Foundations of Chemistry

, Volume 7, Issue 3, pp 289–306 | Cite as

Reflections About Mathematical Chemistry

  • A.T. Balaban


A personal account is presented for the present status of mathematical chemistry, with emphasis on non-numerical applications. These use mainly graph-theoretical concepts. Most computational chemical applications involve quantum chemistry and are therefore largely reducible to physics, while discrete mathematical applications often do not. A survey is provided for opinions and definitions of mathematical chemistry, and then for journals, books and book series, as well as symposia of mathematical chemistry.


Physical Chemistry Mathematical Application Chemical Application Present Status Quantum Chemistry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Balaban, A.T. 1962Contribution to a Systematization of Heterolytic ReactionsRevue de Chimie de l’ Académie Roumaine7675682Google Scholar
  2. Balaban, A.T., Farcasiu, D., Banica, R. 1966Chemical Graphs. II. Graphs of Multiple 1,2-shifts in Carbonium Ions and Related SystemsRevue Roumaine de Chimie1112051227Google Scholar
  3. Balaban, A.T. 1972A Trivalent Graph of Girth TenJournal of Combinatorial Theory, Series B1215CrossRefGoogle Scholar
  4. Balaban, A.T. 1973Trivalent Graphs of Girth Nine and Eleven, and Relationships Among CagesRevue Roumaine de Mathématiques Pures et Appliquées1810331043Google Scholar
  5. Balaban, A.T. eds. 1976Chemical Applications of Graph TheoryAcademic PressLondonGoogle Scholar
  6. Balaban, A.T. 1982Highly Discriminating Distance-Based Topological IndexChemical Physics Letters89399404CrossRefGoogle Scholar
  7. Balaban, A.T., Banciu, M., Ciorba, V. 1987Annulenes, Benzo-, Hetero-, Homo-Derivatives, and their Valence IsomersCRC PressBoca Raton, FloridaGoogle Scholar
  8. Balaban, A.T., Tomescu, I. 1988Alternating 6-Cycles in Perfect Matchings of Graphs Representing Condensed Benzenoid HydrocarbonsKennedy, L.W.Quintas, L.V. eds. Applications of Graphs in Chemistry and PhysicsNorth-HollandAmsterdam516(originally published in Discrete Applied Mathematics, 19, 5–16)Google Scholar
  9. Balaban, A.T. 1991Enumeration of IsomersBonchev, D.Rouvray, D.H. eds. Chemical Graph Theory Introduction and FundamentalsAbacus Press/Gordon and Breach Science PublishersNew YorkGoogle Scholar
  10. Balaban, A.T. 1993Solved and Unsolved Problems in Chemical Graph TheoryGimbel, J.Kennedy, J.W.Quintas, L.V. eds. Quo Vadis Graph Theory?AmsterdamNorth-Holland109126Google Scholar
  11. Balaban, A.T. 1994Reaction GraphsBonchev, D.Mekenyan, O. eds. Graph Theoretical Approaches to Chemical ReactivityKluwer Academic PublishersDordrecht, Netherlands137180Google Scholar
  12. Balaban, A.T. eds. 1997From Chemical Topology to Three-Dimensional GeometryPlenum PressNew YorkGoogle Scholar
  13. Balaban, A.T., Ivanciuc, O. 1999Historical Development of Topological IndicesDevillers, J.Balaban, A.T. eds. Topological Indices and Related Descriptors in QSAR and QSPRGordon and BreachThe Netherlands2157Google Scholar
  14. Balaban, A.T., Randić, M. 2004Partitioning of π-Electrons in Rings of Polycyclic Hydrocarbons. Part 5. Nonalternant CompoundsJournal of Chemical Information and Computer Sciences4417011707and previous parts in the seriesGoogle Scholar
  15. Bermudez, C.I., Deza, E.E., Andrade, E. 1999Characterization and Comparison of Escherichia coli Transfer RNSa by Graph Theory Based on Secondary StructureJournal of theoretical Biology197193205Google Scholar
  16. Bonchev, D.Rouvray, D.H. eds. 2003Mathematical Chemistry Series. Vol. 7: Complexity in Chemistry. Introduction and FundamentalsTaylor and FrancisLondonGoogle Scholar
  17. Braun, T., Schubert, A., Maczelka, H., Vasvari, L. 1995Fullerene Research 1985–1993. A Computer-Generated Cross-Indexed Bibliography of the Journal LiteratureWorld ScientificSingaporeGoogle Scholar
  18. Braun, T., Schubert, A., Schubert, G., Vasvari, L. 1997Fullerene Research 1994–1996. A Computer-Generated Cross-Indexed Bibliography of the Journal LiteratureWorld ScientificSingaporeGoogle Scholar
  19. Brown, A.C. 1866/7On the Classification of Chemical Substances, by Means of Generic RadicalsTransactions of the Royal Society of Edinburgh23707720Google Scholar
  20. Brown, T.L., LeMay, H.E.,Jr., Bursten, D.E. 1991Chemistry – The Central Science5Prentice HallEnglewood CliffsGoogle Scholar
  21. Cayley, A. 1874On the Mathematical Theory of IsomersPhilosophical Magazine67444447Google Scholar
  22. Cayley, A. 1875On the Analytical Figures Called Trees in Mathematics and on Their Application in the Theory of Organic Compounds (in German)Berichte der deutschen chemischen Gesellschaft810561059Google Scholar
  23. Cayley, A. 1889A Theorem on TreesQuarterly Journal of Mathematics23376378Google Scholar
  24. A. Comte. Cours de Philosophie Positive. Available from the Université du Québec à Chicoutimi, 1830
  25. Corey, E.J., Cheng, X.-M. 1989The Logic of Chemical SynthesisWileyNew YorkGoogle Scholar
  26. Cyvin, S., Gutman, I. 1988Kekulé Structures in Benzenoid HydrocarbonsSpringer-VerlagBerlinGoogle Scholar
  27. P. Deuflhard. A Comparison of Related Concepts in Computational Chemistry and Mathematics. In: Chemistry and Mathematics: Two Scientific Languages of the 21st Century, Proc. Symp. Göttingen, October 2001, Nova Acta Leopoldina, Neue Folge, 88, # 330, Deutsche Akademie der Naturforscher Leopoldina, Halle (Saale). 2003Google Scholar
  28. J. Devillers and A.T. Balaban (Eds.), Topological Indices and Related Descriptors in QSAR and QSPR, Amsterdam: Gordon and Breach, 1999Google Scholar
  29. Flapan, E. 2000When Topology Meets Chemistry. A Topological Look at Molecular ChiralityCambridge University PressCambridgeGoogle Scholar
  30. Graovac, A., Gutman, I., Trinajstić, N. 1977Topological Approach to the Chemistry of Conjugated MoleculesSpringer-VerlagBerlinGoogle Scholar
  31. Grassy, G., Calas, B., Yasri, A., Lahana, R., Woo, J., Iyer, S., Kaczorec, M., Floc’h,  R., Buelow, R. 1998Computer-Assisted Rational Design of Immunosuppressive CompoundsNature Biotechnology16748752CrossRefGoogle Scholar
  32. Gutman, I., Polansky, O.E. 1986Mathematical Concepts in Organic ChemistrySpringer-VerlagBerlinGoogle Scholar
  33. Gutman, I., Cyvin, S. 1989Introduction to the Theory of Benzenoid HydrocarbonsSpringer-VerlagBerlinGoogle Scholar
  34. I. Gutman. Book review of “Mathematical Chemistry”, Proceedings of the 3rd International Conference on Mathematical Chemistry. Journal of the Chemical Society, Transactions of the Faraday Society, 88, 160, 1992Google Scholar
  35. Hettema, H., Kuipers, T.A.F. 1988The Periodic Table – Its Formalization, Status, and Relation to Atomic TheoryErkenntnis28387408Google Scholar
  36. Hoffmann, R. 2004A Claim on the Development of the Frontier Orbital Explanation of Electrocyclic ReactionsAngewandte Chemie International Ed.4365866590Google Scholar
  37. Jurs, P.C. 1996Computer Software Applications in Chemistry2WileyNew YorkGoogle Scholar
  38. Kant, I. 1786Metaphysische Anfangsgründe der NaturwissenschaftHartknoch VerlagRigaGoogle Scholar
  39. Kerber, A., Laue, R., Wieland, T. 2000Discrete Mathematics for Combinatorial ChemistryDiscrete Mathematical Chemistry51225229Google Scholar
  40. King, R.B.Rouvray, D.H. eds. 1987Graph Theory and Topology in ChemistryElsevierAmsterdamGoogle Scholar
  41. King, R.B. 2000The Role of Mathematics in the Experimental/Theoretical/Computational Trichotomy of ChemistryFoundations of Chemistry2221236CrossRefGoogle Scholar
  42. Klein, D.J., Schmalz, T.G., Hite, G.E., Seitz, W.A. 1986Resonance in C60 BuckminsterfulleneneJournal of the American Chemical Society10824572458CrossRefGoogle Scholar
  43. Klein, D.J. 1999Advances in Many-Body Valence-Bond TheoryMaksić, Z.B.Orville-Thomas, W.J. eds. Pauling’s Legacy: Modern Modelling of the Chemical Bond. Theoretical and Computational ChemistryElsevierAmsterdam403420Google Scholar
  44. Klein, D.J. 2002Resonating Valence-Bond Theories for Carbon π-Networks and Classical/Quantum ConnectionsCooper, D.L. eds. Valence Bond Theory, Theoretical and Computational ChemistryElsevierAmsterdam447502Google Scholar
  45. Kornberg, A. 1995Understanding Life as ChemistryInternational Journal of Quantum Chemistry53125130CrossRefGoogle Scholar
  46. Laszlo, P. 1999Circulation of ConceptsFoundations of Chemistry1225239CrossRefGoogle Scholar
  47. R.C. Lacher. (Ed.): MATH/CHEM/COMP, Elsevier, Amsterdam, 1987Google Scholar
  48. Lomonosov M.V. Polnye sobranie sochinenii (Complete Works), Vol. 1, Moscow. 1950Google Scholar
  49. Moon, J.W. 1967Various Proofs of Cayley’s Formula for Counting TreesHarary, F. eds. A Seminar on Graph TheoryHolt, Rinehart and WinstonNew York7078Google Scholar
  50. J.W. Moore, Stanitski and P.C. Jurs. Chemistry – The Molecular Science, 2nd edn., Harcourt College Publishers, 2005Google Scholar
  51. M.J. Nye. From Chemical Philosophy to Theoretical Chemistry. Dynamics of Matter and Dynamics of Disciplines, 1800–1950. Barkeley: University of California Press, 1993Google Scholar
  52. Oda, R. 1952‘A General Survey of Organic Reactions and Some New Reactions’Memoirs of the Faculty of Engineering of the Kyoto University14195205(Chemical Abstracts 1954, 48, 1935)Google Scholar
  53. Oda, R., Teramura, K., Tanimoto, S., Nomura, M., Yamamoto, K., Kitamura, K., Miyagi, H., Harada, S. 1954Joint Reaction and Transjointing Reaction, Nippon Kagaku Kaishi (Bulletin of the Chemical Society of Japan)Industrial Chemistry Section57904909Google Scholar
  54. Oda, R., Teramura, K., Tanimoto, S., Nomura, M., Matsuda, K., Suda, H. 1955Joint Reaction and Transjointing Reaction. IINippon Kagaku Kaishi (Bulletin of the Chemical Society of Japan), Industrial Chemistry Section58610613Google Scholar
  55. V.T. Panev, L.L. Konstantinov and M.S. Marinov. ‘The Problem of Geometrization of the Language of Chemistry’, Academic Open Internet Journal ( 2, 1–7, 2000Google Scholar
  56. V.T. Panev and Konstantinov L.L. Geometric Images of Simple and Complex Chemical Objects in the Space of Chemical Structures VM(3). Studying the Relationship between the Languages of Chemistry and Geometry’, Academic Open Internet Journal ( 11, 1–10, 2000Google Scholar
  57. Pólya, G. 1937Kombinatorische Anzahlbestimmungen für Gruppen, Graphen und chemische VerbindungenActa Mathematica68145254Google Scholar
  58. G. Pólya and R.C. Read. Combinatorial Enumeration of Groups, Graphs, and Chemical Compounds, Springer, New York (with a post-script entitled `Fifty Years of Pólya Theory’, and recent bibliography, written by Read). 1987Google Scholar
  59. Randić, M. 1975On Characterization of Molecular BranchingJournal of the American Chemical Society9766096615Google Scholar
  60. Remick, A.E. 1949Electronic Interpretations of Organic Chemistry2WileyNew York585Google Scholar
  61. Robinson, R.W., Harary, F., Balaban, A.T. 1976The Number of Chiral and Achiral Alkanes and Mono-Substituted AlkanesTetrahedron32355361CrossRefGoogle Scholar
  62. D.H. Rouvray and R.B. King (Eds). Topology in Chemistry, Harwood Publishing Ltd.: Discrete Mathematics of Molecules, 2002.Google Scholar
  63. Scerri, E.R. 1997Has the Periodic Table Been Successfully Axiomatized?Erkenntnis47220243CrossRefGoogle Scholar
  64. Scerri, R. 2004Just How Ab-initio Is Ab-initio Quantum Chemistry?Foundations of Chemistry693116and further references thereinGoogle Scholar
  65. Schmalz, T.G., Seitz, W.A., Klein, D.J., Hite, G.E. 1986C60 Carbon CagesChem. Phys. Lett.130203207CrossRefGoogle Scholar
  66. Schmalz, T.G., Seitz, W.A., Klein, D.J., Hite, G.E. 1988Elemental Carbon CagesJ. Am. Chem. Soc.11011131117CrossRefGoogle Scholar
  67. B. Spinoza. Ethica in Ordine Geometrico Demonstrata, published posthumously in 1677 (English translation by W. Hale White and A. Stirling in 1894, 4th revised edition published in 1910). 1677Google Scholar
  68. Sylvester, J.J. 1878On an Application of the New Atomic Theory to the Graphical Representation of the Invariants and Covariants of Binary Quantics – with Three AppendicesAmerican Journal of Mathematics164125Google Scholar
  69. Trinajstić, N., Gutman, I. 2002Mathematical ChemistryCroatica Chemica Acta75329356Google Scholar
  70. Trinajstić, N. eds. 1986Mathematics and Computational Methods in ChemistryHorwood/WileyChichesterGoogle Scholar
  71. Trinajstić, N. 1992Chemical Graph Theory2CRC PressBoca RatonGoogle Scholar
  72. Trinajstić, N. 1997Mathematics and Chemistry – The Unlikely PartnersRouvray, D.H. eds. Concepts in Chemistry – A Contemporary ChallengeWileyNew York1739Google Scholar
  73. Ugi, I., Bauer, J., Bley, K., Dengler, A., Dietz, E., Fontain, E., Gruber, B., Herges, R., Knauer, M., Reitsam, K., Stein, N. 1993Computer-Assisted Solution of Chemical Problemns: A New Discipline in ChemistryAngewandte Chemie International Ed. English32201227Google Scholar
  74. Vernin, G.Chanon, M. eds. 1986Computer Aids to ChemistryHorwood/WileyChichesterGoogle Scholar
  75. D. Vukicević and Randić M. ‘On Kekulé Structures of Buckminsterfullerene’, Chemical Physics Letters, in press. 2004Google Scholar

Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.The Texas A & M University at GalvestonGalvestonUSA

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