Relativistic Four-Component Multireference Coupled Cluster Methods: Towards A Covariant Approach

Abstract

Four-component relativistic all-order methods are the most accurate available for heavy atoms and molecules, and are used extensively in benchmark calculations of these systems. Their current status and perspectives for further development are reviewed, and representative applications are shown. Benchmarking requires continued improvement of the relativistic Hamiltonian towards the goal of a fully covariant description, as well as the development of sophisticated all-order correlation methods suitable for general open shell systems. One of the best relativistic many-body approaches available for the purpose is the multiroot, multireference Fock space coupled cluster (FSCC) method. It is size extensive, and usually gives the most accurate results within the 4-component no-virtual-pair approximation (NVPA). The relativistic FSCC method and its recent applications are described. Relativistic effects beyond NVPA may be studied using quantum electrodynamics (QED). We discuss the challenges of introducing covariant many-body QED methods suitable for use in quantum chemical calculations of general open shell systems. The mathematical and physical foundations for merging the infinite order multireference many-body approach with an all-order QED treatment are presented. A promising technique is the double-Fock-space CC scheme, based on Lindgren’s covariant evolution operator method, implemented within a generalized Fock space scheme with variable numbers of electrons and uncontracted virtual photons. A brief description of this scheme, a covariant multireference multiroot many-body QED approach, concludes this chapter.