# 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.)

• Aromatic or antiaromatic, it is still conjugated, so no wonder it is better off than the all-ethylene analog. The general explanation is precisely where you don't think it is. – Ivan Neretin Mar 21 '19 at 15:31
• With Huckel MOT, aromaticity / antiaromaticity should be determined with reference to a linear conjugated analogue, so e.g. cyclobutadiene is compared with butadiene, not two ethylenes. I am not sure how this carries over to pentalene. Arguably, Huckel's rules were designed for monocyclic systems, not polycyclic ones. – orthocresol Mar 21 '19 at 15:40
• I solved the secular equation of pentalene, whose matrix has two resonance integral in addition to that of cyclooctatetraene. The solutions have no degeneracy, so I think penetalene is not expected to be radical. – Sakai Mar 22 '19 at 4:31
• @sakai right. Pentalene is not a radical. But it will have a low-lying acceptor orbital and thus is highly reactive an an electrophile. Which, of course, is what actually happens. Fill the low-lying acceptor orbital and the resulting dimension is quite stable. – Oscar Lanzi Aug 10 '20 at 22:08