where Âel and Bph are operators in the electronic and photonic Hilbert sub-spaces, respectively, {|ψ α (R)⟩, |ψ β (R)⟩} are electronic adiabatic states, {|n⟩, |m⟩} are photonic Fock/number states, and {C j α,n } is are the expansion coefficients in Eq. 5 in the adiabtic-Fock basis. For example, A αβ may be the molecular dipole matrix, transition density, or natural transition orbitals, while B nm may be the photon number matrix, photonic transition density, or photonic dipole matrix. See Theoretical Details for more information on the computation of the individual electronic and photonic properties.