The Michael addition of cyclohexanone with trans-beta-nitrostyrene catalyzed by a chiral ionic liquid (CIL) pyrrolidine-imidazolium bromide, which represents a prototype of CIL-promoted asymmetric syntheses, has been investigated by performing density functional theory calculations. We show the details of the mechanism and energetics, the influence of the acid additive on the reactivity, and the functional role of the CIL in the asymmetric addition. It is found that the reaction proceeds via two stages, i.e., the initial enamine formation, where the imine complex is first created and then isomerizes into the enamine intermediate, and the subsequent Michael addition involving a three-step mechanism. The calculations show that the presence of the acid additive changes the imine formation mechanism and lowers the reaction barrier, as well as, more importantly, makes the reaction become highly thermodynamically favored. It is also suggested that both the anion and cation of the CIL synergically facilitate the reaction, which act as the proton acceptor in the imine-enamine tautomerism and the stabilizer of the negative charge in the C-C bond formation process, respectively. The present theoretical study rationalizes the early experimental findings well and provides aid to some extent for the rational design of efficient CIL catalysts. Chirality 22:813-819, 2010. (C) 2010 Wiley-Liss, Inc.