Supramolecular Chiral Aggregates Exhibiting Nonlinear CD–ee Dependence

Although a linear relationship between the optical activity (normally the CD signal) and the enantiomeric excess (ee) of chiral auxiliaries has been the most commonly observed dependence in dynamic supramolecular helical aggregates, positive nonlinear CD-ee dependence, known as the "majority-rules effect" (MRE), indicative of chiral amplification, has also been well documented and to some extent understood. In sharp contrast, the negative nonlinear CD-ee dependence has been much less reported and is not well understood. Here, the state of the art of both the positive and negative nonlinear CD-ee dependence in noncovalently bound supramolecular helical aggregates is summarized, with the hope that the vast examples of supramolecular aggregates showing positive nonlinear dependence, in terms of the methods of investigations, variations in the structure of the building block (single species or multiple species), and theoretical modeling using the mismatch penalty energy and helix reversal penalty energy, would help to guide the design of building blocks to form aggregates showing negative nonlinear dependence, and thus to understand the mechanisms. The potential applications of those functional supramolecular aggregates are also discussed.