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