A coupled cluster theory based on quantum electrodynamics: Method for closed shells

An electrodynamical coupled cluster (CC) methodology that is based on the standard QED Hamiltonian written using the Dirac-Fock picture of matter fields and Coulomb gauge is discussed here. It employs the combination of a radiative cluster, a pure matter cluster and its pair modification, and relies on the customary CC approach. Averaging over the radiation state is done first, and the cluster operator for radiative effects leads to Lamb, Breit and hyperfine interactions. Relativistic correlation effects are determined next while using the matter cluster in the traditional way of CC. When the matter cluster is extended to include deexcitations to negative-energy levels, vacuum polarization effects are generated from the pair part of Coulomb interaction. The resulting ground state correlation energy includes both relativistic and QED corrections, the latter including Lamb, Breit, hyperfine and pair energy contributions. The many-electron part of the theory is formulated here for closed shell species.