1st Edition

Solved and Unsolved Problems of Structural Chemistry

    492 Pages 180 B/W Illustrations
    by CRC Press

    492 Pages 180 B/W Illustrations
    by CRC Press

    Solved and Unsolved Problems of Structural Chemistry introduces new methods and approaches for solving problems related to molecular structure. It includes numerous subjects such as aromaticity—one of the central themes of chemistry—and topics from bioinformatics such as graphical and numerical characterization of DNA, proteins, and proteomes. It also outlines the construction of novel tools using techniques from discrete mathematics, particularly graph theory, which allowed problems to be solved that many had considered unsolvable.

    The book discusses a number of important problems in chemistry that have not been fully understood or fully appreciated, such as the notion of aromaticity and conjugated circuits, the generalized Hückel 4n + 2 Rule, and the nature of quantitative structure–property–activity relationships (QSARs), which have resulted in only partially solved problems and approximated solutions that are inadequate. It also describes advantages of mathematical descriptors in QSAR, including their use in screening combinatorial libraries to search for structures with high similarity to the target compounds.

    Selected problems that this book addresses include:

    • Multiple regression analysis (MRA)
    • Insufficient use of partial ordering in chemistry
    • The role of Kekulé valence structures
    • The problem of protein and DNA alignment

    Solved and Unsolved Problems of Structural Chemistry collects results that were once scattered in scientific literature into a thoughtful and compact volume. It sheds light on numerous problems in chemistry, including ones that appeared to have been solved but were actually only partially solved. Most importantly, it shows more complete solutions as well as methods and approaches that can lead to actualization of further solutions to problems in chemistry.

    Problems of Antiquity
    Famous Problems
    Illustrious Problems
    Hilbert Problems
    P versus NP
    On Unsolved Problems
    References and Notes

    Mathematical Chemistry
    Discrete Mathematics and Chemistry
    Partial Order
    Enumeration of Kekulé Valence Structures
    Graph Theory
    Chemical Nomenclature
    Molecular Descriptors
    Canonical Labeling of Vertices
    Counting of Paths
    Experimental Mathematics
    References and Notes

    Graph Theory and Chemistry
    Unfamiliarity with Graph Theory
    On HMO, the Hückel Molecular Orbital Theory
    The Story of Isospectral Graphs
    The Difference in HMO and PPP Bond Orders
    Graphene Edge
    References and Notes

    Characteristic Polynomial
    On Characteristic Polynomial
    On Construction of the Characteristic Polynomial
    Fermat’s Last Theorem
    Common Eigenvalues
    Chemical Mathematics
    Revisiting the Characteristic Polynomial
    On Factoring of Characteristic Polynomial
    Symmetric Function and Newton Identities
    References and Notes

    Two Cultures
    Qualitative Regression Analysis
    QSAR versus "QSAR"
    On Quantitative Characterization of Molecular Structure
    The Criticism That Is Not
    Highly Collinear Descriptors: The Problem That Is Not
    The Single Equation Fallacy
    References and Notes

    Molecular Descriptors
    Structure Descriptors
    The Connectivity Index
    Topological Indices
    Complex Biomolecular Networks and the Connectivity Index 1χ Joseph Boscovic
    Desiderata for Molecular Descriptors
    Higher-Order Connectivity Indices
    Molecular ID Numbers
    Recent Modification of the Higher-Order Connectivity Indices
    Variations of the Connectivity Index
    On Characterization of Hetero-Atoms
    The Variable Connectivity Index
    Surprise, Surprise
    The Structure–Structure Space
    References and Notes

    Partial Ordering
    Searching for Regularities in Structure–Property Data
    On Characterization of Molecular Structures
    Partial Ordering
    13C Chemical Shifts Sums in Alkanes
    Study of Proteome Maps Using Partial Ordering
    References and Notes

    Novel Molecular Matrices
    Novel Molecular Descriptors
    Novel Matrices in Chemistry
    Generalized Distance Matrices
    Ring Closure Matrix
    Spanning Trees
    Canonical Labels for Graphs
    Canonical Labels for Adamantane
    Walk Above Code for Polycyclic Graphs
    Ring Closure Matrix of Adamantane
    References and Notes

    On Highly Similar Molecules
    Search for Structurally Similar Molecules
    Molecular Descriptors for Screening Combinatorial Libraries
    Generalized Connectivity Indices
    Connectivity Index χ(HD)
    References and Notes

    Aromaticity Revisited
    Conjugated Circuits
    Resonance Energies
    In Search of a Generalized Hückel 4n + 2 Rule
    On Classification of Polycyclic Conjugated Compounds
    References and Notes

    Clar Aromatic Sextet
    Qualitative Clar Aromatic Sextet Theory
    Clar Aromatic Sextet Revisited
    Pauling Bond Orders
    Ring Bond Orders
    Quantitative Aromatic Sextet Theory
    Resonance Graphs
    References and Notes

    Renormalization in Chemistry
    Continuum versus Discrete Models
    Ring Currents via the Conjugated Circuits Model
    Normalization of Ring Currents
    Renormalization of Ring Currents
    Concluding Remarks
    Plagiarism That Is Not
    References and Notes

    Graphical Bioinformatics
    Characterization versus Indexing
    Milestones of Graphical Bioinformatics
    Spectral Representation of DNA
    Four-Color 2-D Maps of DNA
    Similarities and Dissimilarities among the DNA Sequences
    Is a Four-Color DNA Map a Useful Novelty?
    Amino Acid Adjacency Matrix
    Decagonal Isometric Matrix
    On the Sequence Alignment Problem
    Amino Acid Sequential Matrix
    Computer Program for the Exact Solution of the Protein Alignment Problem
    References and Notes

    Beauties and Sleeping Beauties in Science
    Sleeping Beauties Revisited
    On Beauty in Science
    Five Sleeping Beauties
    Aromaticity and Conjugation
    4n + 2 and 4n Rule for Polycyclic Conjugated Systems
    Orthogonal Molecular Descriptors
    Variable Connectivity Index
    Proteome Maps: Order or Chaos?
    Graphical Alignment of Proteins
    Sleeping Giants
    References and Notes

    Appendix 1: Early Hostility toward Chemical Graph Theory

    Appendix 2: Editorial Alert to Reviewers on Graph Theoretical Manuscripts

    Appendix 3: Letter Relating to the Calculation of the Symmetry of a Graph

    Appendix 4: On Detection of the Illegal Deck of Cards for Graph Reconstruction

    Appendix 5: Solution to Halmos Handshake Problem

    Appendix 6: The First Page of the Book of Euclid

    Appendix 7: Full Quote of Immanuel Kant

    Appendix 8: Construction of Canonical Labels for Diamantane

    Appendix 9: Twelve Different Canonical Labelings of Diamantane

    Appendix 10: The Eigenvalues and Eigenvectors of Hexatriene

    Appendix 11: The Coefficients of All Antisymmetrical Molecular Orbitals of the Tetracene Derivative C20H14

    Appendix 12: Halogen Compounds and Their Boiling Points

    Appendix 13: "News and Views" on Chemical Topology from Nature, November 15, 1974

    Appendix 14: Conjugated Circuits for the Remaining Five Symmetry Nonequivalent Kekulé Valence Structures of Coronene

    Appendix 15: Hostile Reports of Anonymous Referees on Novelty in Graphical Bioinformatics

    Appendix 16: The Computer Program for Exact Pairwise Protein Alignment

    Appendix 17: An Input and Output of the Program VESPA

    Appendix 18: List of Problems of Structural Chemistry Presented in This Book

    Appendix 19: Rigorous Definitions and Descriptions of a Selection of Mathematical Concepts of Discrete Mathematics


    Milan Randić earned his PhD from the University of Cambridge, England. He founded the Theoretical Chemistry group at the Institute Rudjer Bošković in Zagreb, Croatia, in 1960. He joined the department of chemistry at the University of Zagreb in 1965 before leaving for the United States. He later joined the department of mathematics and computer science at Drake University, Des Moines, Iowa, until his retirement in 1999 as a distinguished professor. He has won several awards and pays annual visits to the Laboratory of Chemometrics, National Institute of Chemistry, Ljubljana, Slovenia. He is a member of the Croatian Academy of Sciences and Arts, an honorary member of the Slovenian Chemical Society, and an honorary member of the National Institute of Chemistry in Ljubljana, from which he received the Grand Pregel Award in 2010. In 2014 he reported the exact solution of the protein alignment problem, which had existed for 45 years.

    Marjana Novic is head of the Laboratory of Chemometrics at the National Institute of Chemistry, Ljubljana, Slovenia, and teaches chemometrics at the University of Ljubljana, where she earned her PhD from the Faculty of Chemistry and Chemical Technology in 1985. She started her career at the National Institute of Chemistry in Ljubljana, initially developing automated information systems for infrared and NMR spectroscopy. Her expertise includes the development of chemometrics methods, QSAR and ANN modeling, structural elucidation of transmembrane segments of membrane proteins, and innovative merging of chemometrics methods with molecular modeling, which facilitates effective drug design.

    Dejan Plavšić is a senior research scientist at the NMR Center at the Rudjer Bošković Institute, Zagreb, Croatia. He earned his PhD in chemistry from the University of Zagreb. His research interests are in mathematical chemistry, chemical graph theory and its applications, metal clusters, organometallic compounds, and catalysis. Since 2003 he has been interested in extending graphical and numerical characterizations to DNA, proteins, and proteome maps using graph theoretical tools, entering thus into bioinformatics. Two of his papers in this area have received recognition as being among the 50 Most Cited Papers in Chemical Physics Letters during the 2003–2007 period. He is also one of the initial founding members of the International Academy of Mathematical Chemistry. In 2006 he was the first recipient of the International Award Latium between Europe and the Mediterranean for Medicine, Physics, or Chemistry.

    "Already in the Preface (on page XIII) the authors declare that their book is 'unusual and unconventional'. Indeed it is! Contrary to many other existing monographs concerned with chemical graph theory or its selected special topics, this book is full of interesting, unusual, and surprising excursions, making its reading a great pleasure. Everywhere in the book, we find historical details and anecdotes, related to physics, chemistry, physical chemistry, and mathematics, often coming from Milan Randic's personal experience. Colleagues interested in philosophy of science (or philosophy in general) will also find a wealth of intriguing ideas. For these colleagues we especially recommend Chapter 14, and its sections 'On Beauty in Science' and 'Sleeping Giants'. The same chapter will be a gold mine for scholars interested in the history of chemistry . . .
    In summary, 'Solved and Unsolved Problems of Structural Chemistry' is a valuable treatise, outlining practically all facets of the research of Milan Randic in various areas of chemical graph theory. ... this book should be a valuable item in the personal library of all those who ever did any work or ever had any interest in chemical graph theory."
     – Ivan Gutman, Match: Communications in Mathematical and in Computer Chemistry, 2016.


    "The book is foremost readable, copiously and suitably illustrated, and set out in a logical manner… I would recommend this book to someone interested in chemical graph theory with any level of knowledge of physical chemistry."
     – Colin F. Poole for Chromatographia (2016) 79:1049–1050. DOI 10.1007/s10337-016-3110-4.