Derivation of the Isoinversion Temperature

Optimization of Enantiomeric Ratio E by Choice of Temperature 5.7.3.1 Derivation of the Isoinversion Temperature 

Many complex reactions consisting of several elementary steps feature a strongly temperature-sensitive overall selectivity as well as an inversion point with a maximum or minimum selectivity parameter. However, the empirical rule that stereoselective reactions should be performed at the lowest possible temperatures to achieve the highest selectivities is not always followed. Instead, the competition of enthalpy and entropy determines the overall selectivity, depending on the temperature range. 

If at a certain temperature no enantioselectivity can be observed, E = 1 and thus according to Eq. (5.104) AAG = 0. The inversion temperature T- can then be calculated from Eq. (5.105) to read. 

---