preferred. If m + 2) = 4n, then the conrotatory (Mobius) closure is predicted. Hence butadiene should undergo a linear cheletropic reaction with singlet carbene (or similar electron deficient species - e.g. SO2) with disrotatory closure, whereas the analogous reaction of hexatriene requires the operation of the conrotatory mode. 

A cyclic array of orbitals is a Mobius system if it has an odd number of phase inversions. For a Mobius system, a transition state with An electrons will be aromatic and thermally allowed, while that with An+ 2 electrons will be antiaromatic and thermally forbidden. For a concerted photochemical reaction, the rules are exactly the opposite to those for the corresponding thermal process. 

Evans-Dewar-Zimmerman criterion. In accordance with this criterion the pericyclic reactions proceed through the cyclic transition state of the Htickel topological type if it contains AN + 2) jt-electrons, and through the state with anti-Hiickel (Mobius) topology if it contains AN ji-electrons. 

An analysis of reaction possibilities in the Hiickel-Mobius theory requires us to construct a fully interacting basis set, which is simply a sketch of the transition state, drawn with the maximum possible bonding character (the fewest nodes possible). Next, draw a line to connect the reactant orbitals as they would be connected by conrotatory and disrotatory processes. This gives a complete model of the transition state for butadiene as shown in Fig. 8.49. 

Sigmatropic shifts represent another important class of pericyclic reactions to which the Woodward-Hoffmann rules apply. The selection rules for these reactions are best discussed by means of the Dewar-Evans-Zimmerman rules. It is then easy to see that a suprafacial [1,3]-hydrogen shift is forbidden in the ground state but allowed in the excited state, since the transition state is isoelectronic with an antiaromatic 4N-HQckel system (with n = 1), in which the signs of the 4N AOs can be chosen such that all overlaps are positive. The antarafacial reaction, on the other hand, is thermally allowed, inasmuch as the transition state may be considered as a Mobius system with just one change in phase. 

Mobius aromaticity A monocyclic array of orbitals in which a single out-of-phase overlap (or, more generally, an odd number of out-of-phase overlaps) reveals the opposite pattern of aromatic character to Hiickel systems with 4n electrons it is stabilized (aromatic), whereas with 4n + 2 it is destabilized (antiaromatic). In the excited state 4n + 2, Mobius pi-electron systems are stabilized, and 4n systems are destabilized. No examples of ground-state Mobius pi systems are known, but the concept has been applied to transition states of PERI-CYCLIC REACTIONS (see AROMATIC [3]). 

The last exception has an unusual twist, literally. The transition state is a strange loop with a half-twist, a Mobius loop. In contrast to a normal loop, Mobius loops are predicted to be stable with An electrons in them. Given enough heat, the cyclobutene sigma bond twists open to form a diene. This and other pericyclic reactions are discussed in more detail in Chapter 12. 

Whereas methylenecyclopropanes only react with highly electron-deficient dienophiles in a [ 2n + 2fT) + 2n] fashion, alkenylidenecyclopropanes 1 readily undergo this cycloaddition type. A number of comprehensive and elaborate investigations with various alkenylidenecyclopropanes and 4-phenyl-l,2,4-triazoline-3,5-dione indicate that these reactions are concerted and proceed via [( 2j+,25+ 2 J -I-, 2 J transition states, involving the terminal double bond in an eight-electron Mobius aromatic transition structure 4. 

We have established earlier in the chapter that there will be favourable Frontier Orbital HOMO-LUMO interactions when two molecules approach for a cycloaddition reaction if there are 4n + 2 electrons involved in a fully suprafacial reaction, or 4n electrons if there is an antarafacial component. For delocalization of electrons in the transition state, the fully suprafacial cycloaddition reaction will result in a continuous cyclic overlap of atomic orbitals in the transition state without a phase change, for which 4n + 2 electrons will give aromatic stabilization. For a cycloaddition with one antarafacial component, the cyclic overlap of orbitals will give a Mobius system for which 4n electrons will provide stabilization. Thus the two approaches, Frontier Orbitals and the Aromatic Transition State will always be in agreement favourable... 

The selection rules for [tt4 + tt2 ] and other cycloaddition reactions can also be derived from consideration of the aromaticity of the TS3 In this approach, the basis set p orbitals are aligned to correspond with the orbital overlaps that occur in the TS. The number of nodes in the array of orbitals is counted. If the number is zero or even, the system is classified as a Htickel system. If the number is odd, it is a Mobius system. Just as was the case for ground state molecules (see p. 716), Htickel systems are stabilized with 4 + 2 electrons, whereas Mobius systems are stabilized with 4n electrons. For the [tt4 + tt2] suprafacial-suprafacial cycloaddition the transition state is aromatic. 

T electrons with one si inversion (Mdbius-like). A Mobius array in the ground state is antiaromatic with six electrons but is aromatic and stable in the excited state. °> Thus the di-ir-methane rearrangement via transition state (3) is photoallowed. The orbital scheme (4) involves a cyclic array of four 17- electrons with no sign inversions (Hiickel-like). Again the ground state is antiaromatic but it is aromatic in the excited state and the reaction is photochemically allowed. 

How do we rationalize this allowed reaction Both FMO and aromatic transition state theory are easy to apply. As shown below, the extra node in the d orbital used in the alkylidene it bond allows the HOMO of the M=Cbond to interact with the UJMOoftheC=C bond constructively. Similarly, the extra node in the d orbital makes the four-electron system Mobius (remember we do not count nodes in the atomic orbitals themselves), and therefore allowed. 

Figure 15.17 B shows the aromatic transition state analysis of these reactions. We draw a picture of an opening pathway with the minimum number of phase changes and examine the number of nodes. The four-electron butadiene-cyclobutene system should follow the Mobius/conrotatory path, and the six-electron hexatriene-cyclohexadiene system should follow the Hiickel/disrotatory path. As such, aromatic transition state theory provides a simple analysis of electrocyclic reactions. The disrotatory motion is always of Hiickel topology, and the conrotatory motion is always of Mobius topology.

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