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Based on our previous work,[1,2,3,4] the computational study on the detailed mechanism of NHC-catalyzed enantioselective [4+2] annulation of oxidized enals and azodicarboxylates[5](Scheme 1)has been performed using density functional thoery.According to the calculated free energy profile,the [4+2] cycloaddition step is the enantioselectivity-determining step associated with the energy barriers of 8.71 kcal/mol for R configuration and 10.72 kcal/mol for S configuration respectively,which is in good agreement with the experimental results.Furthermore,the analysis of global reactivity index has been utilized to disclose the function of NHC catalyst in the [4+2] annulation.