Relativistic calculations of ground states of single-electron diatomic molecular ions

We have performed relativistic calculations of ground-state energies for a series of single-electron homonuclear dimers A ₂ ^(2Z?1)+ with nucleus charge Z = 1, 2, 10, 20, 30, 40, 50, 60, 70, 80, 90, 92, and 100 and internuclear distances R = 2/Z. The work involves the Born-Oppenheimer approximation and the single-electron two-center Dirac Hamiltonian, which describes the interaction between an electron and two immovable point charges. Analysis of the convergence process and comparison with data presented in other works for H ₂ ⁺ and Th ₂ ¹⁷⁹⁺ dimers shows that the relative error of the obtained results is on the order of 10^?11–10^?12. High-accuracy values of ground-state energies for some dimers other than Z = 1 and 90 have been obtained in this work for the first time.