Ring current patterns in annelated bicyclic polyenes

Ring-current maps are constructed by Hückel-London theory for the 36 bicyclic systems CNHN-2 derived by formal cross-linking of even [N]annulenes (N ≤ 18). The patterns of circulation are classified according to the length of perimeter and position of the cross-link, described by the five possible combinations of perimeter and constituent ring sizes. The qualitative predictions are tested by ab initio distributed-origin (CTOCD) calculations of the maps for a subset of 15 bicycles in planar geometries. The ab initio calculations confirm the graph-theoretical prediction that the main current follows the Hückel rule: diatropic for "aromatic" 4n + 2 and paratropic for "antiaromatic" 4n π electrons. A perimeter current is found in the ab initio maps, when the bicycle is formed by fusion of two odd rings ([2l + 1], [2m + 1]), two equal antiaromatic rings ([4l, 4l]) or two (not necessarily equal) aromatic rings ([4l + 2], [4m + 2]). Orbital analysis shows that these perimeter currents are four-electron diatropic or two-electron paratropic, as in the monocycles. In the other cases, of a 4n + 2 bicycle formed by fusion of two unequal antiaromatic rings ([4l, 4m]) or of a 4n bicycle formed from fusion of an antiaromatic and an aromatic ring ([4l, 4m + 2]), the current is concentrated in one of the component rings.