Adiabatic potential curves of H–$p$ and He$^+$–$p$ ions: relativistic treatment

In the present paper, a completely relativistic approach is used to obtain adiabatic potential curves for molecular terms within the A-DKB method. Solving the two-center Dirac equation, two compounds are described: one-electron homonuclear H–$p$ and one-electron heteronuclear He$^+$–$p$ (quasi-)molecular ions. In the framework of the Born–Oppenheimer approximation, the electron binding energies (ground and several first excited states) in a wide range of inter-nuclear distances have been obtained. Using the relativistic approach, energy splittings, crossings, and identification of energy terms are discussed. The results are compared with those characterized within the nonrelativistic approach, widely covered in the literature.