activation energy of the reaction, sometimes called the energy barrier, and is temperature-dependent. Using the Gibbs free energy of the energy barrier, ΔG*, means that the relative rates for opposing stereochemical outcomes at a given temperature, T, is: This temperature dependence means the rate difference, and therefore the enantioselectivity, is greater at lower temperatures. As a result, even small energy-barrier differences can lead to a noticeable effect. {| class="wikitable" |- ! ΔΔG* (kcal) !colspan=2 | at 273 K !colspan=2 | at 298 K !colspan=2 | at 323 K) |- | style="text-align:center;" | 1.0 | | | |- | style="text-align:center;" | 2.0 | | | |- | style="text-align:center;" | 3.0 | | | |- | style="text-align:center;" | 4.0 | | | |- | style="text-align:center;" | 5.0 | | | |} Approaches Enantioselective catalysis Enantioselective catalysis (known traditionally as "asymmetric catalysis") is performed using chiral catalysts, which are typically chiral coordination complexes. Catalysis is effective for a broader range of transformations than any other method of enantioselective synthesis. The chiral metal catalysts are almost invariably rendered chiral by using chiral ligands, but it is possible to generate chiral-at-metal complexes composed entirely of achiral ligands. Most enantioselective catalysts are effective at low substrate/catalyst ratios. Given their high efficiencies, they are often suitable for industrial scale synthesis, even with expensive catalysts. A versatile example of enantioselective synthesis is asymmetric hydrogenation, which is used to reduce a wide variety of functional groups. The design of new catalysts is dominated by the development of new classes of ligands. Certain ligands, often referred to as "privileged ligands", are effective in a wide range of reactions; examples include BINOL, Salen, and BOX. Most catalysts are effective for only one type of asymmetric reaction. For example, Noyori asymmetric hydrogenation with BINAP/Ru requires a β-ketone, although another catalyst, BINAP/diamine-Ru, widens the scope to α,β-alkenes and aromatic chemicals. Chiral auxiliaries A chiral auxiliary is an organic compound which couples to the starting material to form a new compound which can then undergo diastereoselective reactions via intramolecular asymmetric induction. At the end of the reaction the auxiliary is removed, under conditions that will not cause racemization of the product. It is typically then recovered for future use. Chiral auxiliaries must be used in stoichiometric amounts to be effective and require additional synthetic steps to append and remove the auxiliary. However, in some cases the only available stereoselective methodology relies on chiral auxiliaries