1. Catalyst used for the diastereo- and enantioselective carbonyl (trimethylsilyl)allylation from the alcohol, or aldehyde, oxidation level.

2. Catalyst used for the diastereo- and enantioselective carbonyl (hydroxy)allylation to form anti-1,2-diols.

3. Catalyst used for the diastereo- and enantioselective carbonyl (hydroxymethyl)allylation from the alcohol, or aldehyde, oxidation level.

4. Catalyst used for the diastereo- and enantioselective carbonyl tert-prenylation from the alcohol, or aldehyde, oxidation level.

5. Catalyst used for the diastereo- and enantioselective carbonyl double crotylation of 1,3-diols.

6. Catalyst used for the diastereo- and enantioselective carbonyl crotylation from the alcohol or aldehyde oxidation level.