To a 1 L three-necked flask was added tert-butyl (BETAS,4R)-BETA-methyl-GAMA,2-dioxo-4-(phenylmethyl)-3-oxazolidinebutanoate (29.0 g, 83.5 mmol) and a solvent mixture of THF/water (300 mL, V/V=4:1). The reaction system was cooled to 0 °C in an ice bath and 30% H2O2 aqueous solution (17.0 g, 501 mmol) was slowly added dropwise under stirring for a controlled time of 10 min. Subsequently, 2 M LiOH aqueous solution (4.73 g, 117 mmol) was added and the reaction system was kept in an ice bath with continued stirring for 4 hours. Upon completion of the reaction, the reaction was quenched by slow dropwise addition of 2.73 M Na2SO3 aqueous solution for 1 h, during which slight gas escape was observed. THF was removed by distillation under reduced pressure and the remaining suspension was extracted with DCM (400 mL). The aqueous phase (containing the target product (S)-4-(tert-butoxy)-2-methyl-4-oxobutanoic acid) was separated and retained, and the organic phase was washed with 0.1 N aqueous NaOH (100 mL). The organic layer was dried over anhydrous Na2SO4, filtered and concentrated under reduced pressure to recover the chiral auxiliary (reusable). The combined aqueous phases were cooled in an ice bath and the pH was adjusted to 4 with 2 N HCl to form a turbid solution. It was extracted with EtOAc (300 mL), the EtOAc layer was dried over anhydrous Na2SO4, filtered and concentrated under reduced pressure to give the crude product as a colorless oil, which solidified to a white solid on standing. The crude product was purified by Biotage 40 column chromatography with an eluent of 30% EtOAc/hexane, resulting in (S)-4-(tert-butoxy)-2-methyl-4-oxobutanoic acid (13.4 g, 85% yield): [α]D = -6.56° (literature value: [α]D = -7.0°, c 0.86, CHCl3, 9 mg/mL), and the product contained trace amounts of chiral auxiliaries, which may result in a change in the direction of rotation (literature reference: Davies et al. (1998) J. Chem. Soc., Perkin Trans. 1, 17:2635-2644).
