  The cluster multipole (CMP) expansion for magnetic structures provides a
scheme to systematically generate candidate magnetic structures specifically
including noncollinear magnetic configurations adapted to the crystal symmetry
of a given material. A comparison with the experimental data collected on
MAGNDATA shows that the most stable magnetic configurations in nature are
linear combinations of only few CMPs. Furthermore, a high-throughput
calculation for all candidate magnetic structures is performed in the framework
of spin-density functional theory (SDFT). We benchmark the predictive power of
CMP+SDFT with $2935$ calculations, which show that (i) the CMP expansion
administers an exhaustive list of candidate magnetic structures, (ii) CMP+SDFT
can narrow down the possible magnetic configurations to a handful of computed
configurations, and (iii) SDFT reproduces the experimental magnetic
configurations with an accuracy of $\pm0.5\,\mu_\text{B}$. For a subset the
impact of on-site Coulomb repulsion $U$ is investigated by means of $1545$
CMP+SDFT+U calculations revealing no further improvement on the predictive
power.
