Numerical solution of the time-independent Dirac equation for diatomic molecules: B-splines without spurious states

Details Numerical solution of the time-independent Dirac equation for diatomic molecules: B-splines without spurious states Numerical solution of the time-independent Dirac equation for diatomic molecules: B-splines without spurious states

2011-12-05

arxiv.org/abs/1112.1043v2

Physics

Chemical Physics

31 pages, 1 figure, new version has revised text

Scientific paper

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.

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