  Two numerical methods are used to evaluate the relativistic spectrum of the
two-centre Coulomb problem (for the $H_{2}^{+}$ and $Th_{2}^{179+}$ diatomic
molecules) in the fixed nuclei approximation by solving the single particle
time-independent Dirac equation. The first one is based on a min-max principle
and uses a two-spinor formulation as a starting point. The second one is the
Rayleigh-Ritz variational method combined with kinematically balanced basis
functions. Both methods use a B-spline basis function expansion. We show that
accurate results can be obtained with both methods and that no spurious states
appear in the discretization process.
