where the coefficients c denote the contribution of a given term to the wavefunction and we have denoted the electronic excitations in the subscript and the photonic excitations in the superscript of these coefficients. For the case of multiple modes, the photonic basis states will be augmented to consider all possible combinations of the occupations of those modes within a maximum photon number. These coefficients, and the corresponding energy eigenvalues for a given NH-CQED-CIS state I, may be obtained by diagonalizing the Hamiltonian matrix built in the basis shown in Eq. 6. We spin adapt this basis such that