Antiaromaticity can be explained by Hückel method?

Pentalene is one of the most famous antiaromatic molecules. But I obtained its energy of $\pi$ system as $8\alpha+10.46\beta$ by Hückel method (with a bit complicated but straightforward calculation). This value is lower than that of localized form $8(\alpha+\beta)$. So Hückel method looks to be not able to explain antiaromaticity. Are there any misunderstandings? It seems that many of antiaromatic molecules are predicted lower than their all-ethylene counterparts.


(I don't think radicality is a key for antiaromaticity, and I'd like to know a general, quantum mechanical explanation about antiaromatic molecules if it exists.)


