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My contention is that the first azulene structure, with the nitro group on the aromatic cyclopentene ring has a lower ground state energy, as the negative charge can not only resonate into the nitro group, but also through the bridgehead carbon bond. In the second azulene derivate, the negative charge can resonate into the nitro group, but it cannot resonate across bridgehead carbon bond. As such, the first structure has a lower energy ground state because the energy is more delocalized. Is this correct?

First Azulene Ring

Second Azulene Structure

Martin - マーチン
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big_yoshi
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    If you consider the polarity of azulene itself and the effect of methoxy and nitro substituents on benzene, then you should have you answer. – user55119 Aug 25 '23 at 19:42
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    We have a great question on resonance: https://chemistry.stackexchange.com/q/51632/4945 Please read it. Within the concept of resonance there is no resonating. Your viewpoint is somewhat classical, as if the charges are actually localised. They are not. Azulene is an aromatic compound. If you were to substitute it with a similar aromatic compound, would you expect a significant difference? I wouldn't, and I guess that is the case here, too. Btw. the methoxy groups are usually drawn with an angle. – Martin - マーチン Aug 25 '23 at 19:43
  • @user55119 since azulene has more pi electrons on the 7 membered ring, it is more electronegative on that side, so having the nitro group there stabilizes the electron density, while having the electron donating methoxy group on the electron poor cyclopentene also stabilizes that side, which is electropositive, thus structure 2 is more stable? – big_yoshi Aug 25 '23 at 19:56
  • Wrong! As Martin has said, ignore the double bonds. Azulene is aromatic. Consider cyclopentadienyl anion and cycloheptatrienyl cation. – user55119 Aug 26 '23 at 21:30

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