Analysis of the π-electronic structure of infinitely large networks

Hosoya, Haruo; Tsuchiya, Akiko

doi:10.1016/0166-1280(89)85009-2

Cited by 11 publications

(8 citation statements)

References 22 publications

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“…The series in Figures and are examples of the latter. The two different zigzag polymer strips discussed by Hosoya and co-workers are examples of type I and type II π-electronic polymer strips . On the basis of the results of this work, we propose that polymer strips of a given type must approach the same density of states in the infinite limit regardless of the exact nature of the end-groups as the polymer strips in Figures and .…”

Section: Properties Of Strongly Subspectral Seriesmentioning

confidence: 62%

“…The π-electronic polymer strips in Figure are complementary in their density of states. Hosoya and co-workers have shown that the energy levels of the cyclic dimer determine the singular points of the density of states of infinitely large polymers . Using this method, the singular points for the density of states of the polymer strips in Figure were determined.…”

Section: Properties Of Strongly Subspectral Seriesmentioning

confidence: 99%

“…Two types of π-electronic polymer strips are possible. Type I occurs when the end-groups cause all the bonds along the strip to localize, and type II occurs when the end-groups are unable to cause extensive bond localization throughout the total polymer strip . The series in Figures and are examples of the latter.…”

Section: Properties Of Strongly Subspectral Seriesmentioning

confidence: 99%

See 2 more Smart Citations

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

Dias

1998

J. Chem. Inf. Comput. Sci.

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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.

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Section: Properties Of Strongly Subspectral Seriesmentioning

confidence: 62%

Section: Properties Of Strongly Subspectral Seriesmentioning

confidence: 99%

Section: Properties Of Strongly Subspectral Seriesmentioning

confidence: 99%

See 1 more Smart Citation

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

Dias

1998

J. Chem. Inf. Comput. Sci.

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“…Hence, the mediating effects BOs u ðþÞ2 and u ðÀÞ2 of the central bond C 2 = C 5 to the above-mentioned elements are added together (cancel out one another) for the linear (branched) hexatriene and this fact causes the distinction between matrices G (2) (VII) and G (2) (VIII) shown in Eq. (19). The same state of things evidently refers also to individual triplets of linear and cross-conjugated C=C bonds in extended polyenes.…”

Section: Discussionmentioning

confidence: 93%

“…[15]), the vertices and edges of which represent atoms and bonds, respectively. The relevant studies of conjugation energies [4,13,[16][17][18][19][20] are carried out mostly by means of the chemical graph theory [15]. In particular, analysis of the principal Kekulé valence structure of polyene in terms of conjugated paths (CPs) of various lengths (i.e., of linear fragments consisting of C=C and C-C bonds alternately) [4,21] appears to be fruitful in this field.…”

Section: Introductionmentioning

confidence: 99%

A simple rationale for lowered stabilities of branched and cross-conjugated polyenes

Gineitytė

2016

Monatsh Chem

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The study is aimed at revealing the decisive factors for relative stabilities of acyclic p-electron systems of polyenes, the carbon backbones of which are of different type of branching. The systems are modeled as sets of N weakly interacting double (C=C) bonds. The relevant total p-electron energies are represented in the form of power series containing members of even orders with respect to the averaged resonance parameter of single (C-C) bonds. For distinct isomers of the same polyene, both zero-order energies and respective second-order corrections are shown to take uniform values. Relative stabilities of these isomers are then primarily determined by the fourth-order member of the series that, in turn, consists of two additive components of opposite signs, viz., of the stabilizing component expressible as a sum of transferable increments of individual triplets of linearly conjugated C=C bonds [i.e., of the three-membered conjugated paths (CPs)] and of the destabilizing component depending on overall adjacencies (connectivity) of C=C bonds. Lower stabilities of p-electron systems of branched and/or crossconjugated polyenes vs. the linear ones then follow from comparative analyses of the relevant fourth-order energies, and this destabilization is shown to originate either from (a) a reduced number of CPs or from (b) higher adjacencies of C=C bonds in the former isomers. An actual interplay of both factors (c) also is rather common. The three cases (a)-(c) are illustrated by specific examples. Graphical abstract

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Scaling behavior of ground‐state energy cluster expansion for linear polyenes

Griffin

Klein

et al. 2004

Int J of Quantum Chemistry

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Ground-state energies for linear-chain polyenes are additively expanded in a sequence of terms for chemically relevant conjugated substructures of increasing size. The asymptotic behavior of the large-substructure limit (i.e., high-polymer limit) is investigated as a means of characterizing the rapidity of convergence and consequent utility of this energy cluster expansion. Consideration is directed to computations via: simple Hü ckel theory, a refined Hü ckel scheme with geometry optimization, restricted Hartree-Fock selfconsistent field (RHF-SCF) solutions of fixed bond-length Parisier-Parr-Pople (PPP)/Hubbard models, and ab initio SCF approaches with and without geometry optimization. The cluster expansion in what might be described as the more "refined" approaches appears to lead to qualitatively more rapid convergence: exponentially fast as opposed to an inverse power at the simple Hü ckel or SCF-Hubbard levels. The substructural energy cluster expansion then seems to merit special attention. Its possible utility in making accurate extrapolations from finite systems to extended polymers is noted.

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Analysis of the π-electronic structure of infinitely large networks

Cited by 11 publications

References 22 publications

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

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

A simple rationale for lowered stabilities of branched and cross-conjugated polyenes

Scaling behavior of ground‐state energy cluster expansion for linear polyenes

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