Solved and unsolved problems of structural chemistry:
Gespeichert in:
| Beteiligte Personen: | , , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Boca Raton ; London ; New York
CRC Press
2016
|
| Schlagwörter: | |
| Links: | http://digitool.hbz-nrw.de:1801/webclient/DeliveryManager?pid=6780323&custom_att_2=simple_viewer http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029279371&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | xx, 472 Seiten Illustrationen, Diagramme, Portraits |
| ISBN: | 9781498711517 |
Internformat
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| 245 | 1 | 0 | |a Solved and unsolved problems of structural chemistry |c Milan Randić (Professor Emeritus, Drake University, Des Moines, IA), Marjana Novič (The National Institute of Chemistry, Ljubljana, Slovenia), Dejan Plavšić (The Ruđer Bošković Institute, Zagreb, Croatia) |
| 264 | 1 | |a Boca Raton ; London ; New York |b CRC Press |c 2016 | |
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Datensatz im Suchindex
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| adam_text | Titel: Solved and unsolved problems of structural chemistry
Autor: Randić, Milan
Jahr: 2016
Contents Foreword ...................................................................................................................xi Preface ....................................................................................................................xiii Acknowledgments ..................................................................................................xvi i Authors ....................................................................................................................xix Chapter 1 Introduction 1.1 Problems of Antiquity...............................................................3 1.1.1 Doubling a Cube...........................................................3 1.1.2 Trisection of an Angle..................................................3 1.1.3 Squaring a Circle..........................................................4 1.2 Famous Problems......................................................................5 1.2.1 The Four-Color Problem..............................................5 1.2.2 Graph Reconstruction Problem....................................6 1.3 Illustrious Problems...................................................................7 1.3.1 The Seven Bridges of Königsberg ................................9 1.3.2 Haimos Handshake Problem......................................11 1.4 Hilbert Problems.....................................................................12 1.5 P versus NP..............................................................................16 1.6 On Unsolved Problems............................................................17 References and Notes.........................................................................19 Chapter 2 Mathematical Chemistry....................................................................23 2.1 Discrete Mathematics and Chemistry.....................................24 2.2 Partial
Order............................................................................25 2.3 Enumeration of Kekule Valence Structures............................28 2.3.1 Cata-Condensed Benzenoid Hydrocarbons................28 2.3.1.1 Branched Cata-Condensed Benzenoids......29 2.3.2 Benzenoid Lattices.....................................................31 2.3.3 John and Sacks Algorithm.........................................33 2.4 Graph Theory..........................................................................34 2.4.1 Graphs........................................................................35 2.5 Chemical Nomenclature..........................................................39 2.5.1 On Uniform Representations of Molecules................43 2.6 Molecular Descriptors.............................................................44 2.6.1 3-D Descriptors for Spectrum-Like Representation...46 2.7 Canonical Labeling of Vertices...............................................47 2.7.1 Use of Canonical Labeling for Determining Symmetry of Graphs..................................................49 2.8 Counting of Paths....................................................................51
vi Contents 2.9 Experimental Mathematics......................................................54 2.9.1 On Kepler’s Conjecture on Dense Packing of Spheres...................................................................54 2.9.2 Ulam’s Spiral..............................................................56 References and Notes.........................................................................60 Chapter 3 Graph Theory and Chemistry............................................................67 3.1 Unfamiliarity with Graph Theory...........................................67 3.2 On HMO, the Hiickel Molecular Orbital Theory....................69 3.2.1 The Crystal Field Model............................................71 3.2.2 Extended Hiickel Molecular Orbital Method.............71 3.3 The Story of Isospectral Graphs..............................................72 3.3.1 Isospectral Multigraphs..............................................74 3.3.2 Vertex Neighbor Sum Rule........................................79 3.3.3 Isospectral Benzenoid Derivatives.............................80 3.4 The Difference in HMO and PPP Bond Orders......................84 3.4.1 On Modeling Folding of Proteins...............................88 3.5 Graphene Edge........................................................................92 References and Notes.........................................................................95 Chapter 4 Characteristic Polynomial................................................................101 4.1 On Characteristic Polynomial...............................................101 4.2 On Construction of the Characteristic Polynomial...............101 4.2.1 Coulson Graphical Construction of Ch(x)................104 4.3 Fermat’s Last Theorem..........................................................105 4.4 Common Eigenvalues............................................................107 4.5 Chemical
Mathematics..........................................................110 4.5.1 An Illustration of Chemical Mathematics: Subspectral Graphs.................................................. 110 4.6 Revisiting the Characteristic Polynomial.............................. 114 4.7 On Factoring of Characteristic Polynomial........................... 116 4.8 Symmetric Function and Newton Identities..........................122 4.9 Summary...............................................................................126 References and Notes.......................................................................127 Chapter 5 Structure-Activity.............................................................. 131 5.1 Two Cultures..........................................................................131 5.2 Qualitative Regression Analysis............................................135 5.3 QSAR versus QSAR ..........................................................137 5.4 On Quantitative Characterization of Molecular Structure.... 138 5.5 The Criticism That Is Not......................................................140 5.6 Highly Collinear Descriptors: The Problem That Is Not......142
vii 145 147 151 151 151 154 156 159 164 165 166 170 171 173 173 175 177 185 188 192 199 199 199 202 205 209 213 219 219 221 227 228 229 230 231 232 232 5.7 The Single Equation Fallacy.......................................... References and Notes................................................................ Molecular Descriptors............................................................... 6.1 Structure Descriptors...................................................... 6.2 The Connectivity Index.................................................. 6.2.1 On the Success of the Connectivity Index........ 6.3 Topological Indices......................................................... 6.4 Complex Biomolecular Networks and the Connectivity Index ] X ........................................................................... 6.4.1 An Illustration................................................... 6.5 Joseph Boscovic.............................................................. 6.6 Desiderata for Molecular Descriptors............................ 6.7 Fligher-Order Connectivity Indices................................ 6.8 Molecular ID Numbers................................................... 6.9 Recent Modification of the Higher-Order Connectivity Indices............................................................................ 6.10 Variations of the Connectivity Index.............................. 6.11 On Characterization of Heteroatoms.............................. 6.12 The Variable Connectivity Index................................... 6.13 Surprise, Surprise........................................................... 6.14 The Structure-Structure Space...................................... References and Notes................................................................ Partial Ordering......................................................................... 7.1 Searching for Regularities in Structure-Property Data. 7.2
On Characterization of Molecular Structures................ 7.3 Partial Ordering.............................................................. 7.4 l3 C Chemical Shifts Sums in Alkanes........................... 7.5 Study of Proteome Maps Using Partial Ordering.......... References and Notes................................................................ Novel Molecular Matrices......................................................... 8.1 Novel Molecular Descriptors.......................................... 8.2 Novel Matrices in Chemistry......................................... 8.3 Generalized Distance Matrices...................................... 8.3.1 Square Root and «-Root Distance Matrices...... 8.3.2 Distance Squared Matrix and Higher Powers... 8.4 Ring Closure Matrix....................................................... 8.5 Spanning Trees............................................................... 8.6 Canonical Labels for Graphs.......................................... 8.7 Canonical Labels for Adamantane.................................
Contents viii 8.8 Walk Above Code for Polycyclic Graphs..............................234 8.8.1 Walk Above Code for Adamantane.........................235 8.8.2 Walk Above Binary Code........................................236 8.9 Ring Closure Matrix of Adamantane....................................237 8.9.1 Additional Illustration: Fibonacenes........................238 References and Notes.......................................................................241 Chapter 9 On Highly Similar Molecules..........................................................247 9.1 Search for Structurally Similar Molecules............................247 9.2 Molecular Descriptors for Screening Combinatorial Libraries.................................................................................251 9.3 Generalized Connectivity Indices.........................................252 9.3.1 Hamming Distance Matrix (HD).............................252 9.4 Connectivity Index x(HD).....................................................254 9.4.1 Similarity among Nonane Isomers...........................256 References and Notes.......................................................................258 Chapter 10 Aromaticity Revisited.......................................................................261 10.1 Conjugated Circuits...............................................................261 10.2 Resonance Energies...............................................................267 10.3 In Search of a Generalized Hiickel An + 2 Rule....................268 10.4 On Classification of Polycyclic Conjugated Compounds......279 References and Notes.......................................................................282 Chapter 11 Clar Aromatic Sextet........................................................................285 11.1 Introduction...........................................................................285 11.2 Qualitative Clar Aromatic
Sextet Theory.............................286 11.3 Clar Aromatic Sextet Revisited.............................................289 11.4 Pauling Bond Orders.............................................................291 11.5 Ring Bond Orders..................................................................293 11.6 Quantitative Aromatic Sextet Theory...................................296 11.7 Resonance Graphs.................................................................299 References and Notes.......................................................................307 Chapter 12 Renormalization in Chemistry.........................................:•...............311 12.1 Continuum versus Discrete Models.......................................311 12.2 Ring Currents via the Conjugated Circuits Model................312 12.2.1 Illustration: Ring Currents in Pyrene.......................313 12.3 Normalization of Ring Currents............................................317 12.4 Renormalization of Ring Currents........................................318 12.4.1 Naphthalene..............................................................319 12.4.2 Perylene....................................................................320
Contents ix 12.5 Concluding Remarks .............................................................320 12.6 Plagiarism That Is Not...........................................................322 References and Notes.......................................................................323 Chapter 13 Graphical Bioinformatics.................................................................325 13.1 Characterization versus Indexing..........................................327 13.2 Milestones of Graphical Bioinformatics...............................331 13.3 Spectral Representation of DNA...........................................331 13.4 Four-Color 2-D Maps of DNA..............................................332 13.4.1 Four-Color 2-D Map of a Sequence of Cattle DNA... 333 13.4.2 Fladamard Squared Euclidean Distance Matrices.... 334 13.5 Similarities and Dissimilarities among the DNA Sequences... 335 13.6 Is a Four-Color Map of a DNA Sequence a Useful Novelty?.................................................................................337 13.7 Amino Acid Adjacency Matrix.............................................339 13.8 On Transmembrane Proteins.................................................341 13.9 On the Sequence Alignment Problem...................................344 13.10 Amino Acid Sequential Matrix.............................................345 13.10.1 Recovery of Lost Information..................................347 13.11 Computer Program for the Exact Solution of the Protein Alignment Problem...............................................................352 References and Notes.......................................................................361 Chapter 14 Beauties and Sleeping Beauties in Science......................................365 14.1 Sleeping Beauties Revisited...................................................366 14.2 On Beauty in
Science............................................................368 14.3 Five Sleeping Beauties...........................................................373 14.4 Aromaticity and Conjugation................................................374 14.5 An + 2 and An Rule for Polycyclic Conjugated Systems........378 14.5.1 The Conjugated Circuit Model.................................379 14.6 Orthogonal Molecular Descriptors........................................380 14.7 Variable Connectivity Index..................................................382 14.8 Proteome Maps: Order or Chaos?.........................................384 14.9 Graphical Alignment of Proteins..........................................387 14.10 Sleeping Giants......................................................................389 14.11 Summary...............................................................................391 14.12 Apology.................................................................................393 References and Notes.......................................................................394 Appendix 1: Early Hostility toward Chemical Graph Theory ........................397 Appendix 2: Editorial Alert to Reviewers on Graph Theoretical Manuscripts ..........................................................................................................401
X Contents Appendix 3: Letter Relating to the Calculation of the Symmetry of a Graph.............................................................................................................403 Appendix 4: On Detection of the Illegal Deck of Cards for Graph Reconstruction.....................................................................................................407 Appendix 5: Solution to Halmos Handshake Problem.....................................411 Appendix 6: The First Page of the Book of Euclid...........................................413 Appendix 7: Full Quote of Immanuel Kant......................................................415 Appendix 8: Construction of Canonical Labeling for Diamantane................417 Appendix 9: Twelve Different Canonical Labeling of Diamantane ...............419 Appendix 10: The Eigenvalues and Eigenvectors of Hexatriene.....................421 Appendix 11: The Coefficients of All Antisymmetric Molecular Orbitals of the Tetracene Derivative C 20 H 14 .....................................................................423 Appendix 12: Halogen Compounds and Their Boiling Points........................425 Appendix 13: “News and Views” on Chemical Topology from Nature , November 15,1974...............................................................................................427 Appendix 14: Conjugated Circuits for the Remaining Five Symmetry Nonequivalent Kekule Valence Structures of Coronene..................................429 Appendix 15: Hostile Reports of Anonymous Referees on Novelty in Graphical Bioinfomatics.................................................................................433 Appendix 16: The Computer Program for Exact Pairwise Protein Alignment.............................................................................................................437 Appendix 17: An Input and Output of the Program VESPA..........................439
Appendix 18: List of Problems of Structural Chemistry Presented in This Book..........................................................................................................441 Appendix 19: Rigorous Definitions and Descriptions of a Selection of Mathematical Concepts of Discrete Mathematics........................................445 Appendix 20: QSAR Nightmare—No More.....................................................449 Appendix 21: Kekule Valence Structures Weights...........................................451 Appendix 22: Fries Rule Revisited.....................................................................455 Appendix 23: Late Hostility toward Chemical Graph Theory........................457 Subject Index........................................................................................................461 Name Index...........................................................................................................469
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| language | English |
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| physical | xx, 472 Seiten Illustrationen, Diagramme, Portraits |
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| spellingShingle | Randić, Milan 1930- Novič, Marjana 1955- Plavšić, Dejan Solved and unsolved problems of structural chemistry Chemistry, Physical and theoretical |
| title | Solved and unsolved problems of structural chemistry |
| title_auth | Solved and unsolved problems of structural chemistry |
| title_exact_search | Solved and unsolved problems of structural chemistry |
| title_full | Solved and unsolved problems of structural chemistry Milan Randić (Professor Emeritus, Drake University, Des Moines, IA), Marjana Novič (The National Institute of Chemistry, Ljubljana, Slovenia), Dejan Plavšić (The Ruđer Bošković Institute, Zagreb, Croatia) |
| title_fullStr | Solved and unsolved problems of structural chemistry Milan Randić (Professor Emeritus, Drake University, Des Moines, IA), Marjana Novič (The National Institute of Chemistry, Ljubljana, Slovenia), Dejan Plavšić (The Ruđer Bošković Institute, Zagreb, Croatia) |
| title_full_unstemmed | Solved and unsolved problems of structural chemistry Milan Randić (Professor Emeritus, Drake University, Des Moines, IA), Marjana Novič (The National Institute of Chemistry, Ljubljana, Slovenia), Dejan Plavšić (The Ruđer Bošković Institute, Zagreb, Croatia) |
| title_short | Solved and unsolved problems of structural chemistry |
| title_sort | solved and unsolved problems of structural chemistry |
| topic | Chemistry, Physical and theoretical |
| topic_facet | Chemistry, Physical and theoretical |
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