The contribution of the two remaining terms to SOC in case of the open-shell references require the formation of h SOM F L ± not from the full x and y matrices, as in Eqs. ( ) and ( ), but from their parts that will be contracted with transition density matrices of a † pβ a qα and a † pα a qβ types, respectively (see appendix B in Ref. ). This leads to the partitioning of the terms as in Eqs. ( ) and . Different α and β parts of the HF density deteriorate the symmetry of the resulting matrix elements as well. The impact of this violation and a possible fix are discussed in Section III D.