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

Dias, Jerry Ray

doi:10.5562/cca2292

Cited by 5 publications

(3 citation statements)

References 21 publications

(31 reference statements)

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“…In the limit of an infinitely long polyacene, the diradical resonance structures should predominate, [46][47][48] which leads to the conclusion that the HOMO-LUMO gap for such a molecule should be 0, corresponding to an infinitely big relative transmission. This is indeed what is observed for zigzag nanographene.…”

Section: Polycyclic Aromatics-nanographenesmentioning

confidence: 99%

Enhancing the conductivity of molecular electronic devices

Stuyver

Fias

Proft

et al. 2016

The Journal of Chemical Physics

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We show in this work that conjugated π-electron molecular chains can, in quite specific and understood circumstances, become more conductive the longer they get, in contradiction to what would be expected intuitively. The analysis, done in the framework of the source and sink potential method, and supported by detailed transmission calculations, begins by defining "relative transmission," an inherent measure of molecular conduction. This, in turn, for conjugated hydrocarbons, is related to a simple molecular orbital expression-the ratio of secular determinants of a molecule and one where the electrode contacts are deleted-and a valence bond idea, since these secular determinants can alternatively be expressed in terms of Kekulé structures. A plausible argument is given for relating the relative transmission to the weight of the diradical resonance structures in the resonance hybrid for a molecule. Chemical intuition can then be used to tune the conductivity of molecules by "pushing" them towards more or less diradical character. The relationship between relative transmission (which can rise indefinitely) and molecular transmission is carefully analyzed-there is a sweet spot here for engineering molecular devices. These new insights enable the rationalization of a wide variety of experimental and theoretical results for π-conjugated alternant hydrocarbons, especially the striking difference between extended oligophenylenes and related quinoid chains. In this context, oligo-p-phenylene macrocycles emerge as a potential molecular switch.

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Section: Polycyclic Aromatics-nanographenesmentioning

confidence: 99%

Enhancing the conductivity of molecular electronic devices

Stuyver

Fias

Proft

et al. 2016

The Journal of Chemical Physics

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“…considering n , the number of edges connected in the central part of the graph, in the chain of concealed non-kekuléan benzenoid graph the total number of edges are . The equality of the number of starred and unstarred vertices is a essential as well as sufficient requirement for a benzenoid structure to be Kekuléan, as addressed by Gutman in 24 . Even while just two naphthalene compounds benzenoid hydrocarbons and anthracene have a substantial number of applications in the chemical industry, one may argue that pitches and tars have no direct relation for various mechanical and technological applications.…”

Section: Concealed Non-kekuléan Benzenoid Hydrocarbonmentioning

confidence: 99%

Computing edge version of metric dimension of certain chemical networks

Farooq,

Hussain,

Jan

et al. 2024

Sci Rep

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In the modern digital sphere, graph theory is a significant field of research that has a great deal of significance. It finds widespread application in computer science, robotic directions, and chemistry. Additionally, graph theory is used in robot network localization, computer network problems and the formation of various chemical structures for networks. Moreover, it finds uses in exploring diffusion mechanisms and scheduling aircraft as well. The present research project examines and concentrates on the edge version of metric dimension of the Concealed Non-Kekuléan Benzenoid Hydrocarbon, Polythiophene, Backbone DNA network and Bakelite networks. All the mentioned networks have constant edge metric dimension except Bakelite network, as demonstrated by the results. If we talk about the applications of these networks, Polythiophene are used to treat prion disorders. It is also capable of detecting metal ions. The concept of Bakelite, which finds applications in the jewelry, electrical, cookware, sports, and clock industries, had an impact on the invention of modern polymers. The functions of DNA include information encoding, replication, mutation, and recombination gene expression.

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“…Dias used MP to find excellent correlations between Dewar resonance structures and some properties: 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 [110].…”

Section: Matching Polynomialmentioning

confidence: 99%

Counting Polynomials in Chemistry: Past, Present, and Perspectives

Joița,

Tomescu,

Jäntschi

2023

Symmetry

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Counting polynomials find their way into chemical graph theory through quantum chemistry in two ways: as approximate solutions to the Schrödinger equation or by storing information in a mathematical form and trying to find a pattern in the roots of these expressions. Coefficients count how many times a property occurs, and exponents express the extent of the property. They help understand the origin of regularities in the chemistry of specific classes of compounds. Our objective is to accelerate the research of newcomers into chemical graph theory. One problem in understanding these concepts is in the different approaches and notations of each research study; some researchers provide online tools for computing these mathematical concepts, but these need to be maintained for functionality. We take advantage of similar mathematical aspects of 14 such polynomials that merge theoretical chemistry and pure mathematics; give examples, differences, and similarities; and relate them to recent research.

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

Cited by 5 publications

References 21 publications

Enhancing the conductivity of molecular electronic devices

Enhancing the conductivity of molecular electronic devices

Computing edge version of metric dimension of certain chemical networks

Counting Polynomials in Chemistry: Past, Present, and Perspectives

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