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Has this ever been tried? The respective aromatic ions are readily accessible, e. g., in the form of sodium cyclopentadienide and tropylium bromide. It shouldn't be hard to just combine these two salts. People have went down much more intricate ways to obtain exotic aromatics. Especially considering the prospect of a pure hydrocarbon ionic compound (maybe even an ionic liquid?), formally derived from benzene by intermolecular exchange of a CH⁺ charged ring segment. Or call it, with some hand-waving, a heterolytic cleavage of azulene.

I've done some superficial peek into literature (tricky, since there are tons of sources discussing the two aromatic ions separately); best I cold find was https://doi.org/10.1248/cpb.11.126 with their compound VII:

Matsumura/Seto 1963, compound VII

(with some bulky substituents on the cyclopentadienide ion), that “easily formed red crystals” from aqueous solution. Apparently, though, learning about the pure C₇H₇C₅H₅ was none of their priority. But the fact that this is isolatable, and doesn't fall apart/rearrange immediately, sounds promising to me.

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    $\begingroup$ chemistry.stackexchange.com/questions/9212/… $\endgroup$
    – Mithoron
    Commented Aug 29, 2023 at 1:00
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    $\begingroup$ It's not a matter of bulkiness - you need powerful withdrawing groups on cyclopentadienyl and donating ones on tropylium. Otherwise charge density is so high you get covalent bond. $\endgroup$
    – Mithoron
    Commented Aug 29, 2023 at 1:02

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While I can't give a definitive disproof, my intuition is that an unsubstituted cyclopentadienide anion would be far too nucleophilic and react with the tropylium cation at non-cryogenic temperatures (or alternatively, there could be direct charge transfer forming radicals which would then react in various ways). Note that the presence of opposing charges vastly increases the kinetic and thermodynamic propensity towards reaction in the absence of other inert screening charges. All those cyano substituents in the successfully isolated compound you show are really pulling a lot of weight, delocalising and stabilising that negative charge to tame it.

But it is also possible to delocalize the charges in the absence of assisting heteroatoms using larger and larger pi-conjugated systems to eventually stabilize them. The excess charges essentially have to be "diluted" over enough atoms and spaced far enough apart to stop them from mutually reacting. Have a look at these first examples of hydrocarbon salts to get a feel for what's necessary to keep the charges separate. Typically both the cation and the anion have to be extensively overbuilt. Anion 1 and cation 5 can be viewed as a derivative of the cyclopentadienide and tropylium cation, respectively, and their combination does result in an isolable salt (actually the least stable salt of the combinations tried in the study).

Interestingly, this paper also mentions that tropylium acetate is a covalent compound, and the acetate anion is substantially less basic/nucleophilic than unsubstituted cyclopentadiene, so once again the odds of your desired salt existing in reasonable conditions are likely quite low.

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