Mobius approach

An approach very closely related to that of Woodward and Hoffmann is the so-called Hiickel-Mobius approach 35> based on the rule An +2 electron systems prefer Hiickel geometries and An electron systems prefer Mobius geometries 36>. When no symmetry exists and there is no cyclic orbital array the allowedness or forbiddenness of a reaction can be determined by following the form of the MO s during the reaction 37>. A detailed quantum mechanical study of the stereochemistry of thermal and photo cyclo-addition reactions has been reported38), and a quantum mechanical discussion of the applicability of the Woodward-Hoffmann rules can be found in a paper by George and Ross 39>. 

Analysis of electrocyclic reactions using a variety of methods and the various conclusions that are drawn. A. FMO theory for ring-opening. The LUMOs of the ir systems are compared to the HOMO of the C-C o bond in cyclobutene and 1,3-cyclohexadiene. B. The Hiickel/Mobius approach. C. Using the generalized orbital symmetry rule. Note, as always, that all the methods predict the same outcome. 

In the Mobius-Hiickel approach, diagrams similar to Figure 18.4 can be drawn for this case. Here too, the disrotatory pathway is a Hiickel system and the conrotatory pathway a Mobius system, but since six electrons are now involved, the thermal reaction follows the Hiickel pathway and the photochemical reaction the Mobius pathway. 

In Eqs. (27) and (28), p is the contribution of the substrate water molecules, p that of the adsorbate polar head, and p that of the hydrophobic moiety of the adsorbed molecules. Consistently, 8i, 82, and 83 are the effective local permittivities of the free surface of water and of the regions in the vicinity of the polar head and of the hydrophobic group, respectively. The models have been used in a number of papers on adsorbed monolayers and on short-chain substances soluble in water. " Vogel and Mobius have presented a similar but more simplified approach in which p is split into two components only. " Recently some improvements to the analysis using Eq. (27) have been proposed. " An alternative approach suggesting the possibility of finding the values of the orientation angle of the adsorbate molecules instead of local permittivities has been also proposed.""... 

The alternate approach of Dewar and Zimmerman can be illustrated by an examination of the 1,3,5-hexatriene system.<81,92> The disrotatory closure has no sign discontinuity (Hiickel system) and has 4n + 2 (where n = 1) ir electrons, so that the transition state for the thermal reaction is aromatic and the reaction is thermally allowed. For the conrotatory closure there is one sign discontinuity (Mobius system) and there are 4u + 2 (n = 1) ir electrons, so that the transition state for the thermal reaction is antiaromatic and forbidden but the transition state for the photochemical reaction is aromatic or allowed (see Chapter 8 and Table 9.8). If we reexamine the butadiene... 

MObius HJ, StOffler A (2002) New approaches to clinical trials in vascular dementia memantine in small vessel disease. Cerebrovasc Dis 13 (Suppl 2) 61-66 Montgomery JM, Madison DV (2002) State-dependent heterogeneity in synaptic depression between pyramidal cell pairs. Neuron 33 765-777 Montgomery JM, Pavlidis P, Madison DV (2001) Pair recordings reveal all-silent synaptic connections and the postsynaptic expression of long-term potentiation. Neuron 29 691-701... 

Figure 6. The Mobius strip approach (three half-twists) to a trefoil knot.

In contrast, the Mobius strip approach, depicted in Figure 6, also suggested by Frisch and Wasserman in 1961 [36], seemed much more realistic. 

As seen above, the randomness of the Mobius strip approach and numerous difficult steps in Schill s directed approach were highly limiting factors in a trefoil knot synthesis. Both these major obstacles might be circumvented by the use of an unambiguous templated synthesis procedure. 

The relevance of all this may seem tenuous, especially because no example of a simple cyclic polyene with a Mobius 7r system is known. However, the Mobius arrangement is relevant to cycloaddition because we can conceive of alkenes, alkadienes, and so on approaching each other to produce Mobius transition states when An electrons are involved. 

Much of what we have said about the electronic factors controlling whether a cycloaddition reaction can be concerted or not originally was formulated by the American chemists R. B. Woodward and R. Hoffmann several years ago, in terms of what came to be called the orbital symmetry principles, or the Woodward-Hoffmann rules. Orbital symmetry arguments are too complicated for this book, and we shall, instead, use the 4n + 2 electron rule for-normal Hiickel arrangements of tt systems and the An electron rule for Mobius arrangements. This is a particularly simple approach among several available to account for the phenomena to which Woodward and Hoffmann drew special attention and explained by what they call conservation of orbital symmetry.- ... 

Day21 has given a careful account of the relationship between the Woodward-Hoffmann rules and Mobius/Hiickel aromaticity, and has defined the terms supra-facial and antarafacial in terms of the nodal structure of the atomic basis functions. His approach makes quite explicit the assumption that the transition state involves a cyclic array of basis functions. Thus the interconversion of prismane (10) and benzene, apparently an allowed (n2s+ 2S+ 2S) process, is in fact forbidden because there are additional unfavourable overlaps across the ring.2... 

Independent interpretation of mass spectroscopic data by Wolovsky 66> and Ben-Efraim, Batich, and Wasserman 6 ) indicate that cyclic olefins subjected to disproportionation conditions form interlocking rings (catenanes) as well as cyclopolyolefins. The proposed scheme involves four-center transition state and Mobius-Strip approach... 

Unfortunately, the experimental data concerning the distances at which electron exchange reactions in the membranes take place are very scarce. Tsuchida et al. have shown [147], that even when the photoexcited Zn porphyrin embedded in the membrane cannot approach the membrane // water interface closer than 12 A, the electron transfer is still possible to MV2+ located in the water phase outside the membrane. However, when the distance of the closest approach of these reactants is increased up to 17 A, the electron transfer is totally stopped. Examples of electron transfer proceeding presumably via electron tunneling across molecular layers about 20 A thick, which separate electron donor and acceptor molecules, can be found in papers by Mobius [230, 231] and Kuhn [232, 233]. Note, that in... 

When a cyclic polyene is large enough, it can exist in both cis- and iraws-forms. Our approach to polyene cyclization has tacitly assumed an all cis -n chain in the form of a band or ribbon that would slip smoothly on to the surface of a cylinder of appropriate diameter. Should the orbitals of the two polyenes in (36) have a mismatch in their orbital symmetries, a single twist in the tt band of one of them could remedy this (Fig. 10c). Cycloaddition would now be allowed and the reaction would proceed, provided other factors were favorable. Such cases of Mobius (Zimmerman, 1966), anti (Fukui and Fujimoto, 1966b) or axisymmetric (Lemal and McGregor, 1966), as opposed to Hiickel, syn, or sigma-symmetric ring closure are unknown (or, at least, rare). A Mobius form has, however, been proposed as the key intermediate in the photochemical transformations of benzene (Farenhorst, 1966) in (48) in place of the disrotatory cyclization proposed by van Tamelen (1965). 

The Mobius-Huckel approach now has become common to a large number of undergraduate textbooks because of its facile application to ground state chemistry. The method does not really differ in conclusions and derived rules from the Dewar method presented a year later 36). 

Additionally, if only S0 and Sx are considered, these configurations cannot mix as a consequence of Brillouin s theorem. Nevertheless, the situation is not as serious as it appears. Thus it is seen that in an MO approximation the S0 and Si configurations do become degenerate where HOMO-LUMO crossing occurs, and this signifies that where Mobius-Huckel theory predicts a degeneracy, surfaces will at least approach one another. 

The important conclusion is that the Sj state becomes progressively more heavily weighted in S0 and St configurations as a bifunnel is approached. Thus Mobius-Hiickel considerations are relevant. 

Both the Woodward-Hoffmann approach and the Hiickel-Mobius concept are useful for predicting the course of concerted reactions. They both have their limitations as well. The application of the Hiickel-Mobius concept is probably preferable for systems with low symmetry. On the other hand, this concept can only be applied when there is a cyclic array of orbitals. The conservation of orbital symmetry approach does not have this limitation. 

Fig. 9 The Mobius strip approach to catenane synthesis. The number of half-twists in the strip determine the topology of the product after it is cut down the middle. Two half-twists would afford a [2]catenane. Reproduced with permission from [54] (copyright 1985 Elsevier)...

Fig. 7 Depiction of the Mobius strip approach to a trefoil knot...

If the motion had been disrotatory, this would still have been evidence for a cyclic mechanism. If the mechanism were a diradical or some other kind of noncyclic process, it is likely that no stereospecificity of either kind would have been observed. The reverse reaction is also conrotatory. In contrast, the photochemical cyclobutene 1,3-Diene interconversion is disrotatory in either direction. On the other hand, the cyclohexadiene 1,3,5-Triene interconversion shows precisely the opposite behavior. The thermal process is disrotatory, while the photochemical process is conrotatory (in either direction). These startling results are a consequence of the symmetry rules mentioned in Chapter 15 (p. 1208). As in the case of cycloaddition reactions, we will use the frontier orbital and Mobius-Hiickel approaches... 

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