Although the electronic ground states for Zn2,Cd2,and Hg2 have been studied in recent years,the spin-orbit coupling was corrected in perturbation form or even not considered1-6.However,the spin-orbit coupling of Zn2,Cd2,and Hg2 is significant,so we use CFOUR package(http://www.cfour.de.)to study the potential curves of electronic ground states for Zn2,Cd2,and Hg2 with spin-orbit coupling included in the post-HF iteration calculations.All the calculations are based on the two component relativistic effective core potentials and matched basis sets,so the spin-orbit coupling is just considered in the CCSD(T)calculations.Obviously,this treatment of spin-orbit coupling is rather efficient.And the results of equilibrium bond lengths,harmonic frequencies and dissociation energies etc for Zn2,Cd2,and Hg2 are rather reasonable compared to available experimental results.