Carrying out a single cycle of the EHF procedure, i.e., using ESP charges, yields a considerable improvement in excitation energies and oscillator strengths over the FDA. For ECIS+ESP, the RMSD drops to 28 meV for triplets and 33 meV for singlets. This suggests that the quality of the site states-controlled by the choice of the APCs-has a larger impact on the performance of ECI than the extension of the excitonic basis by including excitonic doubles. Indeed, ECISD+ESP charges does not significantly improve the results over ECIS+ESP (RMSDs of 27 meV for triplets and 30 meV for singlets). In other words, ESP embedding produces an ECIS basis for which the description of the dominantly LE states cannot be improved by extending the basis with DLE products in ECISD (in contrast to the FDA calculations, where the addition of doubles improved the results).