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Aufbau Principle and Singlet-Triplet Gap in Spherical Hooke Atoms
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  • Xabier Telleria,
  • Jesus Ugalde,
  • Xabier Lopez,
  • Eduard Matito,
  • Eloy Ramos-Cordoba,
  • Mauricio Rodriguez-Mayorga
Xabier Telleria
Euskal Herriko Unibertsitatea (UPV/EHU)

Corresponding Author:[email protected]

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Jesus Ugalde
Euskal Herriko Unibertsitatea
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Xabier Lopez
Euskal Herriko Unibertsitatea
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Eduard Matito
University of Girona
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Eloy Ramos-Cordoba
Donostia International Physics Center
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Mauricio Rodriguez-Mayorga
Paris-Saclay University
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Singlet and triplet spin state energies for three-dimensionalHooke atoms, i .e. electrons in a quadratic confinement, with even number of electrons (2, 4, 6, 8, 10) is discussed using Full-CI and CASSCF type wavefunctions with a variety of basis sets and considering perturbative corrections up to second order. The effect of the screening of the electron-electron interaction is also discussed by using a Yukawa-type potential with different values of the Yukawa screening parameter (λee =0.2, 0.4, 0.6, 0.8, 1.0). Our results show that the singlet state is the ground state for 2 and 8 electron Hooke atoms, whereas the triplet is the ground spin state for 4, 6 and 10 electron systems. This suggests the following Auf bau structure 1s < 1p < 1d with singlet ground spin states for systems in which the generation of the triplet implies an inter-shell one electron promotion, and triplet ground states in cases when there is a partial filling of electrons of a given shell. It is also observed that the screening of electronelectron interactions has a sizable quantitative effect on the relative energies of both spin states, specially in the case of 2 and 8 electron systems, favouring the singlet state over the triplet. However, the screening of the electron-electron interaction does not provoke a change in the nature of the ground spin state of these systems. By analyzing the different components of the energy, we have gained a deeper understanding of the effects of the kinetic, confinement and electron-electron interaction components of the energy.
06 Apr 2022Submitted to International Journal of Quantum Chemistry
11 Apr 2022Submission Checks Completed
11 Apr 2022Assigned to Editor
12 Apr 2022Reviewer(s) Assigned
11 May 2022Review(s) Completed, Editorial Evaluation Pending
13 May 2022Editorial Decision: Revise Major
26 Jun 20221st Revision Received
20 Jul 2022Submission Checks Completed
20 Jul 2022Assigned to Editor
20 Jul 2022Reviewer(s) Assigned
19 Aug 2022Review(s) Completed, Editorial Evaluation Pending
22 Aug 2022Editorial Decision: Accept