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Title: 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 » 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« less

Authors:
ORCiD logo [1]; ORCiD logo [2]
  1. Hangzhou Normal Univ. (China)
  2. 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:
Journal Article: 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},
issn = {0021-9606},
number = 24,
volume = 147,
place = {United States},
year = {2017},
month = {12}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 2 works
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Figures / Tables:

FIG. 1 FIG. 1: Fitting the optimized exponents of AGTO basis functions for hydrogen atom and hydrogen-like ions in reduced magnetic field strength γ = 1. Empty symbols are optimized exponents from searching {αj} space. Solid curves are fits to those data points, generated by Eqs. (10)–(13). Filled squares are the AGTOmore » basis sets for the hydrogen atom in B = 1 a.u. generated according to Eqs. (10)–(15). Black, red, and blue stand for the 1s, 2p-1, and 3d-2 orbitals, respectively.« less

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