Stochastic and empirical models of the absolute asymmetric synthesis by the Soai-autocatalysis

Absolute asymmetric synthesis (AAS) is the preparation of pure (or excess of one) enantiomer of a chiral compound from achiral precursor(s) by a chemical reaction, without enantiopure chiral additive and/or without applied asymmetric physical field. Only one well-characterized example of AAS is known today: the Soai-autocatalysis. In an attempt at clarification of the mechanism of this particular reaction we have undertaken empirical and stochastic analysis of several parallel AAS experiments. Our results show that the initial steps of the reaction might be controlled by simple normal distribution ("coin tossing") formalism. Advanced stages of the reaction, however, appear to be of a more complicated nature. Symmetric beta distribution formalism could not be brought into correspondence with the experimental observations. A bimodal beta distribution algorithm provided suitable agreement with the experimental data. The parameters of this bimodal beta function were determined by a Pólya-urn experiment (simulated by computer). Interestingly, parameters of the resulting bimodal beta function give a golden section ratio. These results show, that in this highly interesting autocatalysis two or even perhaps three catalytic cycles are cooperating. An attempt at constructing a "designed" Soai-type reaction system has also been made.