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The mechanisms of two kinds of transition metal catalyzed cross-coupling reactions were studied using Density Functional Theory(DFT)calculations.First,simple iron salts turn out to be highly efficient,cheap,nontoxic,and environmentally friendly precatalysts compared with the established palladium and nickel catalyst systems.One example of iron-catalyzed cross-coupling reactions between 4-chlorobenzoic acid methyl ester and n-hexylicmagnesium bromide to form C-C bonds was studied [1].Our results showed that the rate-limiting step was the reductive elimination of [Ar-(n-hexyl)-Fe(MgBr)2] to regenerate the catalyst [Fe(MgBr)2].The salvation effect has been thoroughly investigated using two C-PCM methods.Another example of iron-catalyzed aminohydroxylation reactions between vinyl benzene and N-sulfonyl oxaziridine substrate to form C-X(X=N,O heteroatom)bonds was studied [2].Our calculations showed that the Fe(II)catalyzed process was favored over Fe(III)catalyzed process for the overall catalytic cycle.Second,the Ni-catalyzed reductive cross-coupling reactions can overcome the problems such as β-H elimination and slow reductive elimination of transition metal catalyzed cross-coupling reactions.The mechanisms of Ni-catalyzed reductive cross-coupling of aryl bromide and secondary alkyl bromide [3] and the homo-coupling to form biaryl byproduct in the system [4] were investigated.We have studied four single electron transfer mechanisms and two concerted mechanisms.