In order to consider only a subset of the elements of a mixture, we form a subcomposition (or subsimplex). Given a D-part composition, a C-part subcomposition, for which C < D, may be formed via with a stir bar. The vial was heated at 80 °C for 1 h, and the catalyst mixture became dark red. To a separate vial, was added substrate (0.203 mmol, 5 equiv). The catalyst mixture was added to the substrate, and the vial was sealed with a Teflon-lined cap. The reaction mixture was stirred at room temperature for 18 h. Volatile materials were evaporated with a rotary evaporator to obtain the crude products, which were directly analyzed by 1 H-NMR spectroscopy.