Linear approximation to relativistic minimax (LARM) applied to a LCAO description of the two-centre Coulomb problem

Abstract

In a recent paper (Zhang H et al 2004 J. Phys. B: At. Mol. Opt. Phys. 37 905), we showed that the minimax approach gives an optimal solution to the relativistic two-centre Coulomb problem for the light H+2 and the super-heavy Th179+2 systems, free of any artefacts. However, the non-linear energy dependence of the minimax functional makes the calculations very expensive, if completeness of the (needed) spectrum is to be guaranteed. Now we probe variational linear approximations to it, which lead to double-sized linear eigenvalue problems, the well-known kinetic balance being the simplest, but with a rather poor representation of the small spinor components. In the linear methods, one generates systematic basis sets for both the large and small spinor components and doubles the space of variational coefficients. The best linear scheme comes very close to Minimax LCAO, demonstrating its good projection property against negative continuum contributions in electronic states. Even though one loses the perfect projection properties of Minimax in LARM, the approximation error due to the chosen finite basis for the large components limits the accuracy of the energies very much the same as in Minimax LCAO. Detailed comparisons of different linear approximations together with the previously computed traditional 4-spinor LCAO, Minimax LCAO and 2-spinor finite-element method (FEM) values are given (Zhang H et al 2004 J. Phys. B: At. Mol. Opt. Phys. 37 905; Kullie O et al 2004 Chem. Phys. Lett. 383 215).