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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 ...
Hence the square molecule would be a very reactive triplet diradical (the ground state is actually rectangular without degenerate orbitals). In fact, all cyclic conjugated hydrocarbons with a total of 4n π-electrons share this molecular orbital pattern, and this forms the basis of Hückel's rule.
But in 1969 and 1970 a general formulation was published, [9] [10] namely, A ground-state pericyclic change is symmetry-allowed when the total number of (4q + 2) s and (4r) a components is odd. The 1969–1970 Woodward–Hoffmann general formulation is seen to be equivalent to the Zimmerman Möbius–Hückel concept.
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 ...
The famous Hückel 4n+2 rule for determining whether ring molecules composed of C=C bonds would show aromatic properties was first stated clearly by Doering in a 1951 article on tropolone. [6] Tropolone had been recognised as an aromatic molecule by Dewar in 1945. In 1936, Hückel developed the theory of π-conjugated biradicals (non-Kekulé ...
The method was first used by Roald Hoffmann who developed, with Robert Burns Woodward, rules for elucidating reaction mechanisms (the Woodward–Hoffmann rules). He used pictures of the molecular orbitals from extended Hückel theory to work out the orbital interactions in these cycloaddition reactions.
The cyclopentadienyl anion is a planar, cyclic, regular-pentagonal ion; it has 6 π-electrons (4n + 2, where n = 1), which fulfills Hückel's rule of aromaticity. Each double bond and lone pair provides 2 π-electrons, which are delocalized into the ring. [4] Cyclopentadiene has a pKa of about 16.
D&H use the Helmholtz and Gibbs free entropies and to express the effect of electrostatic forces in an electrolyte on its thermodynamic state. Specifically, they split most of the thermodynamic potentials into classical and electrostatic terms: Φ = S − U T = − A T , {\displaystyle \Phi =S-{\frac {U}{T}}=-{\frac {A}{T}},} where