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I came across this structure which has got pi bonds only in its canonical forms (which are also unstable compared to the Ist structure), is it aromatic?

Also, is it compulsory for an aromatic compound to contain a carbon ring? Can't a conjugate system without carbon be aromatic (as in this case)?

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The modern definition of aromaticity from deep theoreticians is that the π-system needs to support aromatic ring currents. Borazine can support it, so it is technically aromatic.

Aromatic systems that do not contain carbon are not really all that common, but they are known. Pentazole was detected, for example. The problem is, that for aromaticity to be a thing we need a π-system, and π-systems effectively restrict us to BCNOS elements, since other elements are not eager to form π-bonds. Aromatic systems are usually 5- or 6-membered rings. Add in the fact that rings with a lot of N/O atoms often happily go kaboom after a funny look, and it's not surprising we have very few actual examples here. Still, some people insist on doing unreasonable things with results from as far back as the 50s.

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    $\begingroup$ Borazine is slightly controversial, I think the general consensus seems to be aromatic, but not very much. e.g. NICS values borazine -2.1, benzene -11.5. $\endgroup$ – orthocresol♦ Feb 26 '18 at 20:05
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Yes, Borazine is aromatic.

According to Hückel’s rules, a compound is aromatic if it satisfies three conditions:

  1. Planarity
  2. Complete delocalisation of π-electrons
  3. Presence of $(4n+2)$ electrons where $n$ can be $1, 2, 3, \dots$.

Borazine is aromatic as there are 3 nitrogen atoms in the structure of borazine that donate two electrons each. Boron doesn't donate any, but it has an empty p-orbital available through which the electrons can delocalize. Hence, in total it has 6 π-electrons. Though the delocalisation is lesser than that in benzene, it still is aromatic.

FunFact: Borazine is also called inorganic benzene because of its resemblance to benzene by structure.

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    $\begingroup$ Strictly speaking, Hückel's rules is derived from hydrocarbons, and the generalisation to other compounds is neither straight forward, nor necessary correct. Just because it a has been applied before, it does not mean it is founded in rigorous theory. $\endgroup$ – Martin - マーチン♦ Feb 27 '18 at 4:35
  • $\begingroup$ Oh! Alright. Noted! So aromatic ring currents is the only theory to confirm aromaticity for a $\pi$ system? (Systems that don’t have carbon) $\endgroup$ – MollyCooL Feb 27 '18 at 5:03

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