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Möbius (left) and Hückel (right) orbital arrays. The two orbital arrays in Figure 3 are just examples and do not correspond to real systems. In inspecting the Möbius one on the left, plus–minus overlaps are seen between orbital pairs 2-3, 3-4, 4-5, 5-6, and 6-1, corresponding to an odd number (5), as required by a Möbius system.
The Hückel definition of bond order attempts to quantify any additional stabilization that the system enjoys resulting from delocalization. In a sense, the Hückel bond order suggests that there are four π-bonds in benzene instead of the three that are implied by the Kekulé-type Lewis structures.
In organic chemistry, Möbius aromaticity is a special type of aromaticity believed to exist in a number of organic molecules. [ 1 ] [ 2 ] In terms of molecular orbital theory these compounds have in common a monocyclic array of molecular orbitals in which there is an odd number of out-of-phase overlaps, the opposite pattern compared to the ...
Benzene, the most widely recognized aromatic compound with six delocalized π-electrons (4n + 2, for n = 1).. In organic chemistry, Hückel's rule predicts that a planar ring molecule will have aromatic properties if it has 4n + 2 π-electrons, where n is a non-negative integer.
A strange loop is a hierarchy of levels, each of which is linked to at least one other by some type of relationship. A strange loop hierarchy is "tangled" (Hofstadter refers to this as a "heterarchy"), in that there is no well defined highest or lowest level; moving through the levels, one eventually returns to the starting point, i.e., the original level.
In mathematics, a Möbius strip, Möbius band, or Möbius loop [a] is a surface that can be formed by attaching the ends of a strip of paper together with a half-twist. As a mathematical object, it was discovered by Johann Benedict Listing and August Ferdinand Möbius in 1858, but it had already appeared in Roman mosaics from the third century CE .
Möbius was the first to introduce homogeneous coordinates into projective geometry. He is recognized for the introduction of the barycentric coordinate system . [ 4 ] Before 1853 and Schläfli 's discovery of the 4-polytopes , Möbius (with Cayley and Grassmann ) was one of only three other people who had also conceived of the possibility of ...
Above Rudolf Hilsch and Otto Scherzer, in front Erich Hückel, 1935 at Stuttgart. Erich Armand Arthur Joseph Hückel ForMemRS [1] (August 9, 1896, Berlin – February 16, 1980, Marburg) was a German physicist and physical chemist. [2]