Bloch's and des Cloizeaux's effective Hamiltonians for Molecules 1 and 2 built for covalent and ionic configurations from EOM-SF-CCSD/cc-pVTZ are shown in Figure and Eqs. S1, S2, S3 in the SI. We note that des Cloizeaux's transformation either does not change the matrix elements of effective Hamiltonian on the diagonal (Molecule 1) or alter them in a minimal way (Molecule 2). Des Cloizeaux's transformation averages the off-diagonal matrix elements yielding a Hermitian effective Hamiltonian.