Perturbation theoretical approaches to strong light–matter coupling in ground and excited electronic states for the description of molecular polaritons

Quantum chemical methods for the description of molecular polaritonic states in the strong coupling regime based on the Pauli–Fierz Hamiltonian are introduced. Based on a quantum electrodynamic Hartree–Fock (QED-HF) reference, a QED Møller–Plesset perturbation theory of second order for the electronic ground state and a second order quantum electrodynamic algebraic diagrammatic construction scheme for the polarization propagator [QED-ADC(2)] for excited electronic states have been derived, implemented, and tested for polaritons in hydrogen fluoride. Analogous approaches based on a standard non-polaritonic HF reference are also presented and thoroughly compared, both algebraically and numerically, to those based on the QED-HF reference. Furthermore, a promising route to approximate QED-ADC methods based on a unitary transformation of the algebraic expression into a restricted state space is outlined showing excellent agreement in second order with QED-ADC(2). All presented novel methods are compared to and tested against other existing ab initio approaches, mostly QED coupled cluster theory, including single and double excitations, and show qualitative agreement at a reduced computational effort.