Insight on Gaussian basis set truncation errors in weak to intermediate magnetic fields with an approximate Hamiltonian

TL;DR

This study evaluates the accuracy of Gaussian basis sets in atomic calculations under weak to intermediate magnetic fields, revealing significant errors with common sets and highlighting the need for improved basis functions.

Contribution

It provides a comprehensive analysis of basis set truncation errors in magnetic fields, guiding the development of more accurate Gaussian basis sets for such conditions.

Findings

Significant errors with aug-cc-pVTZ basis set in magnetic fields.

Benchmark-quality AHGBSP3-9 basis set yields smaller errors.

Room for improvement in Gaussian basis sets for magnetic field calculations.

Abstract

Strong magnetic fields such as those found on white dwarfs have significant effects on the electronic structure of atoms and molecules. However, the vast majority of molecular studies in the literature in such fields are carried out with Gaussian basis sets designed for zero field, leading to large basis set truncation errors [Lehtola et al, Mol. Phys. 2020, 118, e1597989]. In this work, we aim to identify the failures of the Gaussian basis sets in atomic calculations to guide the design of new basis sets for strong magnetic fields. We achieve this by performing fully numerical electronic structure calculations at the complete basis set (CBS) limit for the ground state and low lying excited states of the atoms $1 \le Z \le 18$ in weak to intermediate magnetic fields. We also carry out finite-field calculations for a variety of Gaussian basis sets, introducing a real-orbital approximation for the magnetic-field Hamiltonian. Our primary focus is on the aug-cc-pVTZ basis set, which has been used in many works in the literature. A study of the differences in total energies of the fully numerical CBS limit calculations and the approximate Gaussian basis calculations is carried out to provide insight into basis set truncation errors. Examining a variety of states over the range of magnetic field strengths from $B = 0$ to $B = 0.6 B_0$, we observe significant differences for the aug-cc-pVTZ basis set, while much smaller errors are afforded by the benchmark-quality AHGBSP3-9 basis set [Lehtola, J. Chem. Phys. 2020, 152, 134108]. This suggests that there is considerable room to improve Gaussian basis sets for calculations at finite magnetic fields.