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In organic chemistry, Hückel's rule estimates whether a planar ring molecule will have aromatic properties. The quantum mechanical basis for its formulation was first worked out by physical chemist Erich Hückel in 1931.〔. . .〕〔.〕 The succinct expression as the 4''n''+2 rule has been attributed to von Doering (1951),〔.〕 although several authors were using this form at around the same time.〔See Roberts et al. (1952) and refs. therein.〕 A cyclic ring molecule follows Hückel's rule when the number of its π-electrons equals 4''n''+2 where ''n'' is zero or any positive integer, although clearcut examples are really only established for values of ''n'' = 0 up to about ''n'' = 6. Hückel's rule was originally based on calculations using the Hückel method, although it can also be justified by considering a particle in a ring system, by the LCAO method and by the Pariser–Parr–Pople method. Aromatic compounds are more stable than theoretically predicted by alkene hydrogenation data; the "extra" stability is due to the delocalized cloud of electrons, called resonance energy. Criteria for simple aromatics are: # the molecule must follow Hückel's rule, having 4''n''+2 electrons in the delocalized, conjugated p-orbital cloud; # the molecule must be able to be planar; # the molecule must be cyclic; and, # every atom in the ring must be able to participate in delocalizing the electrons by having a p-orbital or an unshared pair of electrons. ==Monocyclic hydrocarbons== The rule can be used to understand the stability of completely conjugated monocyclic hydrocarbons (known as annulenes) as well as their cations and anions. The best-known example is benzene (C6H6) with a conjugated system of six pi-electrons, which equals 4n + 2 for n = 1. The molecule has a strong tendency to undergo substitution reactions which preserve the six pi-electron system rather than addition reactions which would destroy it. The stability of this pi-electron system is referred to as aromaticity. The cyclopentadienyl anion (C5H5–) with six pi electrons is considerably more stable than either the neutral cyclopentadienyl radical with five pi electrons or the corresponding cation with four.〔Levine, I.N. ''Quantum chemistry'' (4th ed., Prentice-Hall 1991) p.559-560 ISBN 0-205-12770-3〕 Similarly the tropylium cation (C7H7+) has six pi electrons and is more stable than either the cycloheptatrienyl radical (C7H7•) or its anion.〔 Planar ring molecules with 4n pi electrons do not obey Hückel's rule, and theory predicts that they are less stable and have triplet ground states with two unpaired electrons. In practice such molecules distort from planar regular polygons. Cyclobutadiene (C4H4) with four pi electrons is stable only at temperatures below 35 K and is rectangular rather than square.〔 Cyclooctatetraene (C8H8) with eight pi electrons has a nonplanar ''tub'' structure. However the dianion C8H82– with ten pi electrons obeys the 4n + 2 rule for n = 2 and is planar.〔 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Hückel's rule」の詳細全文を読む スポンサード リンク
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