The here proposed approach allows the following advantages: (i) rigorous evaluation of the most important contributions for 2e-SOC integrals, (ii) full control on the needed accuracy by the choice of the unique Cholesky δ threshold, and (iii) the one-off calculation and the storage of the smallest amount of data needed to numerically represent all the 2e-SOC integrals with absolute accuracy smaller than 2δ , which are then readily available for transformations as in eqs. ( ) and ( ) (this can be really favorable within the self-consistent approaches which include the SOC contribution in the iterative procedure).