[en] A systematic study of the potential-energy surfaces of the ground and first excited states of the H₃^- anion is carried out by means of the recently developed generalized diatomics-in-molecule method in the partial wave representation, making use of the available information for the bound and resonant states of H^-andH₂^-. Both local complex potentials as well as energy-dependent nonlocal complex effective potentials are calculated. The potential-energy surfaces encompass both bound and quasi-stationary (resonant) electronic states. The paper presents the first calculation of the energy-dependent width and level-shift functions of the quasi-stationary states of H₃^-