Mobius 4-rung

After synthesizing the 3-rung Mobius ladder, Walba conjectured that its molecular bond graph was topologically chiral [16]. In contrast with his conjecture, he... 

Figure 23. A 3-rung and a 4-rung molecular Mobius ladder.

Figure 24. A Mobius ladder with three rungs can be deformed so that it has a planar reflection.

Figure 25. A two-rung Mobius ladder can be deformed into a plane.

Figure 27. A topologically achiral embedding of a Mobius ladder with four rungs.

In Figure 34, we have labeled the vertices of the Mobius ladder with 1, 2, 3 and a, b, c, in order to illustrate that the 3-rung Mobius ladder is actually a K3 3 graph. 

Figure 38. A 4-rung Mobius ladder contained in the molecular graph of Figure 37.

Figure 16. Some topologically chiral molecular graphs, (a) The Simmons-Paquette molecule.74 (b) Walba s 3-rung Mobius ladder molecule.75 (c) [4](l,l )[4](3,3 )[3](4 4 )-Ferrocenophan-16-one.76 (d) Triple-layered naphthalenophane.78 Unlabeled vertices represent carbon atoms, and hydrogen atoms are suppressed for clarity. Only one enantiomer of each molecule is shown.

The first flexible, topologically chiral K3j3 molecule is the so-called three-rung Mobius ladder 63 (Fig. 15). It was synthesized by D. M. Walba et al. in 1982 [85] and is represented on Fig. 15, together with several presentations of its graph (64-66). It is important to notice that the rungs of the ladder are different from... 

Fig. 15. The topologically chiral three-rung Mobius ladder (63) and several presentations of its graph (64-66). 64 and 66 are presentations with the minimum number of crossings (1). Note that the edges (1,1 ), (2,2 ) and (3,3 ) are differently coloured than the others (i.e. (l, 2), (2,3 ), etc,. ..)...

Fig. 16. Homotopicity of edges in an uncoloured three-rung Mobius ladder. For example, the vertical edge (rung) (2,2 ) in A is equivalent to the rung (3, 2) in B...

Fig. 17. The four-rung Mobius ladder (67) and its cylindrical constitutional isomer (68)...

Fig. 18. The topologically-relevant step in the synthesis of the chiral three-rung Mobius ladder 63, starting from the linear molecular ladder 69...

Fig. 19. Homotopicity of an olefinic carbon atom ( ) in the chiral three-rung Mobius...

A second possibility of proving the structure of 38 consisted in the cleavage of the double bonds, the rungs of the M6bius- ladder , by ozonolysis [30]. While the cylinder 37 led to two 30-membered cyclic triketones 39, the Mobius strip 38 gave a 60-membered cyclic hexaketone 40. 

A. The synthetic strategy for the preparation of a molecular Mobius strip, and the results of rung cleavage. 

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