Fig. 4: DFT calculations of the reaction pathways over the bulk and confined reactions.

a Bulk reaction at different temperatures using HTiNbO5-X nanosheets as the catalyst. b Comparison of the conversion and reaction time of bulk and confined reactions at 10 °C and 23 °C. Bulk reaction condition: HTiNbO5-X nanosheets (10 mg), alcohol (0.2 M) and acetic anhydride (0.3 M) in CH3CN. Confined reaction condition: HTiNbO5-X membrane (d = 11.0 Å), alcohol (0.2 M) and acetic anhydride (0.3 M) in CH3CN. Free energy profiles for the esterification of benzyl alcohol with acetic anhydride in c bulk and d confined conditions calculated by DFT. Bronsted acid sites are taken as active sites acting as proton sources. The labels TS and IM indicate the transition state and intermediate of the reaction, respectively. The reaction rate is primarily determined by the step from IM1 to TS1, in which the confined energy barrier is clearly smaller than the bulk energy barrier. Error bars represent standard deviation of three measurements.