Relativistic Fock-Space Coupled Cluster Method: Theory and Recent Applications

Four-component relativistic all-order multireference electron correlation approaches are the most accurate methods available for benchmark calculations of properties of heavy atoms and their compounds with complex (frequently quasi-degenerate) electronic shell structures. Benchmarking requires continued improvement of the relativistic Hamiltonian aiming at a fully covariant description, as well as the development of high-level correlation methods suitable for general open shell systems. One of the best relativistic many-body approaches available for the purpose is the multi-root, multi-reference Fock space coupled cluster (FSCC) method. FSCC is size extensive, includes both dynamic and non-dynamic electron correlation effects to infinite order, and usually gives the most precise results within the 4-component no-virtual-pair approximation (NVPA). The relativistic FSCC method and its recent modifications and applications are described. We also briefly discuss perspectives for future developments and applications of relativistic FSCC including the challenges of introducing covariant many-body QED methods suitable for use in Fock space methodology in quantum chemistry and atomic physics.