After the structures of plausible transition state m odels without malonic acidwere fully optimized at the B3LYP/6-31G(d,p) level using PCM model (solvent ¼ethanol), we found that the energy difference was only 0.9 kcal/mol between calculated transition state models giving (S )- and (R)-isomers (see Supplementary data ), indicating that malonic acid would play a key role for both the acceleration of reactions and high stereoselectivities of the products.