# Self-consistent self-interaction corrected density functional theory calculations for atoms using Fermi-Löwdin orbitals: Optimized Fermi-orbital descriptors for Li–Kr

## Abstract

In the Fermi-Löwdin orbital method for implementing self-interaction corrections (FLO-SIC) in density functional theory (DFT), the local orbitals used to make the corrections are generated in a unitary-invariant scheme via the choice of the Fermi orbital descriptors (FODs). These are M positions in 3-d space (for an M-electron system) that can be loosely thought of as classical electron positions. The orbitals that minimize the DFT energy including the SIC are obtained by finding optimal positions for the FODs. In this paper, we present optimized FODs for the atoms from Li–Kr obtained using an unbiased search method and self-consistent FLO-SIC calculations. The FOD arrangements display a clear shell structure that reflects the principal quantum numbers of the orbitals. We describe trends in the FOD arrangements as a function of atomic number. FLO-SIC total energies for the atoms are presented and are shown to be in close agreement with the results of previous SIC calculations that imposed explicit constraints to determine the optimal local orbitals, suggesting that FLO-SIC yields the same solutions for atoms as these computationally demanding earlier methods, without invoking the constraints

- Authors:

- Central Michigan Univ., Mount Pleasant, MI (United States)
- TU Bergakademie Freiberg (Germany); Johns Hopkins Univ., Baltimore, MD (United States). Department of Physics and Astronomy
- Johns Hopkins Univ., Baltimore, MD (United States). Department of Physics and Astronomy; Government College Univ., Faisalabad (Pakistan)
- TU Bergakademie Freiberg (Germany)

- Publication Date:

- Research Org.:
- Central Michigan Univ., Mount Pleasant, MI (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

- OSTI Identifier:
- 1512945

- Alternate Identifier(s):
- OSTI ID: 1402537

- Grant/Contract Number:
- [SC0001330]

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of Chemical Physics

- Additional Journal Information:
- [ Journal Volume: 147; Journal Issue: 16]; Journal ID: ISSN 0021-9606

- Publisher:
- American Institute of Physics (AIP)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY

### Citation Formats

```
Kao, Der-you, Withanage, Kushantha, Hahn, Torsten, Batool, Javaria, Kortus, Jens, and Jackson, Koblar. Self-consistent self-interaction corrected density functional theory calculations for atoms using Fermi-Löwdin orbitals: Optimized Fermi-orbital descriptors for Li–Kr. United States: N. p., 2017.
Web. doi:10.1063/1.4996498.
```

```
Kao, Der-you, Withanage, Kushantha, Hahn, Torsten, Batool, Javaria, Kortus, Jens, & Jackson, Koblar. Self-consistent self-interaction corrected density functional theory calculations for atoms using Fermi-Löwdin orbitals: Optimized Fermi-orbital descriptors for Li–Kr. United States. doi:10.1063/1.4996498.
```

```
Kao, Der-you, Withanage, Kushantha, Hahn, Torsten, Batool, Javaria, Kortus, Jens, and Jackson, Koblar. Tue .
"Self-consistent self-interaction corrected density functional theory calculations for atoms using Fermi-Löwdin orbitals: Optimized Fermi-orbital descriptors for Li–Kr". United States. doi:10.1063/1.4996498. https://www.osti.gov/servlets/purl/1512945.
```

```
@article{osti_1512945,
```

title = {Self-consistent self-interaction corrected density functional theory calculations for atoms using Fermi-Löwdin orbitals: Optimized Fermi-orbital descriptors for Li–Kr},

author = {Kao, Der-you and Withanage, Kushantha and Hahn, Torsten and Batool, Javaria and Kortus, Jens and Jackson, Koblar},

abstractNote = {In the Fermi-Löwdin orbital method for implementing self-interaction corrections (FLO-SIC) in density functional theory (DFT), the local orbitals used to make the corrections are generated in a unitary-invariant scheme via the choice of the Fermi orbital descriptors (FODs). These are M positions in 3-d space (for an M-electron system) that can be loosely thought of as classical electron positions. The orbitals that minimize the DFT energy including the SIC are obtained by finding optimal positions for the FODs. In this paper, we present optimized FODs for the atoms from Li–Kr obtained using an unbiased search method and self-consistent FLO-SIC calculations. The FOD arrangements display a clear shell structure that reflects the principal quantum numbers of the orbitals. We describe trends in the FOD arrangements as a function of atomic number. FLO-SIC total energies for the atoms are presented and are shown to be in close agreement with the results of previous SIC calculations that imposed explicit constraints to determine the optimal local orbitals, suggesting that FLO-SIC yields the same solutions for atoms as these computationally demanding earlier methods, without invoking the constraints},

doi = {10.1063/1.4996498},

journal = {Journal of Chemical Physics},

number = [16],

volume = [147],

place = {United States},

year = {2017},

month = {10}

}

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#### Figures / Tables:

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Works referencing / citing this record:

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Magnetic Signatures of Hydroxyl‐ and Water‐Terminated Neutral and Tetra‐Anionic Mn _{12} ‐Acetate

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Figures / Tables found in this record:

*Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.*