### Abstract

Atomic Shannon information entropies are computed using Hyllerass-type basis functions for the helium isoelectronic series. As one varies the nuclear charge Z for the two-electron atoms, finite size scaling analysis shows that the system exhibits a critical point of the ground state energy at λ_{c} = 1/Z_{c} = 1.0971 ± 0.0005 with a critical exponent α = 1, E(λ) ∼ (λ - λ_{c}) ^{α}. At the critical point, the ground state energy becomes degenerate with the hydrogenic threshold. The Shannon information entropy develops a step-like discontinuity at λ_{c}. Further analysis indicates that the entropy as a function of λ is proportional to the first derivative of the energy with respect to λ. The critical exponent for the entropy α_{s} = 0, S(λ) ∼ (λ - λc)_{αs}.

Original language | English |
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Pages (from-to) | 127-131 |

Number of pages | 5 |

Journal | Chemical Physics |

Volume | 309 |

Issue number | 2-3 |

DOIs | |

Publication status | Published - 14 Mar 2005 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physical and Theoretical Chemistry
- Spectroscopy
- Atomic and Molecular Physics, and Optics

### Cite this

*Chemical Physics*,

*309*(2-3), 127-131. https://doi.org/10.1016/j.chemphys.2004.08.020

**Discontinuity of Shannon information entropy for two-electron atoms.** / Shi, Qicun; Kais, Sabre.

Research output: Contribution to journal › Article

*Chemical Physics*, vol. 309, no. 2-3, pp. 127-131. https://doi.org/10.1016/j.chemphys.2004.08.020

}

TY - JOUR

T1 - Discontinuity of Shannon information entropy for two-electron atoms

AU - Shi, Qicun

AU - Kais, Sabre

PY - 2005/3/14

Y1 - 2005/3/14

N2 - Atomic Shannon information entropies are computed using Hyllerass-type basis functions for the helium isoelectronic series. As one varies the nuclear charge Z for the two-electron atoms, finite size scaling analysis shows that the system exhibits a critical point of the ground state energy at λc = 1/Zc = 1.0971 ± 0.0005 with a critical exponent α = 1, E(λ) ∼ (λ - λc) α. At the critical point, the ground state energy becomes degenerate with the hydrogenic threshold. The Shannon information entropy develops a step-like discontinuity at λc. Further analysis indicates that the entropy as a function of λ is proportional to the first derivative of the energy with respect to λ. The critical exponent for the entropy αs = 0, S(λ) ∼ (λ - λc)αs.

AB - Atomic Shannon information entropies are computed using Hyllerass-type basis functions for the helium isoelectronic series. As one varies the nuclear charge Z for the two-electron atoms, finite size scaling analysis shows that the system exhibits a critical point of the ground state energy at λc = 1/Zc = 1.0971 ± 0.0005 with a critical exponent α = 1, E(λ) ∼ (λ - λc) α. At the critical point, the ground state energy becomes degenerate with the hydrogenic threshold. The Shannon information entropy develops a step-like discontinuity at λc. Further analysis indicates that the entropy as a function of λ is proportional to the first derivative of the energy with respect to λ. The critical exponent for the entropy αs = 0, S(λ) ∼ (λ - λc)αs.

UR - http://www.scopus.com/inward/record.url?scp=12944322206&partnerID=8YFLogxK

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U2 - 10.1016/j.chemphys.2004.08.020

DO - 10.1016/j.chemphys.2004.08.020

M3 - Article

VL - 309

SP - 127

EP - 131

JO - Chemical Physics

JF - Chemical Physics

SN - 0301-0104

IS - 2-3

ER -