Approximation function for the direct calculation of rate constants and Gibbs activation energies of enantiomerization of racemic mixtures from chromatographic parameters in dynamic chromatography

An approximation function for enantioselective dynamic chromatography of racemic mixtures of interconverting enantiomers has been derived that allows the direct calculation of enantiomerization rate constants (k1 and k−1) and Gibbs activation energies of enantiomerization, ΔG#, from chromatographic parameters, i.e., retention times of the enantiomers A and B (tRA and tRB), peak widths at half height (wA and wB) and the relative plateau height (hplateau), without computer simulation. The reaction rate constants of enantiomerization, k−1, obtained with this approximation function, have been validated by comparison with a simulated dataset of 15 625 chromatograms. The mean, standard deviation and confidence interval show a high correlation between the approximated and simulated rate constants. The average deviation from the Gibbs activation enthalpy of enantiomerization, ΔG#, has been estimated to be as small as about ±0.11 RT.