A rationale for the topological approach to chemistry

Abstract Chemists experience considerable difficulty in accepting many of the more exotic ideas of quantum mechanics such as the abolition of particulate matter and its replacement by the wave function. Even though the application of quantum theory in chemistry has been spectacularly successful in many areas, the underlying principles are counterintuitive and at best only vaguely comprehensible. Here we trace the development of our conception of the molecule over the past two centuries. It is shown that our notions have undergone a series of radical changes, starting from the rigid, solid-atom structure of Dalton, through the more flexible structure of Lewis held together by electron-pair bonds, to the modern conception of molecules defined solely in terms of ethereal wave functions. A major adjustment in the thinking of chemists has been necessary within a comparatively short space of time and so it is not surprising that this has left some feeling recalcitrant. A way forward is suggested that all concerned may find acceptable. This is to view the molecule not as a geometric entity but rather as a topological one. Several of the many advantages of adopting this stance are outlined toward the end of our article.

[1]  Count Alexander Humboldt.  XCIII. On the laws observed in the distribution of vegetable forms , 1816 .

[2]  William Hyde Wollaston.  V. On super-acid and sub-acid salts , 1808, Philosophical Transactions of the Royal Society of London.

[3]  W. Kossel.  Über Molekülbildung als Frage des Atombaus , 1916 .

[4]  C. Coulson.  The shape and structure of molecules , 1973 .

[5]  M. Born.  Zur Quantenmechanik der Stoßvorgänge , 1926 .

[6]  C. Lämmerzahl,et al.  On the dimensionality of space–time , 1993 .

[7]  Hermann Staudinger,et al.  From organic chemistry to macromolecules , 1970 .

[8]  R. Bader.  Atoms in molecules : a quantum theory , 1990 .

[9]  A. Brown.  On the theory of Chemical Combination , 1861 .

[10]  A. C. Brown,et al.  XLIV.—On the Theory of Isomeric Compounds , 1864, Transactions of the Royal Society of Edinburgh.

[11]  Colin A. Russell,et al.  The history of valency , 1971 .

[12]  E. W. Hones,et al.  The earth's magnetotail , 1986 .

[13]  Asiri Nanayakkara,et al.  Similarity of atoms in molecules , 1993 .

[14]  Michael Faraday.  Experimental Researches in Electricity , 1839 .

[15]  W. Heisenberg,et al.  Zur Quantentheorie der Molekeln , 1924 .

[16]  D. H. Rouvray.  The pioneering contributions of cayley and sylvester to the mathematical description of chemical structure , 1989 .

[17]  D. Golden,et al.  Additivity rules for the estimation of thermochemical properties , 1969 .

[18]  Max Jammer,et al.  The conceptual development of quantum mechanics , 1966 .

[19]  Dennis H. Rouvray,et al.  The modeling of chemical phenomena using topological indices , 1987 .

[20]  Milan Randić,et al.  In search of structural invariants , 1992 .

[21]  J. J. Thomson,et al.  XL. Cathode Rays , 1897 .

[22]  G Ord,et al.  Fractal space-time: a geometric analogue of relativistic quantum mechanics , 1983 .

[23]  D. H. Rouvray,et al.  Isomer enumeration methods , 1974 .

[24]  J. Boeyens.  Molecular mechanics and the structure hypothesis , 1985 .

[25]  Norbert Adolph Lange,et al.  Handbook of chemistry , 1944 .

[26]  Dennis H. Rouvray.  Computational chemical graph theory , 1990 .

[27]  H. Nagaoka.  LV. Kinetics of a system of particles illustrating the line and the band spectrum and the phenomena of radioactivity , 1904 .

[28]  W. Nernst,et al.  Die elektrolytische Zersetzung wässriger Lösungen , 1897 .

[29]  H. Davy.  I. The Bakerian Lecture, on some chemical agencies of electricity , 1807, Philosophical Transactions of the Royal Society of London.

[30]  XXXV. A tentative theory of light quanta , 1924 .

[31]  B. Sutcliffe.  The chemical bond and molecular structure , 1992 .

[32]  H. Primas.  Chemistry, Quantum Mechanics and Reductionism , 1981 .

[33]  N. Biggs,et al.  Graph Theory 1736-1936 , 1976 .

[34]  R. Woolley.  Molecular shapes and molecular structures , 1986 .

[35]  Some key historical highlights in the evolution of the modern concept of valence , 1992 .

[36]  J. Sylvester.  Chemistry and Algebra , 1878, Nature.

[37]  William Ogilvy Kermack,et al.  LI.—An explanation of the property of induced polarity of atoms and an interpretation of the theory of partial valencies on an electronic basis , 1922 .

[38]  Aug. Kekuié.  Untersuchungen über aromatische Verbindungen Ueber die Constitution der aromatischen Verbindungen. I. Ueber die Constitution der aromatischen Verbindungen. , 1866 .

[39]  On the origin of spacetime topology and some generalizations of quantum field theory , 1993, gr-qc/9307016.

[40]  M. Laue,et al.  Interferenzerscheinungen bei Röntgenstrahlen , 1913 .

[41]  Gilbert N. Lewis,et al.  The Atom and the Molecule , 1916, Resonance.

[42]  Michael Faraday,et al.  VI. Experimental researches in electricity.-Seventh Series , 1834, Philosophical Transactions of the Royal Society of London.

[43]  A. S. Ramsey.  The Mathematical Papers of Sir William Rowan Hamilton , 1931, Nature.

[44]  E. P. Ferreira,et al.  The interactions of π - -mesons with complex nuclei in the energy range (100–800) MeV. III. The interaction lengths and elastic scattering of 300 MeV π - -mesons in G5 emulsion , 1959 .

[45]  Paul G. Mezey,et al.  Molecular electron density lego approach to molecule building , 1993 .

[46]  D. Rouvray.  Predicting chemistry from topology. , 1986, Scientific American.

[47]  R. Zahradník,et al.  Elements of quantum chemistry , 1980 .

[48]  J. F. Liebman,et al.  From Atoms to Polymers: Isoelectronic Analogies , 1989 .

[49]  Alexandru T. Balaban,et al.  Applications of graph theory in chemistry , 1985, J. Chem. Inf. Comput. Sci..

[50]  Niels Bohr.  I. On the constitution of atoms and molecules , 1913 .

[51]  Paul G. Mezey,et al.  Shape in Chemistry: An Introduction to Molecular Shape and Topology , 1993 .

[52]  W. Pauli,et al.  Über den Zusammenhang des Abschlusses der Elektronengruppen im Atom mit der Komplexstruktur der Spektren , 1925 .

[53]  Zlatko Mihalic,et al.  Graphical bond orders: Novel structural descriptors , 1994, J. Chem. Inf. Comput. Sci..

[54]  Irving Langmuir,et al.  THE ARRANGEMENT OF ELECTRONS IN ATOMS AND MOLECULES. , 1919 .

[55]  Dennis H. Rouvray,et al.  The limits of applicability of topological indices , 1989 .