Following a similar procedure, the single-determinant nature of density functional theory can be used to simplify the Pauli-Fierz Hamiltonian to that of the GSC representation without the direct coupling term. However, due to the ad hoc nature of density functional theory, there are many ways to approximate the exchange-correlation kernel to arrive at various levels of corrections to the electron-electron, electron-photon, and photon-photon correlations. In fact, the simplest choice (albeit the least motivated) is to ignore the electron-photon and photon-photon terms in the exchange-correlation kernel. In this case, the only responses of the single-particle orbitals {p, q } are those induced by the dipole self-energy contributions (the last term in Eq. 31). This is the simplest approach since no novel exchangecorrelation functionals need to be used/created, and one can rely on the already-developed, high-level functionals for the complicated electron-electron correlation, such as CAM-B3LYP 83 , ωB97XD 84;85 , and SCAN. Recently, novel exchange-correlation functionals for electronic and photonic DOFs have been constructed based on a variety of frameworks, such as the optimized effective potential (OEP) approach, and the fluctuation-dissipation theorem approach. In any case, the ground state energy can be loosely written as