When are Antiaromatic Molecules Paramagnetic?

Magnetizabilities and magnetically induced current densities have been calculated and analyzed for a series of antiaromatic cyclo[4k]carbons (k = 2-11), iso[n]phlorins (n = 4-8), expanded porphyrinoids, and meso-meso, beta-beta,beta-beta triple-linked porphyrin and isophlorin arrays. The cyclo[4k]carbons with k = 2-6 are predicted to be closed-shell paramagnetic molecules due to the very strong paratropic ring current combined with its large radius. Larger cyclo[4k]carbons with k = 6-11 are diamagnetic because they sustain a paratropic ring current whose strength is weaker than -20 nA T-1, which seems to be the lower threshold value for closed-shell paramagnetism. This holds not only for cyclo[4k]carbons but also for other organic molecules like expanded porphyrinoids and oligomers of porphyrinoids. The present study shows that meso-meso, beta-beta, beta-beta triple-linked linear porphyrin and isophlorin arrays have a domainlike distribution of alternating diatropic and paratropic ring currents. The strength of their local paratropic ring currents is weaker than -20 nA T-1 in each domain. Therefore, linear porphyrin and isophlorin arrays become more diamagnetic with increasing length of the ribbon. For the same reason, square-shaped meso-meso, beta-beta, beta-beta triple-linked free-base porphyrin and isophlorin tetramers as well as the Zn(II) complex of the porphyrin tetramer are diamagnetic. We show that closed-shell molecules with large positive magnetizabilities can be designed by following the principle that a strong paratropic current ring combined with a large ring-current radius leads to closed-shell paramagnetism.