Validity and Limitations of the Bridged Annulene Model for Porphyrins

Abstract

According to the bridged annulene model, macrocyclic aromaticity of a porphyrinoid species can be attributed to the annulene-like main macrocyclic conjugation pathway (MMCP). Macrocyclic aromaticity, however, is given theoretically as a sum of contributions from all macrocyclic circuits. We found that the aromaticity due to each macrocyclic circuit is determined formally but broadly by Hückel's [4n + 2] rule of aromaticity. Nitrogen atoms in the pyrrolic rings effectively suppress the variation in the number of π electrons staying along each macrocyclic circuit. As a result, all or most macrocyclic circuits in oligopyrrolic macrocycles are made aromatic (or antiaromaitc) in phase with the MMCP. Thus, the MMCP is not a determinant of macrocyclic aromaticity but can be regarded as a good indicator of this quantity. This is why the bridged annulene model appears to hold for many porphyrins.

Graph Theory of Ring-Current Diamagnetism

“…The MRE-to-TRE ratios for aromatic porphyrins are comparable in magnitude to those for familiar aromatics, whereas the ratios are somewhat larger for antiaromatic porphyrins. 145 Antiaromatic porphyrins may be similar in this respect to antiaromatic hydrocarbons.…”

“…It is worth noting that, in such polycyclic π-systems, the aromaticity of aromatic circuits and the antiaromaticity of the coexisting antiaromatic circuits are often intensified at the same time. 145,146 As can be seen from the last column of Table 15, the average CRE for 5-circuits in antiaromatic porphyrins are about twice as large as that in aromatic porphyrins. This is the same phenomenon as observed among the circuits of bicyclo[6.2.0]decapentaene (84), the CREs for which were analyzed in some detail in section 10.2.…”

“…The macrocyclic circuit chosen along the MMCP exhibits the largest positive or negative CRE among the macrocyclic circuits. 145 MRE for a porphyrin molecule is equal to the sum of CREs for the macrocyclic circuits (i.e., m-SSE) and those for the local 5-circuits. Since all porphyrins are globally aromatic with positive MREs, antiaromatic porphyrins necessarily have both aromatic and antiaromatic circuits.…”

“…For each porphyrin, the main stream of the macrocyclic component (i.e., the sum of currents induced in all macrocyclic circuits) really runs along the MMCP. 145 Local circuits in both porphyrins (95d and 97d) are all diatropic.…”

“…As for 95, the main stream of the macrocyclic circulation (main macrocyclic circulation pathway) in the global ring-current map (95b) still runs along the MMCP or the [22]annulene pathway. 145,146 The main stream of the macroscopic circulation in 97 (97b), however, deviates from the [20]annulene-like MMCP and runs along the inner periphery, passing through all nitrogen atoms. 145149 Note that a main macrocyclic circulation pathway and the MMCP (i.e., the conventional annulene pathway) are two different manifestations of macrocyclic conjugation.…”