where |Φ pl 0 ⟩ is the polaritonic ground state calculated at the uncorrelated HF level (see previous section) and |Φ HF ⟩ is the uncorrelated HF electronic ground state. Here, |0⟩ Z is the photon vacuum state in the rotated coherent state representation with |0⟩ Z = ÛZ |0⟩ (see Eq. 120) at the variationally optimized coherent state parameter Z after the HF self-consistent procedure. T is the cluster operator (not to be confused with the kinetic energy operator TR or Tr in Eq. 20). This cluster operator involves a sum of electronic, photonic, and mixed electron-photon excitations as follows