Directed toward the Development of a Unified Structure Theory of Polycyclic Conjugated Hydrocarbons:  The Aufbau Principle in Structure/Similarity Studies

Abstract

This work introduces two new concepts applicable to structure/similarity studies of conjugated hydrocarbons: (1) The first concept deals with orthogonal strongly subspectral series of molecular graphs and their properties. (2) In the second concept, if a relationship exists among set of strongly subspectral molecular graphs, then an equivalent relationship exists among the complementary molecular graphs of that set. Two sets of triplet series having strongly subspectral molecular graphs are presented. Collections of subspectral molecular graphs and their eigenvalues are tabulated for the first time.

Advances in Asphaltene Petroleomics. Part 3. Dominance of Island or Archipelago Structural Motif Is Sample Dependent

“…On the other hand, on the addition of aromatic rings to generate archipelago structures, where the bridges between the individual cores are either aryl–aryl or naphthenic rings, the slope decreases to ∼0.62. Blanco-Combariza et al reported an approach to extract structural information from FT-ICR MS data of fossil fuels on the basis of periodic tables of benzenoid hydrocarbons. − The authors suggested that compositions close to the PAH limit, with slopes near ∼0.90, are less diverse (fewer isomers) because they consist of pure pericondensed structures. As the molecular formulas move toward the right side of the homologous series or the planar limit slope decreases there is greater structural diversity: the benzenoid periodic tables predict the presence of catacondensed compounds and species with multiple cores linked by aryl–aryl bridges, like the archipelago structures found by Schuler et al…”

Two-Dimensional Arrays in the Analysis of Trends in Series of Molecules: Strongly Subspectral Molecular Graphs, Formula Periodic Tables, and Number of Resonance Structures

“…Similarly, twodimensional NMR gives more information than onedimensional NMR. In our prior work, two-dimensional arrays consisting of strongly subspectral molecular graphs 1 and formula periodic tables for benzenoids, 2 fluorenoids/fluoranthenoids, 3 and indacenoids 4 have been put forth and numerous algorithms and molecular trends discussed; the C-C σ-bond skeleton representation of a fully conjugated polyene structure is called a molecular graph. In this paper, we will provide new examples of two-dimensional arrays which uniquely provide novel insights concerning the number of resonance structures of free-radical benzenoids.…”

Eigen-Persistence in Graphs

“…[4][5][6][7][8][9][10][11][12][13][14][15][16] and many more), though there are several other interesting regularities. Some attention has been directed to the occurrence of excessive (eigenvalue) degeneracies [17][18][19][20][21][22][23], sometimes viewed as manifestations of "local" structures [24][25][26][27][28][29][30][31][32]. Since degeneracies arose early on in the context of symmetry (and group theory), there has been a natural effort [33][34][35][36][37][38][39] to investigate excessive degeneracies in terms of symmetries, most simply in terms of a graph's automorphism group, which generally goes beyond standard point-group symmetries.…”