We apply the CQED-RHF and NH-CQED-CIS approaches to a few simple polaritonic chemical systems. First we examine the ground-state of formaldehyde strongly coupled to a single photon mode, which has been explored by several groups that have been developing density functional theorybased ab initio-QED methods . We optimize the geometry of lone formaldehyde at the RHF/cc-pVDZ level and perform all calculations at that geometry (see Ref. 50). At this level, the RHF ground-state has a dipole moment oriented purely along the z-axis with µ z = -1.009 atomic units. The CQED-RHF equations are solved for a fixed magnitude of the coupling vector |λ | = 0.1 atomic units with the following three polarizations: λ y = (0, |λ |, 0), λ z = (0, 0, |λ |), and