Both chirality and aromaticity are cornerstone concepts for organic chemistry. Both had their origins in the 1840s or thereafter in the work of Pasteur, van't Hoff and LeBel for the former and Faraday, Loschmidt, Kekule, Armstrong for the latter, this reaching its first stage of theoretical maturity with Huckel's quantum mechanical analysis in the 20th Century (the famous 4n+2 rule).
For a long period, these two concepts were thought to be exclusive; after all aromaticity manifested almost entirely in flat (achiral) benzenoid rings!
Another concept, topology, also originated in the 1840s, having been coined by the mathematician Johann Listing, who also proposed fascinating topological objects such as trefoil knots, and rings now better known by their co-discoverer, Mobius. In the 1960s, the concepts of Mobius topologies and aromaticity started merging. The chemist Heilbronner proposed aromaticity rules for Mobius cycles, although he did not identify such cycles as being chiral (this property appears to have been gradually realised only years later, although its difficult to find this expressed in print). The first such Mobius molecule was only synthesized in 2003; it was not however particularly aromatic! Meanwhile, in 1978 molecular biologists had discovered the fascinating twists and knots in cyclic DNA, via James Wang's topoisomerase enzymes. This was expressed using a concept known as supercoiling, and a new generation of mathematicians formalised this into an equation expressing a so-called linking number, which is comprised of twist and writhe;
Lk = T + W ...(1)
Applied extensively to the properties of cyclic DNA, these concepts did not migrate at all to organic chemists, who by and large dealt with much smaller molecules. Listing in 1847 had also introduced the concept of paradromic winding, which in modern language maps to imparting further twists to the basic Mobius topology. In 2005, we fused these various concepts from chemistry, topology and molecular biology, recognising that a new form of aromaticity based on double- and higher twisted conjugated, and importantly chiral, rings could be possible. We identified various interesting candidate molecules, but were surprised by how relatively stable they appeared (by computation), given they were at least twice as twisted as the classical Mobius rings.
We found a resolution to this paradox in equation (1). The (quantum mechanical) instability we realised is associated with T and not with W. We have now computed values of T and W for a range of topologically interesting (and chiral!) systems, and approximately, those that appear the most synthetically interesting have large values of W compared to T. So W (the writhe) can be regarded as a fundamentally new property of cyclic conjugated molecules, and one moreover that might be associated with stability. This has led to our proposal that eqn (1) and the Huckel 4n+2 rule can be combined as follows;
Intriguingly both T and W are chiral indices, and they can act together or oppose to create some fascinating novel chiral isomerisms. In a general sense, this type of aromaticity is chiral, and benzene like systems are very much the achiral exceptions (having Lk = 0).
At the end of the talk, I will speculate on some potential real world applications of this fascinating new form of chiral aromaticity, particularly to the design of new chiral metal ligands, and perhaps even mention another interest of ours, the Semantic Web, and how this might in the future enable more efficient fusion of diverse ideas and concepts (linking is a fundamental concept there as well!).