where {p, q} indicate all possible molecular orbitals, and {i} and {ν} indicate strictly occupied, and strictly virtual HF electronic orbitals, and F el pq is the bare molecular Fock matrix in the HF orbital basis. {n, m} are the photonic Fock/number basis states. The Fock matrix here, by construction, is similar to Eq. 123 and does not contain the electron-photon interaction term, which necessarily drops out in this picture since that term mixes states with varied numbers of photon basis states while the DSE term connects only electronic states. Noting that the solution to the bare molecular Fock matrix is achieved if F el iν = 0, the QED-HF energy can be written as 100