Synchronous enantiomeric enrichment of both reactant and product by absolute asymmetric synthesis using circularly polarized light. Part 2.¹ Verification of the validity of assuming first-order kinetics upon deriving the equation for the relationship between conversion and enantiomeric excess

Kagan et al. (G, Balavoine, A. Moradpour and H. B. Kagan, J. Am. Chem. Soc., 1974, 96, 5152) derived an equation showing the relationship between the enantiomeric excess (ee) and the conversion for the irradiation of racemic reactants with circularly polarized light (CPL). The equation was derived based on the assumption of first-order kinetics for the reaction. However, the same equation can be derived from the general expression of the photochemical rate equations without assuming first-order kinetics. The only assumption that is necessary for deriving Kagan's equation is Lambert-Beer's law for the absorbance of the solutions. The relationship between ee and the conversion does not depend on the initial absorbance of the solution, but depends only on the g factor. Kagan's equation proved to be applicable to asymmetric photodestruction and also asymmetric one-way photoisomerization reactions. Numerical simulation is also a powerful method, particularly if the analytical solution of the differential equations is not available. In such a case, by expressing the ee as a function of the conversion, a relationship that does not depend on the initial absorbance is obtained.