  Effective potentials of the relativistic m\alpha^6 order correction for the
ground state of the Coulomb two-center problem are calculated. They can be used
to evaluate the relativistic contribution of that order to the energies of
hydrogen molecular ions or metastable states of the antiprotonic helium atom,
where precision spectroscopic data are available. In our studies we use the
variational expansion based on randomly chosen exponents that permits to
achieve high numerical accuracy.
