a 10% theoretical uncertainty to the $D$ constant due to its stable convergence trend with the increasing size of the virtual orbital set. However, it is difficult to evaluate the theoretical uncertainty for the $C/\Omega$ constant since it strongly depends on the computational model, as discussed below. We are, however, confident in the sign and order of magnitude of this octupole constant.

The magnetic octupole HFS constant has proven to be sensitive to the electron correlations, as they flip the sign of the DHF result. [We systematically investigated the dependence of the calculated $C/\Omega$ values on the size of computational model space, see Table \[CV\_effects\]. For example, in this table, the results in the “no opened subshells" row demonstrate the effect of correlation between electrons in the valence subshells. Because the octupole coupling operator has high multiplicity (tensor of rank 3) and we are interested in the properties of the $l=3$ $f$-state hole, we include up to $l=6$ virtual orbitals in each layer. The results including the valence-valence correlation show a good convergence pattern (first row of Table \[CV\_effects\]). However, the convergence pattern worsens when we start including core-valence correlations by opening core subshells (columns of Table \[CV\_effects\]). While the 