A chiral ruthenium carbene complex of the formula: wherein: X 1 and X 2 are independently selected from the group consisting of anionic ligands and polymers, or X 1 and X 2 may be taken together to form a cyclic group; R 1 is selected from the group consisting of hydrogen, silyl, hydrocarbyl, substituted hydrocarbyl, heteroatom-containing hydrocarbyl, substituted heteroatom-containing hydrocarbyl, and carboxyl; R 2 is selected from the group consisting of hydrogen, silyl, hydrocarbyl, substituted hydrocarbyl, heteroatom-containing hydrocarbyl, and substituted heteroatom-containing hydrocarbyl, or R 1 and R 2 may be taken together to form a cyclic group; Y 1 and Y 2 are heteroatoms independently selected from the group consisting of N, O, S, and P, with the proviso that when Y 1 or Y 2 is O or S, then the appended aryl group is absent; R 5 and R 6 are independently selected from the group consisting of polymers, hydrocarbyl, substituted hydrocarbyl, heteroatom-containing hydrocarbyl, substituted heteroatom-containing hydrocarbyl, and functional groups, optionally substituted with one or more moieties selected from the group consisting of C 1-10 alkyl, C 1-10 alkoxy, C 5-20 aryl, hydroxyl, sulfhydryl, - -H, halo, and functional groups; or R 5 and R 6 are linked together to form a substituted or unsubstituted, saturated or unsaturated ring structure, which may itself be substituted; R 20 and R 21 are independently selected from the group consisting of hydrogen, C 1-20 alkyl, substituted C 1-20 alkyl, perfluoronated C 1-20 alkyl, C 1-20 heteroalkyl, substituted C 1-20 heteroalkyl, C 1-20 alkoxy, C 5-20 aryl, substituted C 5-20 aryl, heteroaryl, C 5-30 aralkyl, C 5-30 alkaryl, and halo; and L is a neutral electron donor ligand. X 1 and X 2 are independently selected from the group consisting of anionic ligands and polymers, or X 1 and X 2 may be taken together to form a cyclic group; R 1 is selected from the group consisting of hydrogen, silyl, hydrocarbyl, substituted hydrocarbyl, heteroatom-containing hydrocarbyl, substituted heteroatom-containing hydrocarbyl, and carboxyl; R 2 is selected from the group consisting of hydrogen, silyl, hydrocarbyl, substituted hydrocarbyl, heteroatom-containing hydrocarbyl, and substituted heteroatom-containing hydrocarbyl, or R 1 and R 2 may be taken together to form a cyclic group; Y 1 and Y 2 are heteroatoms independently selected from the group consisting of N, O, S, and P, with the proviso that when Y 1 or Y 2 is O or S, then the appended aryl group is absent; R 5 and R 6 are independently selected from the group consisting of polymers, hydrocarbyl, substituted hydrocarbyl, heteroatom-containing hydrocarbyl, substituted heteroatom-containing hydrocarbyl, and functional groups, optionally substituted with one or more moieties selected from the group consisting of C 1-10 alkyl, C 1-10 alkoxy, C 5-20 aryl, hydroxyl, sulfhydryl, - -H, halo, and functional groups; or R 5 and R 6 are linked together to form a substituted or unsubstituted, saturated or unsaturated ring structure, which may itself be substituted; R 20 and R 21 are independently selected from the group consisting of hydrogen, C 1-20 alkyl, substituted C 1-20 alkyl, perfluoronated C 1-20 alkyl, C 1-20 heteroalkyl, substituted C 1-20 heteroalkyl, C 1-20 alkoxy, C 5-20 aryl, substituted C 5-20 aryl, heteroaryl, C 5-30 aralkyl, C 5-30 alkaryl, and halo; and L is a neutral electron donor ligand.