Samarium-catalyzed1,5-regioselective azide-alkyne [3+2]-cycloaddition,as the first example of rare earth metal-catalyzed cycloaddition of terminal alkynes to azides resulting in the formation of 1,5-disubstituted 1,2,3-triazoles,is a worthy supplement to the famous“clikck reaction”[1-2].In the present work,the reaction mechanisms have been proposed and validated with DFT computations both in the gas and solution phase using Gaussian09 software at B3LYP/6 -31++G(d,p)(ECP51MWB)level.Especially,the novel quantitative analysis of molecular surface also has also been applied to explain the mechanism and regioselectivity of the title reaction[3].Based on our computation,the present cycloaddition mechanism for the title reaction favors the step-wise pathway(COM-COM1-COM2-COMP)over the concerted one(Scheme 1).In the stepwise pathway,the step linking COM and COM1 is the rate-determining step.In addition,the reaction regioselectivity is controlled by the structures of the two Sm complexes(Fig.1)which can be well explained by the analysis of ESP on vdW surface of the reactants(Fig.2).