A Comprehensive Theory for Relativistic Polaritonic Chemistry: A Four-Component Ab Initio Treatment of Molecular Systems Coupled to Quantum Fields

We present an ab initio approach to study molecules containing heavy atoms strongly interacting with quantum fields in optical devices. The theory has been derived from relativistic quantum electrodynamics (QED), introducing the approximations needed to provide a formalism suitable for relativistic quantum chemistry. This framework represents the ideal starting point to extend the main quantum chemistry methods to relativistic polaritonic. In this article, we present the polaritonic Dirac-Hartree-Fock (Pol-DHF) approach based on this theory. The Pol-DHF approach allows for the simulation of field-induced effects on the ground- and excited-state properties of heavy transition metal molecular complexes. The method is able to include not only the effects of the photons but can in principle be extended also to include explicit interactions with positrons. Application of Pol-DHF to three metal hydrides shows that the magnitude of both polaritonic and relativistic effects can be comparable when relativistic effects become more important. Due to an accurate description of spin-orbit coupling, the method is able to reproduce polaritonic effects happening at the crossing between singlet and triplet potential energy surfaces.