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We applied the finite-size scaling method using the B-splines basis set toconstruct the stability diagram for two-electron atoms with a screened Coulombpotential. The results of this method for two electron atoms are very accuratein comparison with previous calculations based on Gaussian, Hylleraas, andfinite-element basis sets. The stability diagram for the screened two-electronatoms shows three distinct regions: a two-electron region, a one-electronregion, and a zero-electron region, which correspond to stable, ionized anddouble ionized atoms. In previous studies, it was difficult to extend thefinite size scaling calculations to large molecules and extended systemsbecause of the computational cost and the lack of a simple way to increase thenumber of Gaussian basis elements in a systematic way. Motivated by recentstudies showing how one can use B-splines to solve Hartree-Fock and Kohn-Shamequations, this combined finite size scaling using the B-splines basis set,might provide an effective systematic way to treat criticality of largemolecules and extended systems. As benchmark calculations, the two-electronsystems show the feasibility of this combined approach and provide an accuratereference for comparison.

Ground-state stability and criticality of two-electron atoms with screened Coulomb potentials using the B-splines basis set