The orbital basis and reference determinant utilized in the NH-CQED-CIS theory results from solving the CQED-RHF equations. We start with a Hermitian version of Eq. 1 that utilizes a pure real value of ω, and following Ref. 26 and 29, we introduce a product wavefunction between an electronic Slater determinant (which in practice may be initialized using a canonical RHF wavefunction) and a zero-photon number state,