where D λ yz µν are elements of the converged CQED-RHF density matrix in the λ yz case and D µν are elements of the CQED-RHF density matrix in the absence of coupling to a photon (i.e., the canonical RHF density matrix). We tabulate the changes in these various CQED-RHF contributions for the λ z , λ y , and λ yz cases in Table . The 1-electron quadrupolar and 2-electron dipolar terms that arise from Ĥdse typically comprise the largest changes to the CQED-RHF energy from the three polarizations considered in Table . However, the changes in the canonical RHF 1and 2-electron terms (denoted ∆ 1E and ∆ 2E ) suggest changes to the ground-state electron density via the CQED-RHF orbitals arise from coupling to the cavity modes. Although these changes largely cancel each other in the total energy (i.e. ∆ 1E ≈ -∆ 2E in all three cases), it is nevertheless interesting to view the impact of cavity coupling on the CQED-RHF orbitals. The RHF orbitals for the HOMO (2B 2 ) and LUMO+1 (6A 1 ) of formaldehyde uncoupled to a photon are compared to their corresponding CQED-RHF orbitals for the λ yz case ( 7A and 8A ) where the orbitals are noticeably distorted (see Figure ). The reshaping of the CQED-RHF orbitals in the λ yz case results in a loss of symmetry from C 2v to C s and impacts both ground-state energy and properties. As seen in Table , there is no 1-electron dipole contribution to the energy shift in the λ y case since the ground state dipole moment is oriented purely along the z-axis. However, in the λ yz case, the distortion of the ground-state orbitals results in a reorientation of the dipole moment to point along the yz axis with value µ = (0, -0.025, -1.16) atomic units. We see that this reorientation of the ground-state dipole moment is accompanied by changes in the ground-state energy specifically attributable to the 1-electron dipolar terms CQED-RHF Fock operator (see Table ). In principle, this change in ground-state dipole moment could be experimentally confirmed through rotational spectroscopy. In particular, because the oscillator strength of a given transition involves integrals over the dipole moment