Novel approaches in quantum chemistry: Self-consistent density-functional embedding and polaritonic coupled-cluster theory

[EN]: Subtleties in molecular electronic structure that arise from electronic correlations dictate most of chemistry. Important processes such as molecular bond breaking or charge migration are direct consequences of these correlations becoming dominant. Even the most successful theoretical approaches, such as density functional theory, however, still often struggle to describe these effects due to the nature of employed approximations and therefore require additional developments. Moreover, recent experiments in the field of quantum electrodynamical chemistry show that important chemical mechanisms such as those described above can be drastically modified by using photonic environments, which opens a whole new field of possible applications. Theoretical tools that address these situations from first principles are only now being developed. To address the first of the outlined challenges, we present a novel self-consistent density-functional embedding technique, which directly targets at approximating the density-potential mapping of exact density functional theory and therefore leaves the realm of standard energyfunctional approximations. Inspired by the density-matrix embedding theory, we project the full system onto a set of small interacting fragments that can be solved accurately. Based on the rigorous relation of density and potential in density functional theory, we then invert the fragment densities to local potentials. Combining these results in a continuous manner provides an update for the Kohn-Sham potential of the full system, which is then used to update the projection. We benchmark our approach for notoriously difficult examples of molecular bond stretching in one and two dimensions and show that in these cases the scheme provides accurate approximations for densities and the Kohn-Sham potentials. We demonstrate that signatures of strong correlations present in the exact exchange-correlation potential, even those that so far have been missing in all approximate approaches, are reproduced by our method with remarkable accuracy. Therefore, the methods provides a promising new path for functional development in density functional theory and its extensions, such as quantum electrodynamical density functional theory. To provide a theoretical tool for quantum electrodynamical (or polaritonic) chemistry, we develop a coupled-cluster theory for systems of electrons strongly coupled to photons. We show benchmark results for ground and excited state properties of a model molecule in high-Q optical cavities. By comparing to full configuration interaction results, we demonstrate that our method quantitatively captures all key features present in the exact reference, including Rabi splittings and multi-photon processes in all considered coupling regimes. Therefore, not only does our method go beyond standard quantum optical approaches, since it includes an accurate treatment of electronic structure, it also goes beyond existing ab intio methods in terms of accuracy. A clear path on how to incorporate the developed extension of coupled-cluster theory into existing quantum chemistry programs is provided, paving the way for high-accuracy modeling and interpretation of experiments in the field of polaritonic chemistry with a perspective of application to all types of fermion-boson coupled systems.