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I believe that a compound which is planar and having parallel p orbital with $4n\,\pi$ electrons is antiaromatic, but azirene has a lone pair in a $\text{sp}^3$ hybrid orbital.

Shouldn't it be non-aromatic rather than antiaromatic?

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Wikipedia, in a short article, indicates that there are actually two types of azirenes:

  • 1H-azirenes, where there is one ligand on each ring atom as shown in the question. Since all the ring atoms have ligands the lone pair contributed by nitrogen enters the conjugated pi system, which then has four conjugated electrons and is antiaromatic. Such a molecule is thereby unstable and prone to rearrange into the alternative structure that follows.

  • 2H-azirenes have two ligands on one carbon, saturating that atom so we no longer have a conjugated ring. The other ring carbon has one ligand and is still unsaturated. The nitrogen atom is left without a ligand, and its lone pair now replaces the missing ligand in an outward pointing in-plane orbital. The only pi bonding is an isolated bond between the nitrogen and the remaining unsaturated carbon. These compounds are non- (not anti-)aromatic and may be isolated.

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