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Strong magnetic fields such as those found on white dwarfs have significanteffects on the electronic structure of atoms and molecules. However, the vastmajority of molecular studies in the literature in such fields are carried outwith Gaussian basis sets designed for zero field, leading to large basis settruncation errors [Lehtola et al, Mol. Phys. 2020, 118, e1597989]. In thiswork, we aim to identify the failures of the Gaussian basis sets in atomiccalculations to guide the design of new basis sets for strong magnetic fields.We achieve this by performing fully numerical electronic structure calculationsat the complete basis set (CBS) limit for the ground state and low lyingexcited states of the atoms $1 \le Z \le 18$ in weak to intermediate magneticfields. We also carry out finite-field calculations for a variety of Gaussianbasis sets, introducing a real-orbital approximation for the magnetic-fieldHamiltonian. Our primary focus is on the aug-cc-pVTZ basis set, which has beenused in many works in the literature. A study of the differences in totalenergies of the fully numerical CBS limit calculations and the approximateGaussian basis calculations is carried out to provide insight into basis settruncation errors. Examining a variety of states over the range of magneticfield strengths from $B = 0$ to $B = 0.6 B_0$, we observe significantdifferences for the aug-cc-pVTZ basis set, while much smaller errors areafforded by the benchmark-quality AHGBSP3-9 basis set [Lehtola, J. Chem. Phys.2020, 152, 134108]. This suggests that there is considerable room to improveGaussian basis sets for calculations at finite magnetic fields.

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