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

Abstract

Two numerical methods are used to evaluate the relativistic spectrum of the two-centre Coulomb problem (for the $H_2^{+}$ and $T{h}_2^{179+}$ 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.

31 pages, 1 figure, new version has revised text

References in corpus (3)

• Dual kinetic balance approach to basis set expansions for the Dirac equation
• On the eigenvalues of operators with gaps. Application to Dirac operators
• Polarization operator approach to electron-positron pair production in combined laser and Coulomb fields

Cited by in corpus (13)

• Multidimensionally-constrained relativistic mean field models and potential energy surfaces of actinide nuclei
• A Split-Step Numerical Method for the Time-Dependent Dirac Equation in 3-D Axisymmetric Geometry
• Solution of two-center time-dependent Dirac equation in spherical coordinates: Application of the multipole expansion of the electron-nuclei interaction
• Galerkin method for unsplit 3-D Dirac equation using atomically/kinetically balanced B-spline basis
• Solution of the two-center Dirac equation with 20 digits precision using the finite-element technique
• The use of Slater-type spinor orbitals in algebraic solution of two-center Dirac equation
• High-precision solution of the Dirac Equation for the hydrogen molecular ion using a basis-set expansion
• Estimating the radiative part of QED effects in superheavy nuclear quasimolecules
• K-shell ionization of heavy hydrogen-like ions
• Plunging in the Dirac sea using graphene quantum dots
• Light one-electron quasi-molecular ions within the finite-basis-set method for the two-center Dirac equation
• High-precision minmax solution of the two-center Dirac equation
• Improvement of the Basis for the Solution of the Dirac Equation in Cassini Coordinates