Is [7]сirculene aromatic or anti-aromatic?

Question

This compound is called [7]circulene and is one of the examples of non-planar aromatic systems (1). From the first overview of this compound, it is observed that there are 7 benzene rings so one would conclude that it is an aromatic compound:

There are $7 \times 4 = 28$ $\pi$-electrons, so this compound satisfies the criteria of anti-aromacity. Then how come this compound is aromatic?

(1) Smith, M. March’s advanced organic chemistry: reactions, mechanisms, and structure, 7th ed.; Wiley: Hoboken, New Jersey, 2013, p. 48, compound 40.

Answer 1

TL;DR: We don't count π electrons here, rather the π conjugated circuits [1]. [7]-сirculene has all conjugated circles of size $4n + 2,$ and none of $2n,$ what makes it an aromatic compound.

Strictly speaking, the aromaticity $4n + 2$ and antiaromaticity $4n$ rules in their original interpretation are very limited and cannot be universally applied. According to the original Hückel $4n + 2$ rule, if a monocyclic, planar molecule has $4n + 2$ π electrons, it is considered aromatic.

But the count of π electrons is not what matters for polycyclic compounds, therefore a generalized $4n + 2$ rule exists: if a conjugated molecule has only $4n + 2$ π conjugated circuits, it is considered aromatic.

Non-benzenoid compounds can have both $4n + 2$ as well as $4n$ number of conjugated circuits counted by taking into account all Kekule structures. Among non-benzenoid non-alternant polycyclic hydrocarbons [5]-сirculene and [7]-сirculene both have only $4n + 2$ $(6, 10, 14, \dots)$ numbers of circuits.

Further reading: Is there any special rules for checking the aromaticity of polycyclic compounds?

Reference

1. Gutman, I.; Cyvin, S. J. Conjugated Circuits in Benzenoid Hydrocarbons. J. Mol. Struct. THEOCHEM 1989, 184 (1), 159–163. DOI: 10.1016/0166-1280(89)85141-3.