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Electrodynamical coupled cluster (CC) methodologies have been formulatedemploying standard QED Hamiltonian that is written in Coulomb gauge while usingthe DF and the MCDF pictures of the matter field for closed-shell andopen-shell cases respectively. The general methodology employs a radiativecluster, pure matter clusters and their pair modifications, and a number statedistribution of photons in thermal equilibrium. The closed-shell treatmentrelies on the customary CC approach. For open shells, QED and electroncorrelation through CC are treated on the same footing. An averaging over theradiation state is done to generate Lamb, Breit and hyperfine interactions fromthe radiative cluster. Because of the thermal distribution, it leaves aresidual transverse interaction that may modify the static correlation in openshells. Dynamical correlation effects are determined next by using theexponential matter cluster in traditional ways of single- and multi-referenceCC. When the matter cluster is extended to include de-excitations tonegative-energy levels, vacuum polarization effects are generated from the pairpart of Coulomb interaction. The dynamical correlation energy includesrelativistic corrections as well as QED contributions, namely, Lamb, Breit,hyperfine and pair energy. This work has three novelties: (i) QED interactions(Lamb, Breit and hyperfine) are obtained from a single procedure based on theradiative cluster; (ii) pair energy is determined from an extended mattercluster formalism; and (iii) additional correlation energy can be had fromradiative effects and pair terms, while the option for higher order pair energyin high-Z atoms is kept open. The open-shell formalism has one more novelty infinding an additional static correlation in certain cases when the radiation isnot isotropic.

Coupled cluster theory based on quantum electrodynamics: Physical aspects of closed shell and multi-reference open shell methods