Preparation method for optically active bicyclic gamma-amino acid compound

A compound of formula (I) or (I′):

• wherein R1 and R2 are each independently selected from a hydrogen atom and a C1-6 alkyl group, or R1 and R2 are bonded to each other to form an isopropylidene group;
• and
• R3 is a cyano group or a nitromethyl group.

A method of producing a compound of formula (Ia), an enantiomer thereof, or both a compound of formula (Ia) and an enantiomer thereof, comprising

• mixing a compound of formula (II), an enantiomer thereof, or both a compound of formula (II) and an enantiomer thereof, with an alkali metal salt of hydrogen cyanide in a solvent to produce the compound of formula (Ia), an enantiomer thereof, or both a compound of formula (Ia) and an enantiomer thereof:
• wherein R1 and R2 are each independently selected from a hydrogen atom and a C1-6 alkyl group, or R1 and R2 are bonded to each other to form an isopropylidene group.

A method of producing a compound of formula (Ib), an enantiomer thereof, or both a compound of formula (Ib) and an enantiomer thereof, comprising

• mixing a compound of formula (II), an enantiomer thereof, or both a compound of formula (II) and an enantiomer thereof, with nitromethane in the presence of a base in a solvent to produce the compound of formula (Ib), an enantiomer thereof, or both a compound of formula (Ib) and an enantiomer thereof:
• wherein R1 and R2 are each independently selected from a hydrogen atom and a C1-6 alkyl group, or R1 and R2 are bonded to each other to form an isopropylidene group.

A method of separating a compound of formula (V) and a compound of formula (V′), comprising

• allowing a mixture of the compound of formula (V) and the compound of formula (V′) to form a salt with an optically active organic amine:
• wherein R3 is a cyano group or a nitromethyl group.

A method of producing a compound of formula (VI), comprising

• allowing a compound of formula (V) to form a salt with an organic amine in the presence of a solvent:
• wherein R3 is a cyano group or a nitromethyl group.