The recently developed method [M. Musiał, J. Chem. Phys. 136, 134111 (2012)] to study double electron attached states has been applied to the description of the ground and excited state potential energy curves of the alkali metal dimers. The method is based on the multireference coupled cluster scheme formulated within the Fock space formalism for the (2,0) sector. Due to the use of the efficient intermediate Hamiltonian formulation, the approach is free from the intruder states problem. The description of the neutral alkali metal dimers is accomplished via attaching two electrons to the corresponding doubly ionized system. This way is particularly advantageous when a closed shell molecule dissociates into open shell subunits while its doubly positive cation generates the closed shell fragments. In the current work, we generate the potential energy curves for the ground and multiple excited states of the Li2 and Na2 molecules. In all cases the potential energy curves are smooth for the entire range of interatomic distances (from the equilibrium point to the dissociation limit). Based on the calculated potential energy curves, we are able to compute spectroscopic parameters of the systems studied.