Analysis of the π‐electronic structure of infinitely large networks. I. Some remarks on the characteristic polynomial and density of states of large polycyclic aromatic hydrocarbons

Hosoya, Haruo; Aida, Misako; Kumagai, Reiko; Watanabe, Kazu

doi:10.1002/jcc.540080412

Cited by 33 publications

(41 citation statements)

References 29 publications

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“…The aufbau unit for generation of successive structures in Figures 3 and 4 is C 6 H 4 compared to C 4 H 2 for the structures of Figure 2. As shown by Hosoya and co-workers and Hall and Arimoto, 10 infinite poly(pphenylene), the limit member of the upper series in Figure 3, has a nonzero bandgap and is expected to be nonconductive. Since infinite poly(p,p-bisallylphenylene), the limit member of the lower series in Figure 3, has the same density of states, it is also expected to be nonconductive; note that its doubly degenerate zero level contains only two electrons, which makes an insignificant contribution compared to the remaining infinite number of electrons.…”

Section: Polyacenesmentioning

confidence: 93%

“…This pairwise matching of eigenvalues between the upper and lower molecular graphs of Figure 1 constitutes a proof that both infinitely large linear and cyclic polyenes have the same density of states, in agreement with the work of Hosoya and co-workers. 10 …”

Section: Almost-isospectral Series Of Conjugated Hydrocarbon Moleculesmentioning

confidence: 97%

“…The bandgaps of the limit members to every row series in Figure 7 were deduced to be zero by Hosoya and co-workers, 10,33 whereas the bandgap is zero only for the limit members of the second, fifth, eighth, and so on (per modulo-3) columns. Since the limit member of every row makes up the limit column which by necessity must be made up of all members with zero bandgaps, it is deduced that the nonzero bandgaps associated with the limit members of each non modulo-3 column also approach a zero bandgap as one moves to the right in Figure 7.…”

Section: Infinite Two-dimensional Motifs Of Almost-isospectral Seriesmentioning

confidence: 99%

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Strongly Subspectral Conjugated Molecular Systems. From Small Molecules to Infinitely Large π-Electronic Networks

Dias

1997

J. Phys. Chem. A

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Series of molecular graphs having a preponderance of common eigenvalues are identified, and their structural relationships studied. A framework for the analysis of graphitic polymers is provided by an infinite twodimensional mapping. Collections of subspectral structures (molecular graphs) and their eigenvalues are tabulated for the first time.The analysis of π-electronic structure of polymer networks continues to attract the interest of theoretical 1 and synthetic 2-7 researchers. One of the major objectives of these studies is to gain insight on the design of potential organic conductors and ferromagnets. Extended pπ-conjugated systems represent the simplest models for molecular wires. The reduction of the HOMO-LUMO bandgap in conjugated systems will enhance the thermal population of the conduction band and thus increase the number of charge carriers, and minimizing the degree of bond length alternation in a conjugated path which is the origin of Peierls instability will help preserve the proximity or degeneracy between the HOMO-LUMO electronic levels. Thus, researchers need to learn what structural variables control the HOMO-LUMO energy gap and bond length alternation in pπ-electronic systems before organic conductors can be designed. There is no such thing as a ferromagnetic molecule. However, if parallel spin alignment can be induced in molecules, like polymethyleneacetylene, while it is in the condensed phase, a paramagnetic (and possibly a ferromagnetic) material would be produced. 2 Since electron spins tend to align antiparallel to one another, currently no organic ferromagnetic material has yet been designed and synthesized.Three general theoretical approaches can be identified: study of infinitely long strips, belt-shaped rings, and a series of strips that are progressively incremented (i.e., a homologous series). This latter approach follows more closely the way experimentalists are capable of studying very large molecules and is analogous to the standard methodology in which molecular systems are partitioned into smaller elementary substructures. For example, infinitely long polyacene strips and cyclic polyacene rings have been frequent objects of theoretical study, but are experimentally unknown, whereas members of the homologous acene series from naphthalene to heptacene are known to progressively decrease in stability and ease of experimental manipulation. Nevertheless, these experimental results for smaller homologues along with theoretical molecular modeling studies 1 suggest that polyacenes will be conductive and reactive materials but not ferromagnetic. 8 By assuming infinitely long polyacenes can be modeled as infinite belt-shaped rings ([∞]cyclacenes), its irreducible substructure can be obtained. 9,10 Hosoya and co-workers have shown that the density of states of cyclic and linear polyene systems having common repetitive units are identical in the infinite limit. Also, they showed that the singular points of the density of states of infinitely large polyenes correspond to the energy levels ...

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Section: Polyacenesmentioning

confidence: 93%

Section: Almost-isospectral Series Of Conjugated Hydrocarbon Moleculesmentioning

confidence: 97%

Section: Infinite Two-dimensional Motifs Of Almost-isospectral Seriesmentioning

confidence: 99%

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Strongly Subspectral Conjugated Molecular Systems. From Small Molecules to Infinitely Large π-Electronic Networks

Dias

1997

J. Phys. Chem. A

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“…However, the zigzag polyacenes were found to give the best correlation against their biradical character (BRC). 19 In the plot of BRC versus HOMO, the zigzag phenacenes in Figure 7 appears to approach the Hosoya calculated limit HOMO value of 0.382 β as the number of rings increases; 8 (determined from the characteristic polynomial) divided by that of the hypothetical polyene reference which is devoid of cyclic contributions (determined from the matching polynomial) and is a measure of kinetic stability. 24 The contrasting difference in reactivity (kinetic stability) of the linear acenes versus the phenacenes is emphasized by the plots (Figures 8 and 9) of the number of Dewar resonance structures versus the reduced HOMO-LUMO gap index of Aihara.…”

Section: Dsmentioning

confidence: 73%

“…Hosoya and coworkers showed 8 that the infinite linear polyacene had a zero band gap whereas the infinite zigzag polyacene had a HMO band gap of HOMO-LUMO = 0.7639 β. In regard to topological resonance energy (TRE), linear and zigzag polyacene isomers were compared to their cyclo-counterparts by Aihara.…”

Section: Introductionmentioning

confidence: 99%

Correlations of the Number of Dewar Resonance Structures and Matching Polynomials for the Linear and Zigzag Polyacene Series

Dias¹

2013

Croat. Chem. Acta

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Abstract. Linear and zigzag polyacene series have been the subject of numerous studies because of their contrasting electronic and stability characteristics. The correlation of the properties of these series is examined in regard to their number of Dewar resonance structures (DS). Since resonance-theoretic methods require algorithms for determining the number of Dewar resonance structures (DS), recursion equations for calculating DS for these series are presented for the first time. Excellent correlations between DS and the absorption p-band, ionization energies, Hückel HOMO, Aihara's reduced HOMO-LUMO gap, topological resonance energy (TRE), aromatic stabilization energy (ASE), and the Klein and Randić innate degree of freedom are presented and rationalized. (doi: 10.5562/cca2292)

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Analysis of ?-electronic structures of small alternant hydrocarbons to infinitely large polymeric strips: The aufbau principle and end-group effects

Dias

1999

Int. J. Quant. Chem.

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Paired series of strongly subspectral molecular graphs which possess a preponderance of common eigenvalues can be constructed by successive attachment of Ž . specific aufbau units repeated subgraphs to certain seed graphs. Recursion relations for the characteristic polynomials of such series are identical and differ only in the input of initial characteristic polynomials. A new operator method for the derivation of recursion relations for singly connected polymeric series is presented. Strongly subspectral series devolve to the same infinite-limit member and density of states, and two types of end-group effects are demonstrated.

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Analysis of the π‐electronic structure of infinitely large networks. I. Some remarks on the characteristic polynomial and density of states of large polycyclic aromatic hydrocarbons

Cited by 33 publications

References 29 publications

Strongly Subspectral Conjugated Molecular Systems. From Small Molecules to Infinitely Large π-Electronic Networks

Strongly Subspectral Conjugated Molecular Systems. From Small Molecules to Infinitely Large π-Electronic Networks

Correlations of the Number of Dewar Resonance Structures and Matching Polynomials for the Linear and Zigzag Polyacene Series

Analysis of ?-electronic structures of small alternant hydrocarbons to infinitely large polymeric strips: The aufbau principle and end-group effects

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