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

We applied the finite-size scaling method using the B-splines basis set to construct the stability diagram for two-electron atoms with a screened Coulomb potential. The results of this method for two electron atoms are very accurate in comparison with previous calculations based on Gaussian, Hylleraas, and finite-element basis sets. The stability diagram for the screened two-electron atoms shows three distinct regions: a two-electron region, a one-electron region, and a zero-electron region, which correspond to stable, ionized and double ionized atoms. In previous studies, it was difficult to extend the finite size scaling calculations to large molecules and extended systems because of the computational cost and the lack of a simple way to increase the number of Gaussian basis elements in a systematic way. Motivated by recent studies showing how one can use B-splines to solve Hartree-Fock and Kohn-Sham equations, this combined finite size scaling using the B-splines basis set, might provide an effective systematic way to treat criticality of large molecules and extended systems. As benchmark calculations, the two-electron systems show the feasibility of this combined approach and provide an accurate reference for comparison.