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arXiv · 1112.1043

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

F. Fillion-Gourdeau·E. Lorin·A. D. Bandrauk
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Abstract

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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F. Fillion-Gourdeau, E. Lorin, A. D. Bandrauk. 2012-02-06. Numerical solution of the time-independent Dirac equation for diatomic molecules: B-splines without spurious states. https://doi.org/10.1103/physreva.85.022506

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