  The ground-state energies of one-electron homonuclear quasi-molecules for the
nuclear charge number in the range Z=1-100 at the "chemical" distances R= 2/Z
(in a.u.) are calculated. The calculations are performed for both point- and
extended-charge nucleus cases using the Dirac-Fock-Sturm approach with the
basis functions constructed from the one-center Dirac-Sturm orbitals. The
critical distances R_cr, at which the ground-state level reaches the edge of
the negative-energy Dirac continuum, are calculated for homonuclear
quasi-molecules in the range: Z=85-100. It is found that in case of U_2^{183+}
the critical distance R_cr = 38.42 fm for the point-charge nuclei and R_cr =
34.72 fm for extended nuclei.
