The performance of ECIS can be further improved by employing EHF embedding. In this case, ECIS+EHF shows an RMSD of around 20 meV for both singlets and triplets. Thus, the EHF embedding prepared such site states that only GS and LE products are needed to construct the full-system states in almost perfect match with the direct method. The addition of DLE products by switching to ECISD+EHF yields negligible improvement, leaving the RMSD values untouched.