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Hückel's rule is not valid for many compounds containing more than one ring. For example, pyrene and trans-bicalicene contain 16 conjugated electrons (8 bonds), and coronene contains 24 conjugated electrons (12 bonds). Both of these polycyclic molecules are aromatic, even though they fail the 4n + 2 rule. Indeed, Hückel's rule can only be ...
Inspection of the Hückel one on the right, plus–minus overlaps are seen between orbital pairs 2-3, 3-4, 4-5, and 6-1, corresponding to an even number (4), as required by a Hückel system. The plus–minus orientation of each orbital is arbitrary since these are just basis set orbitals and do not correspond to any molecular orbital.
[1] [2] [3] It provides the theoretical basis for Hückel's rule that cyclic, planar molecules or ions with + π-electrons are aromatic. It was later extended to conjugated molecules such as pyridine, pyrrole and furan that contain atoms other than carbon and hydrogen (heteroatoms). [4]
A Hückel-Möbius aromaticity switch (2007) has been described based on a 28 pi-electron porphyrin system: [11] [note 2] The phenylene rings in this molecule are free to rotate forming a set of conformers: one with a Möbius half-twist and another with a Hückel double-twist (a figure-eight configuration) of roughly equal energy.
[2] = + K is the Wolfsberg–Helmholz constant, and is usually given a value of 1.75. In the extended Hückel method, only valence electrons are considered; the core electron energies and functions are supposed to be more or less constant between atoms of the same type.
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It has 6 π-electrons (4n + 2, where n = 1), which fulfills Hückel's rule of aromaticity. It can coordinate as a ligand to metal atoms. The structure shown is a composite of seven resonance contributors in which each carbon atom carries part of the positive charge.