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I thought since both phenyl rings are not coplanar, the resonance between them is not possible. But my book says the following:

Resonance effect is partially nullified

Partially nullified means resonance is relatively weak but it's taking place

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    $\begingroup$ What book are you referring to, please cite your source. $\endgroup$ – NotEvans. Jul 21 '17 at 10:00
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    $\begingroup$ Looking at amazon, there are many books by that author- are you looking at a specific one? A title and page ref would be helpful $\endgroup$ – NotEvans. Jul 21 '17 at 10:02
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    $\begingroup$ Rule of thumb: DOI for a paper, ISBN for a book. This makes things easier. $\endgroup$ – andselisk Jul 21 '17 at 10:04
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    $\begingroup$ If I weren't a mod I might have vtc'd as unclear, as I have no idea what "partial nullification" of resonance means. Is there any explanation or justification in the book? $\endgroup$ – orthocresol Jul 21 '17 at 10:07
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    $\begingroup$ Coplanarity is in no way a condition for resonance. In its widest scope resonance simply means, how delocalised is a certain system. In biphenyl, you still have two highly delocalised aromatic rings. The overlap, and further delocalisation of those two aromatic systems might not be as large as in a planar system, but it is certainly there. || Please edit in the complete citation to the quoted statement, so that it can be seen in context. You might want to tag it erratum, too. $\endgroup$ – Martin - マーチン Jul 21 '17 at 13:08
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I thought since both phenyl rings are not coplanar, the resonance between them is not possible.

This is not correct. If the rings are coplanar you get the best orbital overlap and the strongest resonance effect, while if you twist it the effect will be smaller but still present until you are at an dihedral angle of 90°, where no overlap can take place.

Let us look at phenyl-tetrazine. The phenyl substituent loweres the LUMO of the tetrazine through conjugation and raises the HOMO. The most favored confomer is the planar one, so the ideal system to study this. If it's correct that resonance only takes place at a planar conformation we should see a sudden jump in LUMO energy between planar conformation and any other and for all angles not equal to 0° the LUMO level should be the same.

enter image description here

In addition resonance is stabilizing, so the energy should drop rapidly between non-planar and planar.

Calculated energies (M06-2X/6-311+(d,p)) while twisting the bond looks like this:

enter image description here

So the energy goes up continuously if we twist the phenyl ring, there's no jump in energy. Since there's basically no steric effect, unlike in biphenyl, the energy is most likely only influenced by resonance.

Let us look at the HOMO level. I just picked some angles:

enter image description here

As expected the HOMO is raised in case of planar conformation in contrast to 90°, where we expect no overlap but we can clearly see that there's an influence on the HOMO at nearly every angle getting much stronger if we get near planarity.

Since the HOMO is completely localized at the tetrazine even in the planar form let's look at the HOMO-3 as an example. This orbital is part of the conjugated aromatic system and looks like this if the angle is 0°. Of course orbital energies will get shifted if we twist the rings and finding "the same" orbital is hard, but I'll show the orbital with the same symmetry at the tetrazine.

Here's the picture for 0°, a nice conjugated system: enter image description here

Here's the picture for 90°, there's no conjugation with the pi-system, little bit with some, I assume, sigma* orbitals. enter image description here

Now here for 15,30 and 60°: enter image description here enter image description here enter image description here

We can see quite nicely that the orbital in case of 15 and 30° still looks quite similar to the one at 0°, while the one at 60° already looks quite like the one at 90°, with a little bit of orbital in para position at the phenyl ring. Showing that there's a gradual loss of conjugation.

In addition, if the conjugation would be possible only at exact 0° dihedral angle then two things could happen: Either we won't see the effect of conjugation ever, since the molecules move all the time and if rotation around that bond is possible then the chance that the molecule is at exact 0° is basically zero. But we know that conjugation exists. Or the planar conformation would be much more stable due to the conjugation and it would be exact 0° all the time, but from experiments we actually know that those bonds rotate quite well.

coplanarity the topmost condition for resonance –

The most important condition is an overlap between the orbitals, this usually works best if planar, but it most certainly doesn't have to be planar.

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