The Mathematics and Topology of Fullerenes

The Mathematics and Topology of Fullerenes PDF

Author: Franco Cataldo

Publisher: Springer Science & Business Media

Published: 2011-12-01

Total Pages: 294

ISBN-13: 9400702213

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The Mathematics and Topology of Fullerenes presents a comprehensive overview of scientific and technical innovations in theoretical and experimental studies. Topics included in this multi-author volume are: Clar structures for conjugated nanostructures; counting polynomials of fullerenes; topological indices of fullerenes; the wiener index of nanotubes; toroidal fullerenes and nanostars; C60 Structural relatives: a topological study; local combinatorial characterization of fullerenes; computation of selected topological indices of C60 and C80 Fullerenes via the Gap Program; 4valent- analogues of fullerenes; a detailed atlas of Kekule structures of C60. The Mathematics and Topology of Fullerenes is targeted at advanced graduates and researchers working in carbon materials, chemistry and physics.

An Atlas of Fullerenes

An Atlas of Fullerenes PDF

Author: P. W. Fowler

Publisher: Courier Corporation

Published: 2007-01-01

Total Pages: 418

ISBN-13: 0486453626

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An introduction to the current state of theory in a new and lively field, this volume offers both students and researchers a practical guide. It features a comprehensive set of pictures of fullerene structures and tabulates their properties. In addition, it lists a computer program that will extend the tables as needed. Seven chapters of descriptive material precede over 200 pages of tables with corresponding diagrams and serve as a self-contained introduction. Topics include fullerene cages, electronic structure, steric strain, symmetry and spectroscopy, fullerene isomerization, and carbon gain and loss. Each chapter concludes with references and notes.

Topological Modelling of Nanostructures and Extended Systems

Topological Modelling of Nanostructures and Extended Systems PDF

Author: Ali Reza Ashrafi

Publisher: Springer Science & Business Media

Published: 2013-05-19

Total Pages: 575

ISBN-13: 9400764138

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Topological Modelling of Nanostructures and Extended Systems completes and expands upon the previously published title within this series: The Mathematics and Topology of Fullerenes (Vol. 4, 2011) by gathering the latest research and advances in materials science at nanoscale. It introduces a new speculative area and novel concepts like topochemical reactions and colored reactive topological indices and provides a better understanding of the physical-chemical behaviors of extended systems. Moreover, a charming new family of space-filling fullerenic crystals is here analyzed for the first time. Particular attention is given to the fundamental influences exercised by long-range connectivity topological mechanisms on the chemical and physical properties of carbon nanostructures. Systems consisting in graphenic layers with structural and topological defects are investigated in their electronic and magnetic behaviors also in presence of metallic particles. More specifically, the book focuses on: - Electronic Properties of low dimensional nanostructures including negatively-curved carbon surfaces; Pariser-Parr-Pople model hamiltonian approach to graphene studies; - Topochemistry and Toporeactcivity of extended sp2-nanocarbons: PAH, fullerenes, nanoribbons, Moebius-like nanoribbons, nanotubes and grapheme; - Novel class of crystal networks arising from spanning fullerenes; - Nanostructures and eigenvectors of matrices and an extended treatise of topological invariants; - Enumeration hetero-fullerenes by Polya theory. Topological Modelling of Nanostructures and Extended Systems represents a valuable resource to advances graduates and researchers working in mathematics, chemistry, physics and material science.

Advances in Mathematical Chemistry and Applications:

Advances in Mathematical Chemistry and Applications: PDF

Author: Subhash C. Basak

Publisher: Elsevier

Published: 2016-02-11

Total Pages: 354

ISBN-13: 1681080524

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Advances in Mathematical Chemistry and Applications highlights the recent progress in the emerging discipline of discrete mathematical chemistry. Editors Subhash C. Basak, Guillermo Restrepo, and Jose Luis Villaveces have brought together 27 chapters written by 68 internationally renowned experts in these two volumes. Each volume comprises a wise integration of mathematical and chemical concepts and covers numerous applications in the field of drug discovery, bioinformatics, chemoinformatics, computational biology, mathematical proteomics, and ecotoxicology. Volume 2 explores deeper the topics introduced in Volume 1, with numerous additional topics such as topological approaches for classifying fullerene isomers; chemical reaction networks; discrimination of small molecules using topological molecular descriptors; GRANCH methods for the mathematical characterization of DNA, RNA and protein sequences; linear regression methods and Bayesian techniques; in silico toxicity prediction methods; drug design; integration of bioinformatics and systems biology, molecular docking, and molecular dynamics; metalloenzyme models; protein folding models; molecular periodicity; generalized topologies and their applications; and many more. Brings together both the theoretical and practical aspects of the fundamental concepts of mathematical chemistry Covers applications in diverse areas of physics, chemistry, drug discovery, predictive toxicology, systems biology, chemoinformatics, and bioinformatics About half of the book focuses primarily on current work, new applications, and emerging approaches for the mathematical characterization of essential aspects of molecular structure, while the other half describes applications of structural approach to new drug discovery, virtual screening, protein folding, predictive toxicology, DNA structure, and systems biology

Distance, Symmetry, and Topology in Carbon Nanomaterials

Distance, Symmetry, and Topology in Carbon Nanomaterials PDF

Author: Ali Reza Ashrafi

Publisher: Springer

Published: 2016-08-16

Total Pages: 477

ISBN-13: 3319315846

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This contributed volume is inspired by the seminal discovery and identification of C60. Starting with a comprehensive discussion featuring graphene based nanostructures, subsequent chapters include topological descriptions of matrices, polynomials and indices, and an extended analysis of the symmetry and topology of nanostructures. Carbon allotropes such as diamond and its connection to higher-dimensional spaces is explored along with important mathematical and topological considerations. Further topics covered include spontaneous symmetry breaking in graphene, polyhedral carbon structures, nanotube junction energetics, and cyclic polyines as relatives of nanotubes and fullerenes. This book is aimed at researchers active in the study of carbon materials science and technology.

Chemical Topology

Chemical Topology PDF

Author: D Bonchev

Publisher: CRC Press

Published: 1999-04-23

Total Pages: 354

ISBN-13: 9789056991746

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Topology is becoming increasingly important in chemistry because of its rapidly growing number of applications. Here, its many uses are reviewed and the authors anticipate what future developments might bring. This work shows how significant new insights can be gained by representing molecular species as topological structures known as topographs. The text explores carbon structures, establishing how the stability of fullerene species can be accounted for and also predicting which fullerenes will be most stable. It is pointed out that molecular topology, rather than molecular geometry, characterizes molecular shape and various tools for shape characterization are described. Several of the fascinating ideas that arise from regarding topology as a unifying principle in chemical bonding theory are discussed, and in particular, the novel concept of the molecular topoid is shown to have numerous uses. The topological description of polymers is examined and the reader is gently guided through the realms of branched and tangled polymers. Overall, this work outlines the fact that topology is not only a theoretical discipline but also one that has practical applications and high relevance to the whole domain of chemistry.

Electronic Structure Calculations on Fullerenes and Their Derivatives

Electronic Structure Calculations on Fullerenes and Their Derivatives PDF

Author: Jerzy Cioslowski

Publisher: Oxford University Press, USA

Published: 1995

Total Pages: 310

ISBN-13:

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This book provides a comprehensive overview of the latest approaches to electronic structure calculations of fullerenes. Topics include C(60) and C(70) molecules, the medium-size fullerenes, large carbon clusters, hypothetical allotropic forms of carbon, small fullerenes, endohedral complexes, heterofullerenes, fullerene derivatives, and solid-state fullerenes. A summary of recent research breakthroughs and a discussion of potential future directions round out the book. Far-reaching and well-written, the book will be welcomed by students and researchers in chemistry and quantum physics.

New Frontiers in Nanochemistry: Concepts, Theories, and Trends

New Frontiers in Nanochemistry: Concepts, Theories, and Trends PDF

Author: Mihai V. Putz

Publisher: CRC Press

Published: 2020-05-06

Total Pages: 401

ISBN-13: 0429663153

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New Frontiers in Nanochemistry: Concepts, Theories, and Trends, Volume 2: Topological Nanochemistry is the second of the new three-volume set that explains and explores the important basic and advanced modern concepts in multidisciplinary chemistry. Under the broad expertise of the editor, this second volume explores the rich research areas of nanochemistry with a specific focus on the design and control of nanotechnology by structural and reactive topology. The objective of this particular volume is to emphasize the application of nanochemistry. With 46 entries from eminent international scientists and scholars, the content in this volume spans concepts from A-to-Z—from entries on the atom-bond connectivity index to the Zagreb indices, from connectivity to vapor phase epitaxy, and from fullerenes to topological reactivity—and much more. The definitions within the text are accompanied by brief but comprehensive explicative essays as well as figures, tables, etc., providing a holistic understanding of the concepts presented.

The Role of Topology in Materials

The Role of Topology in Materials PDF

Author: Sanju Gupta

Publisher: Springer

Published: 2018-04-21

Total Pages: 297

ISBN-13: 3319765965

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This book presents the most important advances in the class of topological materials and discusses the topological characterization, modeling and metrology of materials. Further, it addresses currently emerging characterization techniques such as optical and acoustic, vibrational spectroscopy (Brillouin, infrared, Raman), electronic, magnetic, fluorescence correlation imaging, laser lithography, small angle X-ray and neutron scattering and other techniques, including site-selective nanoprobes. The book analyzes the topological aspects to identify and quantify these effects in terms of topology metrics. The topological materials are ubiquitous and range from (i) de novo nanoscale allotropes of carbons in various forms such as nanotubes, nanorings, nanohorns, nanowalls, peapods, graphene, etc. to (ii) metallo-organic frameworks, (iii) helical gold nanotubes, (iv) Möbius conjugated polymers, (v) block co-polymers, (vi) supramolecular assemblies, to (vii) a variety of biological and soft-matter systems, e.g. foams and cellular materials, vesicles of different shapes and genera, biomimetic membranes, and filaments, (viii) topological insulators and topological superconductors, (ix) a variety of Dirac materials including Dirac and Weyl semimetals, as well as (x) knots and network structures. Topological databases and algorithms to model such materials have been also established in this book. In order to understand and properly characterize these important emergent materials, it is necessary to go far beyond the traditional paradigm of microscopic structure–property–function relationships to a paradigm that explicitly incorporates topological aspects from the outset to characterize and/or predict the physical properties and currently untapped functionalities of these advanced materials. Simulation and modeling tools including quantum chemistry, molecular dynamics, 3D visualization and tomography are also indispensable. These concepts have found applications in condensed matter physics, materials science and engineering, physical chemistry and biophysics, and the various topics covered in the book have potential applications in connection with novel synthesis techniques, sensing and catalysis. As such, the book offers a unique resource for graduate students and researchers alike.

New Frontiers in Nanochemistry: Concepts, Theories, and Trends, 3-Volume Set

New Frontiers in Nanochemistry: Concepts, Theories, and Trends, 3-Volume Set PDF

Author: Mihai V. Putz

Publisher: CRC Press

Published: 2022-05-30

Total Pages: 1479

ISBN-13: 0429634099

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New Frontiers in Nanochemistry: Concepts, Theories, and Trends, 3-Volume Set explains and explores the important fundamental and advanced modern concepts from various areas of nanochemistry and, more broadly, the nanosciences. This innovative and one-of-a kind set consists of three volumes that focus on structural nanochemistry, topological nanochemistry, and sustainable nanochemistry respectively, collectively forming an explicative handbook in nanochemistry. The compilation provides a rich resource that is both thorough and accessible, encompassing the core concepts of multiple areas of nanochemistry. It also explores the content through a trans-disciplinary lens, integrating the basic and advanced modern concepts in nanochemistry with various examples, applications, issues, tools, algorithms, and even historical notes on the important people from physical, quantum, theoretical, mathematical, and even biological chemistry.