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Molecular Topology – An Introduction
Marshall MoritzMAT 598, Geometry and Topology of Manifolds
12/12/12
Relatively new field of study, founded in the early 1960s by E. Wasserman, N. van Gulick◦ Had been researched as early as 1910s, but first
successful synthesis and breakthrough in 1961 Rooted in basic topological and graph
theory ideas, applies these ideas to molecular structures
Identifies topological surfaces which could yield stable, functional molecules
What is Molecular Topology?
Vertices = Atoms, Edges = Bonds Often depicted as Hydrogen Depleted Molecules show geometrical symmetry, reflected in
molecular properties which are dependent on spatial structure
Molecular topology reveals the topological symmetry -- defined in terms of connectivity◦ Expresses the equivalence relationships between elements
of graph: vertices, bonds or larger subgraphs. ◦ It makes use of groups theory formalism in modeling an N -
dimensional space. Similarity molecular structures expresses the
common features within a set of molecules. Symmetry and similarity provide equivalence classes◦ First at the level of molecular graph and its subgraphs ◦ Second among the members of a whole set of molecules.
Graphs, Symmetry
Chemical graphs can be physically described by a variety of matrices
Adjacency Matrix Kirchoff Matrix Distance Matrix
Graphs, Cont’d
Adjacency Matrix, Methyl Cyclopropane
Kirchoff/Laplacian Matrix, T-butyl Cyclopropane
Molecular Topology builds on the same set of tools we’ve already learned.
Cutting and Pasting Reactions Graphs
and Mechanisms 2 Dimensional vs 3
Dimensional Surfaces
Graphs, Cont’d
In R3, Chemical Graphs are more revealing
Another degree of freedom, new molecular orientation.
Chirality: A molecule with a non-superimposable mirror image
Stereoisomers – Same molecules, different orientations
Enantiomers – One of two stereoisomers which differ in orientation
Chirality
Enantiomers are equivalent to the Mobius bands with clockwise, counterclockwise twists
Passing a chemical graph around a Mobius band reverses stereochemistry
A surface containing a Mobius band is non-orientable A chiral molecule is chiral
Chirality and the Mobius Band
Molecules are naturally free flowing; Requires “tying” down structure.
Mobius Molecule has two mechanisms; two sided band, or pi-electron system
Formed as intermediate structure in reaction to obtain larger ring structures
Mobius Molecules
Catenanes (rotoxanes), Rings, Knots◦ Are all topologically interesting surfaces.
Chemically, presented a difficult challenge to intertwine molecules, but with great potential◦ Stable surfaces unlike the Mobius molecules are
much more highly desirable
More Complex Surfaces
Catenanes, Knotane, and a Molecular Borromean Ring
Hydrogen Bonding Metal Ligand
Interactions
Syntheses and Mechanisms
Interlocked Molecules have exciting physical properties which can be easily manipulated◦ Translational Motion◦ Rotational Motion◦ Elasticity
Submolecular Motions can be controlled◦ Inter- and Intra- Molecular Interactions
Submolecular motion is leading to creation of functional molecules which change their properties in response to some external stimulus (e.g. light, electricity or a chemical reagent).
Such molecules will form the basis of molecular machines and devices which are predicted to be the key protagonists in the development of a “bottom-up” nanotechnology.
WHY Molecular Topology?
Promise in pursuit of electronic paper, nanovalves, molecular switches, and other nanoelectronic components.
The only difference between a single ring and an [n]-catenane is linkage, and the chemical differences are likely a direct result of the interlocked architecture.◦ Unique way in which different parts of the
molecule can move with respect to the rest of the system. ◦ Multi-Functional Molecules
Motivation, Cont’d
[1] Chemical Topology: Introduction and Fundamentals. Chapter 5. Eds. Bonchev D., Rouvray R., 1999, Gordon and Breach Publ., Reading, pp.167 - 264.;
[2] Diudea, M. V., Gutman, I. , Lorentz, J., Molecular Topology; [3] Herges, R. Chem Rev. 2006. 106, 4820-4842; [4] Walba, D. M.; Richards, R. M. ,Haltiwanger, R. C. J. Am.
Chem. Soc. 1982. 104, 3219; [5] M.C.T. Fyfe, J. F. Stoddart, Acc. Chem. Res. 1997, 30, 393; [6] C. O. Dietrich-Buchecker, J.-P. Sauvage, Chem.
Rev. 1987, 87, 795; [7] http://en.wikipedia.org/wiki/Molecular_knot,
http://en.wikipedia.org/wiki/Catenane, http://en.wikipedia.org/wiki/Molecular_Borromean_rings
References