Ab initio calculations of spectroscopic constants and low-lying electronic states of Ag₂ and Ag⁺₂ dimers are reported. They are made by the Hartree-Fock (HF) method and the restricted active space self-consistent field (RASSCF) method with the aid of semilocal nonrelativistic and relativistic 11-electron effective core potentials (ECP and RECP). To find the quality of the potential constructed in this way, we made nonrelativistic calculations by the HF method of the Ag₂ molecule, both all-electron calculations using an original approach in the basis of numerical HF occupied orbitals and virtual Sturmian orbitals and also the calculations of 11-electron ECP based on Gaussian orbitals. The comparison of one-electron spectra of Ag₂ energies in non-relativistic HF calculations using ECP with the all-electron numerical calculation shows that the difference between the corresponding orbitals does not exceed 2 × 10^-3 au. For the Ag₂ molecules, calculations are made, with both ECP and RECP, of the energy of two vertical dipole-allowed optical transitions. For the Ag⁺₂ molecular ion, energies of five dipole-allowed optical transitions are predicted. The nature of low-lying electronic states of Ag₂ is studied by analyzing Mulliken populations and the leading configurations that make the dominant contribution to the wave function of a many-electron state. The characteristics calculated in the paper are compared with experimental data and results of other theoretical papers.