A Formula Periodic Table for Benzenoid Hydrocarbons and the Aufbau and Excised Internal Structure Concepts in Benzenoid Enumerations

Abstract

The genesis of two concepts of recent importance to isomeric polyhex enumeration is traced. As it will become evident from this review, the philosophy of our approach stresses the enumeration of select benzenoid groups of practical interest to chemists. These concepts were pivotal to the first published enumerations of the strictly peri-condensed, non-Kekulean, and essentially strain-free total resonant sextet benzenoid groups.

New Insights into Aromaticity through Novel Delta Polynomials and Delta Aromatic Indices

“…Tables 5 and 6 consider three polycyclic isomers of C 22 H 12 and the corresponding circumscribed structures of the three isomers, respectively. The three isomers have been enumerated in the handbook by Dias [57] on polycyclic aromatic compounds. The three isomers, namely, triangulene, anthanthrene and benzo[ghi]perylene, represent interesting cases for our study.…”

“…Furthermore, macrocyclic compounds find applications in the environmental remediation through the selective sequestration of metal ions, and consequently, they find important applications in the sequestration of toxic metal ions, for example, in high-level nuclear wastes. Hosoya [21] has carried out pioneering studies connecting symmetry and matchings of graphs and extensive work has been carried out by Hosoya [18][19][20][21][22][23][24], Aihara [13,23,25,26,[29][30][31][32][33]35,40,[49][50][51][52][53][54][55], Dias [34][35][36][37][38][39]53,[56][57][58] and the author and coworkers [16,[66][67][68][69][70][71][72][73][74][75]…”

Formula Periodic TablesTheir Construction and Related Symmetries

“…This strategy was sufficient for benzenoids having less than five internal third degree vertices. For five or more internal third degree vertices, one needed to supplement the enumerations by deployment of the excised internal structure concept …”