• SC-QED-CCSD
• SC-QED-HF
• strong light-matter coupling
• polaritonic chemistry
• optical cavity
• QED methods

In recent years, there has been a surge of interest into the manipulation of molecular states and properties through strong-coupling with external electromagnetic fields. Inside optical cavities, the light strongly interacts with the molecular system, originating new hybrid light-matter states called polaritons. This mixed nature of the states is such that modification in the frequency and polarization of the field and the dimension of the cavity are able to change molecular energy surfaces and thus change the properties of the molecular system. Many groups have developed theoretical frameworks to model these new types of systems, which has given rise to QED Hartree Fock (QED-HF), QED density functional theory (QEDFT), QED coupled cluster (QED-CCSD) and QED full configuration interaction (QED-FCI). In 2022, a new QED Hartree Fock method was proposed for strong coupling regimes, called SC-QED-HF, to obtain a molecular orbital theory consistent with origin invariance, and many other methods are being developed to complete the repertoire of tools available to the scientific community. In this thesis, a new coupled cluster method called SC-QED-CCSD has been developed, starting from SC-QED-HF as reference wavefunction, suitable for strong coupling regimes. The performance of this new method and existing methods is compared on different systems, varying the frequency and polarization of the electromagnetic field and the coupling strength. A multilevel QED-CC in SC-QED-HF method is also proposed to extend the usability of QED-CC methods to the description of larger systems, allowing for the inclusion of environmental effects at SC-QED-HF level to QED-CC calculations.