Clar Formulas: How to Draw and How not to Draw Formulas of Polycyclic Aromatic Hydrocarbons

Cyclic conjugation in benzo- and benzocyclobutadieno-annelated terrylenes and higher rylenes

“…In tetra-angularly annelated perylene, each of the four six-membered rings adjacent to ring 1 has ef = 0.0437, which is smaller than ef(1) = 0.0522. This contradicts the predictions of classical theories, [8][9][10] according to which there is no cyclic conjugation in the "empty" ring.…”

“…1 Its details and an exhaustive bibliography can be found in the reviews, 2,3 whereas the mathematical details by which the quantity ef is computed are outlined in recent articles. 4,5 When the ef-method was applied to benzo-annelated perylenes, 6,7 a remarkable phenomenon was discovered: Contrary to what standard methods [8][9][10] predict, benzo-annelation significantly influences the intensity of cyclic conjugation in the "empty" central ring of perylene; in some cases it even exceeds the intensity of cyclic conjugation in the "full" rings. Characteristic results of this kind are shown in Fig.…”

The Clar formulas of a benzenoid system and the resonance graph

“…Hence, Kekuléan benzenoid systems pertain to those benzenoid hydrocarbons that have the most chemical interest [3]. Replacing the three alternating double bonds in a single hexagon of a Kekulé structure with a circle such that circles are not drawn in adjacent hexagons [2], one obtains a generalized Clar formula of a benzenoid system. As a consequence, an invariant of a Kekuléan benzenoid system called Clar number can be introduced.…”

Crocker, Not Armit and Robinson, Begat the Six Aromatic Electrons

“…In contrast, the prior work of an unknown American, Ernest C. Crocker, who identified the generality of six aromatic electrons clearly in 1922, has been almost completely overlooked. We only have found brief mention of Crocker in the Kekulé Cen- 35 But before turning to Crocker's contribution, let us consider Armstrong's even earlier prescient insights. He anticipated Robinson's aromatic "circle" even before the electron was discovered!…”