Four-component electronic structure methods

Four-component relativistic methods are the most accurate available for heavy atoms and molecules. Their history, current status and perspectives for further development are reviewed. Their main application is for benchmark calculations of heavy element compounds. Benchmarking requires continued improvement of the relativistic Hamiltonian towards the goal of fully covariant description, as well as 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. It is size extensive, and usually gives the most precise results within the four-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 chemistry. Mathematical and physical foundations for merging many-body relativistic approaches, in particular FSCC, with QED theory are presented. A promising technique is Lindgren’s covariant evolution operator (CEO) method, in combination with the generalized Fock space with variable numbers of electrons and uncontracted virtual photons. The relationship of the CEO approach to the Bethe-Salpeter covariant equation and other QED schemes is discussed. Size-consistent computational schemes, combining variational treatment of first order QED effects (Lamb shifts) at the SCF step with infinite order treatment of QED and correlation, are under development. For cases of quasidegenerate levels, common in heavy systems, multireference approaches must be used. Double (electronic and photonic) Fock-space CC, a covariant multireference multi-root many-body-QED approach, is presented.