## Accurate and balanced anisotropic Gaussian type orbital basis sets for atoms in strong magnetic fields

## Abstract

In high magnetic field calculations, anisotropic Gaussian type orbital (AGTO) basis functions are capable of reconciling the competing demands of the spherically symmetric Coulombic interaction and cylindrical magnetic (B field) confinement. However, the best available a priori procedure for composing highly accurate AGTO sets for atoms in a strong B field [W. Zhu et al., Phys. Rev. A 90, 022504 (2014)] yields very large basis sets. Their size is problematical for use in any calculation with unfavorable computational cost scaling. Here we provide an alternative constructive procedure. It is based upon analysis of the underlying physics of atoms in B fields that allow identification of several principles for the construction of AGTO basis sets. Aided by numerical optimization and parameter fitting, followed by fine tuning of fitting parameters, we devise formulae for generating accurate AGTO basis sets in an arbitrary B field. For the hydrogen iso-electronic sequence, a set depends on B field strength, nuclear charge, and orbital quantum numbers. For multi-electron systems, the basis set formulae also include adjustment to account for orbital occupations. Tests of the new basis sets for atoms H through C (1 ≤ Z ≤ 6) and ions Li+, Be+, and B+, in a widemore »

- Authors:

- Hangzhou Normal Univ. (China)
- Univ. of Florida, Gainesville, FL (United States)

- Publication Date:

- Research Org.:
- Univ. of Florida, Gainesville, FL (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1512938

- Alternate Identifier(s):
- OSTI ID: 1414872

- Grant/Contract Number:
- SC0002139; SC- 0002139

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of Chemical Physics

- Additional Journal Information:
- Journal Volume: 147; Journal Issue: 24; Journal ID: ISSN 0021-9606

- Publisher:
- American Institute of Physics (AIP)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

### Citation Formats

```
Zhu, Wuming, and Trickey, S. B. Accurate and balanced anisotropic Gaussian type orbital basis sets for atoms in strong magnetic fields. United States: N. p., 2017.
Web. doi:10.1063/1.5004713.
```

```
Zhu, Wuming, & Trickey, S. B. Accurate and balanced anisotropic Gaussian type orbital basis sets for atoms in strong magnetic fields. United States. doi:10.1063/1.5004713.
```

```
Zhu, Wuming, and Trickey, S. B. Tue .
"Accurate and balanced anisotropic Gaussian type orbital basis sets for atoms in strong magnetic fields". United States. doi:10.1063/1.5004713. https://www.osti.gov/servlets/purl/1512938.
```

```
@article{osti_1512938,
```

title = {Accurate and balanced anisotropic Gaussian type orbital basis sets for atoms in strong magnetic fields},

author = {Zhu, Wuming and Trickey, S. B.},

abstractNote = {In high magnetic field calculations, anisotropic Gaussian type orbital (AGTO) basis functions are capable of reconciling the competing demands of the spherically symmetric Coulombic interaction and cylindrical magnetic (B field) confinement. However, the best available a priori procedure for composing highly accurate AGTO sets for atoms in a strong B field [W. Zhu et al., Phys. Rev. A 90, 022504 (2014)] yields very large basis sets. Their size is problematical for use in any calculation with unfavorable computational cost scaling. Here we provide an alternative constructive procedure. It is based upon analysis of the underlying physics of atoms in B fields that allow identification of several principles for the construction of AGTO basis sets. Aided by numerical optimization and parameter fitting, followed by fine tuning of fitting parameters, we devise formulae for generating accurate AGTO basis sets in an arbitrary B field. For the hydrogen iso-electronic sequence, a set depends on B field strength, nuclear charge, and orbital quantum numbers. For multi-electron systems, the basis set formulae also include adjustment to account for orbital occupations. Tests of the new basis sets for atoms H through C (1 ≤ Z ≤ 6) and ions Li+, Be+, and B+, in a wide B field range (0 ≤ B ≤ 2000 a.u.), show an accuracy better than a few μhartree for single-electron systems and a few hundredths to a few mHs for multi-electron atoms. The relative errors are similar for different atoms and ions in a large B field range, from a few to a couple of tens of millionths, thereby confirming rather uniform accuracy across the nuclear charge Z and B field strength values. Residual basis set errors are two to three orders of magnitude smaller than the electronic correlation energies in multi-electron atoms, a signal of the usefulness of the new AGTO basis sets in correlated wavefunction or density functional calculations for atomic and molecular systems in an external strong B field},

doi = {10.1063/1.5004713},

journal = {Journal of Chemical Physics},

number = 24,

volume = 147,

place = {United States},

year = {2017},

month = {12}

}

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Works referenced in this record:

##
Self—Consistent Molecular Orbital Methods. XII. Further Extensions of Gaussian—Type Basis Sets for Use in Molecular Orbital Studies of Organic Molecules

journal, March 1972

- Hehre, W. J.; Ditchfield, R.; Pople, J. A.
- The Journal of Chemical Physics, Vol. 56, Issue 5, p. 2257-2261