Is a compound aromatic if it also has anti-aromatic rings?

Is 5,6,11,12-tetradehydrodibenzo[*a*,*e*][8]annulene aromatic?


![5,6,11,12-tetradehydrodibenzo[a,e][8]annulene](https://i.stack.imgur.com/yJZjM.png)


If I use Hückel's rule for the whole molecule, I get the answer as anti-aromatic. But the compound has two benzene rings which are individually aromatic.




**The molecule actually optimizes to a planar, delocalized $\pi$ system**


Using B3LYP/6-31G(d) optimizations, we see that the molecule optimizes to become planar. (The initial configuration was intentionally bent.)


[![enter image description here](https://i.stack.imgur.com/hipD0.png)](https://i.stack.imgur.com/hipD0.png)


Moreover, if I plot the HOMO, it's highly delocalized:


[![enter image description here](https://i.stack.imgur.com/33Tnv.png)](https://i.stack.imgur.com/33Tnv.png)


Similarly, the LUMO is also delocalized across the entire molecule:


[![enter image description here](https://i.stack.imgur.com/OJuJa.png)](https://i.stack.imgur.com/OJuJa.png)


Consequently, I don't see any indication that the "side" benzene rings are localized from the cycloocta-1,5-diyne ring. The bond lengths are in fairly good agreement with the crystal structure:


[![enter image description here](https://i.stack.imgur.com/eQJDD.png)](https://i.stack.imgur.com/eQJDD.png)


Here's the [crystal structure](http://dx.doi.org/10.1021/ja00836a041) from [*J. Am. Chem. Soc.*, **1975**, 97 (3), 658–659](http://dx.doi.org/10.1021/ja00836a041). Note there is a profound triple bond character, but the bridging bonds (1.44 Å) are somewhere between a typical aromatic bond length (1.40 Å) and a full single bond (~1.54 Å).


[![enter image description here](https://i.stack.imgur.com/ZYsoy.png)](https://i.stack.imgur.com/ZYsoy.png)


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