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 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.

Trendbericht Theoretische Chemie 2022: Quantenchemie für Atome und Moleküle in starken Magnetfeldern

“…Ein gängiger Workaround ist die Dekontraktion der Standardbasissätze, was allerdings den Rechenaufwand erhöht. Weitere Ansätze sind numerische Techniken 20) und anisotrope Basissätze, 21) die aber bislang noch nicht standardmäßig genutzt werden.…”

Insight on Gaussian Basis Set Truncation Errors in Weak to Intermediate Magnetic Fields with an Approximate Hamiltonian

“…An alternative is to use anisotropic GTOs; , however, they introduce new types of challenges. As the magnetic field interaction confines movement in the direction orthogonal to the field (see section ), the anisotropic GTO basis set splits the exponents in the directions parallel and orthogonal to the field, which complicates the optimization of the exponents. − Moreover, because the basis set is formed by the product of these two sets of exponents, the number of basis functions explodes if the basis is required to be accurate for a range of magnetic field strengths. The use of anisotropic GTOs also requires dedicated approaches, , and such basis functions are supported in few programs.…”

Ground States of Few Electron Atoms in a Strong Magnetic Field Using Diffusion Monte Carlo Method

“…Accurate theoretical and experimental methods used to investigate the behavior of atoms in a strong magnetic field. W. Zhu and S. B. Trickey [18] used anisotropic Gaussian type orbital basis functions to calculate H through C (1 ≤ Z ≤ 6) and ions Li + , Be + and B + in a wide range of magnetic field (B) (0 ≤B ≤2000 (a.u.)) which showed an accuracy better than single-electron basis sets.…”