Knots theoretic approach

In this section we shall describe two approaches to the shape characterization of the large-scale features of chain molecules one based on a graph-theoretical method, the other on a family of knot theoretical polynomials [112,197,198]. 

Knot theoretical techniques are easily applicable to polymer chains that do form actual knots or links, such as some DNA fragments or various catenanes [59-72,204-213]. By appropriate modifications, the knot theoretical polynomials are also applicable to the analysis of chirality properties of general molecules that may not form knots by themselves, but the space around them can be represented by a knot. This approach has led to the concept of chirogenicity, and to a nonvisual, algorithmic, computer-based analysis of molecular chirality [62]. 

Calculation of the CD spectra of these interlocked molecules should assign their absolute configuration. However, the theoretical approach to such supermolecules has not been extensively investigated probably because of the complexity in these systems. One rare example is reported for the absolute configuration determination of a knot-type molecule (- -)-28 (Figure 15b) by using semiempirical... 

ABSTRACT. Knots and interlaced designs have been part of human artistry and culture since the earliest times. In chemistry, knots have been the focus of theoretical investigations for several decades. In pandlel, a few experimental approaches have been attempted by synthetic chemists. Until recent years, the only preparative routes pursued used the tools of classical organic chemistry. Despite their intellectual elegance, they have not succeeded. By taking advantage of the three-dimensional template effect of a transition metal (copper I), it has recently been possible to interlace two molecular threads prior to cyclisation and formation of a dimetallic trefoil knot. The demetallated knotted molecule and its di-copper(I) precursor have been fully characterized and studied. The X-ray structure of the dimetallic trefoil knot has been solved. It confirms the topology of the system. 

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