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Butalene and related compounds: aromatic or antiaromatic?

Density functional theory (DFT) has been used to study the first three members of the condensed cyclobutadienoid series, butalene (3), bicyclobutadienylene (12), and dicyclobutenobutalene (20). The first is planar and is judged "aromatic" by comparisons with suitable models using both energetic and magnetic criteria. The second is nonplanar, and not aromatic, but not so antiaromatic as cyclobutadiene (11). The third is slightly more antiaromatic and best viewed as a butalene fused to two cyclobutadiene rings; its properties are the sum of aromatic and antiaromatic components, like benzocyclobutadiene. Ring-opening transition states for both 3 and 12 have been located, and these are conrotatorily twisted. The ring-opening barrier for 12 is more than twice that for 3. Ring-opening of 20 involves ring inversion as the only barrier.