For each system, six variants of ECI were tested, obtained by combining ECIS or ECISD expansions with the three choices for APCs discussed in Section 3.3: zero APCs, APCs from ESP fits, APCs from EHF. These three choices will be referred to as FDA, ESP embedding, and EHF embedding, respectively. In practice, they are achieved by conducting EHF calculations with zero cycles, one cycle, or until convergence, respectively. We note that with the FDA calculations in MgG , we found that the Mg 2+ charge perturbs the site states on guanines very strongly, such that setting the corresponding APC to zero (as it should be done in FDA) leads to completely wrong results. Hence, in the computation of the site states for the FDA calculations, we included a +2 APC on the Mg atom (all other APCs were zero).