### Abstract

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, i.e. a two-electron region, a one-electron region and a zero-electron region, which correspond to stable, ionized and double ionized atoms, respectively. 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.

Original language | English |
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Article number | 235003 |

Journal | Journal of Physics B: Atomic, Molecular and Optical Physics |

Volume | 45 |

Issue number | 23 |

DOIs | |

Publication status | Published - 14 Dec 2012 |

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### ASJC Scopus subject areas

- Condensed Matter Physics
- Atomic and Molecular Physics, and Optics

### Cite this

**Ground-state stability and criticality of two-electron atoms with screened Coulomb potentials using the B-splines basis set.** / Serra, Pablo; Kais, Sabre.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Ground-state stability and criticality of two-electron atoms with screened Coulomb potentials using the B-splines basis set

AU - Serra, Pablo

AU - Kais, Sabre

PY - 2012/12/14

Y1 - 2012/12/14

N2 - 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, i.e. a two-electron region, a one-electron region and a zero-electron region, which correspond to stable, ionized and double ionized atoms, respectively. 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.

AB - 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, i.e. a two-electron region, a one-electron region and a zero-electron region, which correspond to stable, ionized and double ionized atoms, respectively. 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.

UR - http://www.scopus.com/inward/record.url?scp=84870467688&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84870467688&partnerID=8YFLogxK

U2 - 10.1088/0953-4075/45/23/235003

DO - 10.1088/0953-4075/45/23/235003

M3 - Article

AN - SCOPUS:84870467688

VL - 45

JO - Journal of Physics B: Atomic, Molecular and Optical Physics

JF - Journal of Physics B: Atomic, Molecular and Optical Physics

SN - 0953-4075

IS - 23

M1 - 235003

ER -