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Why are some annulenes such as [14] and [18]annulenes are aromatic even though they are not fully planar as cited by Wikipedia? What does it mean that they can achieve planar form?

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It means very little, at least in terms of stabilization. Perfectly planar or not, larger aromatic rings bring less stability than smaller ones, so they react more like mere conjugated polyenes than what we think of as "aromatic rings". Wikipedia:

When the annulene is large enough, [18]annulene for example, there is enough room internally to accommodate hydrogen atoms without significant distortion of bond angles. [18]Annulene possesses several properties that qualify it as aromatic.[1] However, none of the larger annulenes are as stable as benzene, as their reactivity more closely resembles a conjugated polyene than an aromatic hydrocarbon.

Cited reference:

1. Oth, Jean F. M.; Bünzli, Jean-Claude; De Julien De Zélicourt, Yves (1974-11-06). "The Stabilization Energy of [18] Annulene. A thermochemical determination". Helvetica Chimica Acta. 57 (7): 2276–2288.

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