Fully numerical electronic structure calculations on diatomic molecules in weak to strong magnetic fields

ABSTRACT

We present fully numerical electronic structure calculations on diatomic molecules exposed to an external magnetic field at the unrestricted Hartree–Fock limit, using a modified version of a recently developed finite-element programme, HelFEM. We have performed benchmark calculations on a few low-lying states of H${}_2$, HeH${}^{+}$, LiH, BeH${}^{+}$, BH and CH${}^{+}$ as a function of the strength of an external magnetic field parallel to the molecular axis. The employed magnetic fields are in the range of $B=[0,10]B_0$ atomic units, where $B_0\approx 2.35\times {10}^5$ T. We have compared the results of the fully numerical calculations to ones obtained with the LONDON code using a large uncontracted gauge-including Cartesian Gaussian (GICG) basis set with exponents adopted from the Dunning aug-cc-pVTZ basis set. By comparison to the fully numerical results, we find that the basis set truncation error (BSTE) in the GICG basis is of the order of 1 kcal/mol at zero field, that the BSTE grows rapidly in increasing magnetic field strength, and that the largest BSTE at $B=10B_0$ exceeds 1000 kcal/mol. Studies in larger Gaussian-basis sets suggest that reliable results can be obtained in GICG basis sets at fields stronger than $B=B_0$, provided that enough higher-angular-momentum functions are included in the basis.

GRAPHICAL ABSTRACT

KEYWORDS:

• Magnetic field
• finite element
• Hartree–Fock
• intermediate regime
• basis set truncation error

Acknowledgments

We thank Trygve Helgaker and Erik Tellgren for a copy of the London code, and Stella Stopkowicz and Florian Hampe for their tool for determining orbital symmetry.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by Luonnontieteiden ja Tekniikan Tutkimuksen Toimikunta, The Academy of Finland through projects 311149 and 314821 as well as by the Magnus Ehrnrooth Foundation. The authors acknowledge CSC – the Finnish IT Center for Science as well as the Finnish Grid and Cloud Infrastructure (persistent identifier urn:nbn:fi:research-infras-2016072533) for computer time.