Asymmetric synthesis to provide enantiomerically pure compounds is a promising research area in the field of organic chemistry. Especially, the asymmetric Michael addition is very widely used and viable strategy for the carbon-carbon (C-C) bond formation. 1,2 Organo-catalyzed asymmetric Michael addition reactions have been developed recently and attracted significant attention in the area of asymmetric synthesis because of their prospective applications. 3 This reaction represents one of the most efficient pathways for the C-C bond formation in synthetic organic chemistry. Many proline derivatives, such as proline-triazole, 4 pyrrolidinepyridine, 5 pyrrolidine-sulfonamide, 6 and pyrrolidine-pyrazole 7 have been employed as efficient organocatalysts for asymmetric Michael addition. These organic catalysts are applied not only to the Michael addition reactions, but also to the other reactions, such as Aldol reactions, and Domino process. A large number of cyclic ketones and nitroolefins as Michael donors and Michael acceptors, respectively were used in this process, which proceeds with very good enantioselectivity and diastereoselectivity. 7 In the present computational mechanistic study, cyclohexanone (1) and trans-β-nitrostyrene (2) were chosen as Michael donor and Michael acceptor, respectively. Achiral (S)-pyrrolidine-pyrazole (3) catalyst, which has shown excellent catalytic cycle in the Michael addition of carbonyl compounds to various nitroolefins with very good enantio-and diastereoselectivities (up to 99% ee), was chosen as the organic catalyst. The reaction between cyclohexanone (1) and transβ-nitrostyrene (2) yielded the Michael adduct (4) (Scheme 1).Four possible transition geometries related to the C-C bond forming step of the reaction (vide supra) were investigated by employing the density functional theory (DFT), both in the presence and absence of an acid additive. Insights on the diastereo-and enantio-selectivities in the formation of Michael adduct were gained by the transition state analysis. This reaction proceeds through a mechanism involving the initial formation of an enamine between the cyclohexanone and pyrrolidine-pyrazole catalyst with the simultaneous loss of one water molecule. As the enamine formation and the hydrolysis of the Michael adduct (Figure 1) are rapid and have no effect on the rate and stereoselectivity of the reaction, 8 this study focused on the transition states involved in the rate-limiting C-C bond formation step, the nucleophilic attack of the enamine on trans-β-nitrostyrene. Figure 1 presents the mechanism of this reaction from the earlier reports 7 .The two transition states arising from the approach of trans-β-nitrostyrene to the diastereotopical Re and Si faces of the anti-enamine are represented as TS A , and TS B , respectively. Similarly, the other two transition states are formed with syn-enamine and represented as TS C , and TS D . The formation of four transition states and corresponding products are shown in the Scheme 2.The structures of the transition stat...