when the contributions of the interaction ( Ĥe-ph ) or dipole self-energy ( ĤDSE ) become large, the many adiabatic and Fock states will be needed in the description of the polaritonic wavefunctions. Other choices exist for the description of the photonic DOFs, such as the grid basis, which diagonalizes qc ∝ â † + â and has been extensively used. The choice of basis can significantly enhance computational efficiency or reduce the conceptual complexity of a problem, depending on the light-matter coupling strength and cavity frequency parameters. One such basis, aimed for use in the strong light-matter coupling regime, is the recently proposed polarized Fock State (PFS) basis introduced in Ref. 61. Here, the Pauli-Fierz Hamiltonian is rewritten using an entangled electronic-photonic basis, where the electronic states are represented by the eigenstates of the dipole operator ν P μ P = µ νν (R) |φ ν ⟩ ⟨φ ν | and is referred to as the Mulliken-Hush (MH) representation (Eq. 11). The polaritonic Hamiltonian (see Eq. 13) in the MH basis can be written as,