Structures in the long range potential curves of the Na₂ molecule: comparison between ab initio and asymptotic calculations

We have performed model potential and pseudo-potential ab initio calculations for the excited states of the Na₂ molecule over a wide range of internuclear distances. We compare these results with long range calculations using a multipolar expansion for the Coulomb interaction and asymptotic estimation of the exchange term. For the first excited molecular states, the results of the two methods are in good agreement for R>15 au. For the Rydberg states, some potential curves display structures due to pseudo-crossings between covalent curves (correlated to Na(nl)+Na(n'l') dissociation limits) and ionic curves (dissociating into Na⁺+Na^-, the negative ion being in a stable or in an autoionizing state). For instance, we find a well of 2800 cm^-1) at R=30 au in the 6¹ Sigma _g⁺ curve correlated to Na(3s)+Na(5s). These structures can be confirmed in case of ¹ Sigma _g⁺ symmetry by long range calculations including the interaction between the covalent states and an ionic state.