Conjugation and aromaticity of macrocyclic systems

Abstract

Using a graph theoretical approach we have analyzed the aromatic stability of macrocyclic systems having ten and fewer fused benzene rings. The approach requires construction and examination of Kekule valence structures of the macrocyclic systems considered. The Kekule valence structures for a molecule were systematically derived and the conjugated circuits in the individual Kekule formulas were enumerated subsequently. The counting results is the expression for molecular resonance energy, from which relative aromatic stabilities can be established. We report also on molecular local features, including ring benzene characters and Pauling bond orders.

Aromaticity of Polycyclic Conjugated Hydrocarbons

“…In contrast, the compounds shown in Figure have on their peripheries 4 n carbon atoms. Hence, conjugated circuits involving the peripheries of such structures will necessarily have contributions from the 4 n conjugated circuits . However, the smallest such circuits will have already 12 carbon atoms and will make a small, if any, negative contribution to the molecular RE.…”

“…For some coronoids it was possible to get an adequate mathematical formulation, 456 or a practical and relatively simple algorithm. 457 We should add that Yen 458 in 1971 presented equations for the determination of the number of Kekule ´valence structures for several families of peri-condensed benzenoids, including the square (parallelogram) model, symmetric circular systems, the rectangular model, and a skew strip model. Sheng 459 outlined an economical two-vertex elimination method for deciding whether a polycyclic benzenoid hydrocarbon has Kekule ´valence structure, and brothers He Wenjie (mathematician) and He Wenchen (chemist) discuss enumeration of Kekule śtructures using a matrix corresponding to "peak" and "valley" carbon atoms.…”

“…Hence, conjugated circuits involving the peripheries of such structures will necessarily have contributions from the 4n conjugated circuits. 457 However, the smallest such circuits will have already 12 carbon atoms and will make a small, if any, negative contribution to the molecular RE. So, from the practical point of view, the corannulenes shown in Figures 63 and 64 will show little differences in their properties from the benzenoids already considered, except for properties associated with the presence of the inner hydrogen atoms.…”

“…Enumeration of Kekulé valence structures has also been extended to a class of generalized benzenoid hydrocarbons, the so-called coronoid hydrocarbons, which are built from fused benzene rings, but permitting in the interior one or more larger “holes”. For some coronoids it was possible to get an adequate mathematical formulation, or a practical and relatively simple algorithm . We should add that Yen 458 in 1971 presented equations for the determination of the number of Kekulé valence structures for several families of peri-condensed benzenoids, including the square (parallelogram) model, symmetric circular systems, the rectangular model, and a skew strip model.…”

Computer generation of Pauling bond orders using heuristic search

“…For instance, in the graph referred to in Figures 2 and 3, edge (1,5) is selected first, and then the partition containing (2,6) and (2,8) is the FFDP. If (1,5) is deleted from the graph along with its incident edges, bond (2,8) becomes the pendant bond and (6,10) (8,13) (1U5) (17,22) (20,23) (26,29) hence is taken as a constraint (Figure 3). This is repeated in the subsequent frames of search.…”