Non-linear effects

In enantioselective synthesis, a non-linear effect refers to a process in which the enantiopurity of the catalyst (or the chiral auxiliary) does not correlate linearly with the enantiopurity of the product produced. This deviation from linearity is described as the non-linear effect, NLE. The linearity can be expressed mathematically, as shown in Equation 1. Stereoselection (i.e. the ee_product) that is higher or lower than the enantiomeric excess of the catalyst (ee_catalyst, relative to the equation) is considered non-routine behavior.

${\displaystyle ee_{\text{product}}=ee_{\max }ee_{\text{catalyst}}}$

For an ideal asymmetric reaction, the ee_product may be described as the product of ee_max multiplied by the ee_catalyst. This is not the case for reactions exhibiting NLE's.

In 1976, Wynberg and Feringa observed different chemical behavior in the reaction of an enantiopure and racemic substrate in a phenol coupling reaction. In 1981, Kagan and collaborators described the first non-linear effects in asymmetric catalysis and gave rational explanations for these phenomena. General definitions and mathematical models are essential for understanding nonlinear effects and their application to specific chemical reactions. In recent decades, the study of nonlinear effects has helped elucidate reaction mechanism and guide synthetic applications.