Relativistic Coupled Cluster theory for excited states at a general excitation rank. Applications to diatomic molecules.

This thesis focuses on methodological developments of the theoretical evaluation of the quantum and relativistic energy of electronically excited states of an atom or a molecule. The wave-function method Coupled Cluster (CC) is currently one of the most accurate methods to calculate these states for many-body systems. The implementation presented is based on the many-body relativistic 4-component Dirac-Coulomb Hamiltonian and a Coupled Cluster wave function at arbitrary excitation rank. The excited states are evaluated using linear response theory by diagonalizing the Coupled Cluster Jacobian matrix. The work focuses on the evaluation of these second-quantized elements using a new commutator-based algorithm, and on its adaptation to a Dirac 4-component relativistic formalism. Finally, I present some applications of the code to challenging diatomic molecules.