A glossary of abbreviations and terms used to discuss the results is provided in Table HeH + is a 2-electron system as shown in Figure that has a permanent ground-state dipole moment and a dipole-allowed optical transition (S 0 → S 2 with transition energy of 26.1 eV), which will permit us to study the behavior of the dipole self-energy on the ground and polariton states using scQED and pQED approaches as we approach the complete basis limit. We optimize the geometry of this system at the FCI/cc-pVTZ level; at this level, the equilibrium bond length is approximately 0.776 Angstroms and the dipole moment has a magnitude of 1.73 Debye along the internuclear axis. We study the ground state and polariton states at the PF-FCI and pPF levels using cc-pVXZ basis sets, where X is D, T, and Q, to progress towards the complete orbital basis limit.