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

## TL;DR

This paper introduces fully numerical electronic structure calculations for diatomic molecules in magnetic fields, benchmarking against Gaussian basis sets and analyzing errors across various field strengths.

## Contribution

It develops and applies a fully numerical method for diatomic molecules in magnetic fields and compares its accuracy to Gaussian basis set approaches.

## Key findings

- Basis set truncation error increases with magnetic field strength.
- Fully numerical results serve as benchmarks for Gaussian basis sets.
- Reliable Gaussian basis results require high-angular-momentum functions at strong 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 program, HelFEM. We have performed benchmark calculations on a few low-lying states of H2, 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 in the gauge-including Gaussian basis set is of the order of 1 kcal/mol at zero field, that the truncation error grows rapidly when the strength of the magnetic field increases, and that the largest basis set truncation error at $B=10~B_0$ 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 a sufficient coverage of higher-angular-momentum functions is included in the basis set.