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1,1'-biphenyl

Biphenyl has 12 π-electrons and according to Hückel’s rule, it should not be aromatic because $12 \neq 4n+2$, but it nevertheless is aromatic. Why is that so?

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    $\begingroup$ @henry It isn't a single aromatic system but two independent ones (there is mostly free rotation around the c-c bond that joins the two rings). $\endgroup$ – matt_black May 20 '16 at 8:24
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    $\begingroup$ Huckel's rule only applies to monocyclic systems without side groups. In fact, this rule is so frequently misused I'd rather have people forget about it altogether. $\endgroup$ – Ivan Neretin May 20 '16 at 8:38
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    $\begingroup$ I see no point in such a modification. How would you know when to apply it and when not to? Will it work with corannulene, for example? (It will not.) No, stick to the Huckel's rule when it is applicable, and when it is not, resort to the more complicated math (finding the eigenvalues, etc). Alternatively, you can point out that in the real biphenyl molecule the rings are twisted (non-coplanar), and hence not conjugated, so that each $\pi$ system is pretty much on its own. $\endgroup$ – Ivan Neretin May 20 '16 at 8:56
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    $\begingroup$ @Henry Pyrene is a fused-ring system which is why you need more sophisticated rules about aromaticity. That isn't needed here as the two rings are not fused and can be treated independently due to the relatively free rotation about the linking bond (strictly there is a small steric barrier to rotation which results in a preferred confirmation where the rings are ~40 degrees from being planar, which also implies they are two separate aromatic systems and not one single one.) $\endgroup$ – matt_black May 20 '16 at 8:57
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    $\begingroup$ Math does apply in chemistry, but... Well, see this: en.wikipedia.org/wiki/H%C3%BCckel_method $\endgroup$ – Ivan Neretin May 20 '16 at 8:59
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The two rings in biphenyl are inclined at an angle of 44° to each other because of the large steric repulsion between the ortho hydrogens on each ring.

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For Hückel's rule to be applied, the molecule must be able to be planar and it must be monocyclic.

Due to the molecule not being planar, the two rings are not strongly conjugated to each other and you cannot apply Hückel's rule to the whole system. Additionally, the whole system is not monocyclic. Hückel's rule can be applied to each ring individually and they are both aromatic.

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    $\begingroup$ I think I'd disagree that there isn't conjugation between the rings in biphenyl. Yes, there is more delocalization if you can force the system into planarity, but there's definitely electronic communication even in twisted systems. $\endgroup$ – Geoff Hutchison May 20 '16 at 20:26
  • $\begingroup$ When you say that both the rings are inclined to each other at an angle of 44°, it is the most stable conformer you are talking of, isn't it? Just being sure $\endgroup$ – Aumkaar Pranav Oct 6 '19 at 14:04

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