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When counting the number of pi electrons, in furan only one lone pair was included, but the other one was not.

In the cyclopentadienyl anion (2nd aromatic compound in the picture) the lone pair was counted.

When to include and exclude lone pairs in Hückel's rules?

enter image description here

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As written on Chemistry Libre Texts,

Perhaps the toughest part of Hückel's Rule is figuring out which electrons in the compound are actually π electrons. Once this is figured out, the rule is quite straightforward. π electrons lie in p orbitals and sp2 hybridized atoms have 1 p orbital each. So if every molecule in the cyclic compound is sp2 hybridized, this means the molecule is fully conjugated (has 1 p orbital at each atom), and the electrons in these p orbitals are the π electrons.

In furan, there are two lone pairs, one in the sp2-orbital, and the other in the p-orbital. The latter is hence the set of π electrons.

In the cyclopentadienyl anion, the lone pair is present in the p-orbital, as all the sp2-orbitals are involved in bonding.

Thus, π electrons and not just lone pairs are to be counted in Huckel's Rule.

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    $\begingroup$ hybridization state cannot be easily deduced from the structure formula though.. $\endgroup$ – mykhal Jul 25 '18 at 16:42
  • $\begingroup$ @mykhal Hybridisation can, in most cases, be deduced from the structure directly, especially for organic compounds $\endgroup$ – Abhigyan Chattopadhyay Jul 25 '18 at 16:50
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    $\begingroup$ Argh, how I dislike the Chemistry Libre Texts. For the following reasons: (1) π electrons lie in p orbitals is not necessarily true, as long as the symmetry fits the pi orbitals, others can participate, too. (2) sp2 hybridized atoms - only orbitals can hybridise. (3) So if every molecule in the cyclic compound is sp2 hybridized, this means the molecule is fully conjugated - No. Point in case: Why is cyclooctatetraene non planar but the cyclooctatetraenide anion planar?. $\endgroup$ – Martin - マーチン Jul 25 '18 at 17:58
  • $\begingroup$ @Martin Thanks... Good to know... What's a more trusty website to refer? $\endgroup$ – Abhigyan Chattopadhyay Jul 25 '18 at 18:11
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    $\begingroup$ chemistry.stackexchange.com :P $\endgroup$ – Martin - マーチン Jul 25 '18 at 18:16

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