Density functional (B3PW91) method with relativistic effective core potential (RECP) has been used to optimize the structure of ScH+ and ScH2+ molecule ions, whose equilibrium nuclear distance, dissociation energies spectral constants and harmonic frequencies have been obtained. The Murrell-Sorbie potential energy function of ScH+ molecule ions has been derived to be fitted to ab initio data through the least square fitting, and the potential energy function of ScH2+ molecule ions is driven by many-body expansion theory. The potential energy surface precisely represents the equilibrium structure of ScH2+ (C2v) structure. The static state of reactive potential energy surface is also discussed according to the potential energy function contours, and the structure of the ScH2+ molecule ions has been also explained by the hybrid orbital theory.作者简介：冉鸣.E-mail:ranming2004@126.com.通讯作者