Asymptotic Behavior of the Rydberg States of Molecular Hydrogen in the Limit of a United Atom

The asymptotic behavior of the Born–Oppenheimer (BO) potential curves of excited electronic states of molecular hydrogen at short and medium internuclear distances R is studied in the context of the single-channel quantum defect theory and the analytical model of the core-polarization potential. It is shown that the electronic states of the H₂ molecule with gerade and ungerade symmetry converge smoothly in the limit of a united atom to the singlet and triplet states of a hypothetical helium atom ²He I(^1,3L), in states S, D, G, … and P, F, H, …, respectively. The considered molecular states are matching according to principal quantum number n and angular momentum l of a Rydberg electron at both the limit of dissociation H(1s) + H(nl) and when R → 0. Places of the incorrect attribution of BO energies obtained using precision ab initio calculations for states with high values of l are established by analyzing the shape of the constructed quantum defect functions μ_lΛ(R) and the degree of smoothness of their first derivative with respect to R.