Numerical solution of the time-independent Dirac equation for diatomic   molecules: B-splines without spurious states
  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. 
F. Fillion-Gourdeau, E. Lorin and A. D. Bandrauk
physics.chem-ph physics.atom-ph physics.comp-ph