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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 method or Hückel molecular orbital theory, proposed by Erich Hückel in 1930, is a simple method for calculating molecular orbitals as linear combinations of atomic orbitals. The theory predicts the molecular orbitals for π-electrons in π-delocalized molecules , such as ethylene , benzene , butadiene , and pyridine .
In contrast to the rarity of Möbius aromatic ground state molecular systems, there are many examples of pericyclic transition states that exhibit Möbius aromaticity. The classification of a pericyclic transition state as either Möbius or Hückel topology determines whether 4N or 4N + 2 electrons are required to make the transition state aromatic or antiaromatic, and therefore, allowed or ...
Hückel's rule can also be applied to molecules containing other atoms such as nitrogen or oxygen. For example, pyridine (C 5 H 5 N) has a ring structure similar to benzene, except that one -CH- group is replaced by a nitrogen atom with no hydrogen. There are still six π electrons and the pyridine molecule is also aromatic and known for its ...
Hückel is most famous for developing the Hückel method of approximate molecular orbital (MO) calculations on π electron systems, a simplified quantum-mechanical method to deal with planar unsaturated organic molecules. In 1930 he proposed a σ/π separation theory to explain the restricted rotation of alkenes (compounds containing a C=C ...
The method works poorly for molecules that contain atoms of very different electronegativity. To overcome this weakness, several groups have suggested iterative schemes that depend on the atomic charge. One such method, that is still widely used in inorganic and organometallic chemistry is the Fenske-Hall method. [7] [8] [9]
Being on a circle means the four points are the image of four real points under a Möbius transformation, and hence the cross ratio is a real number. The Poincaré half-plane model and Poincaré disk model are two models of hyperbolic geometry in the complex projective line .
Hückel or Huckel may refer to: Erich Hückel (1896-1980), German physicist and chemist Debye–Hückel equation (named after Peter Debye and Erich Hückel), in chemistry, a method of calculating activity coefficients; Hückel method (named after Erich Hückel), a method for the determination of energies of molecular orbitals