Within the framework of two-component pseudo-potentials, the coupled-cluster theory with spin-orbit interaction and the equation-of-motion coupled-cluster theory with spin-orbit interaction for ionized states are employed to obtain the spectroscopic constants of the ground-state Cu2, Ag2, and Au2 in this work. The spin-orbit interaction is only calculated iteratively in the post-Hartree-Fock, i.e. the coupled-cluster procedure. It is shown that the CCSD(T) approach with spin-orbit interaction is capable of providing the rather accurate equilibrium distances and harmonic frequencies. Furthermore, the equation-of-motion coupled-cluster approach with spin-orbit interaction for ionized states is able to reasonably estimate the spin-orbit contribution to the binding energy. Hence, the accurate binding energies are obtained by the scalar-relativistic CCSD(T) calculations with the correction of spin-orbit contribution. In addition, the spectroscopic constants have a weak basis set dependence for all the title species.