Practical Ab Initio Methods for Molecular Electronic Structure Studies. IV. Relativistic Many-Body Perturbation Theory

Abstract

The generalization of the familiar non-relativistic diagrammatic many-body perturbation theory of atomic and molecular electronic structure to the relativistic case is surveyed. It is noted that the treatment of relativistic and quantum electrodynamic effects in atoms and molecules requires the reintroduction of physics that was discarded in early studies of the many-body problem by Goldstone and others in which interactions were taken to be instantaneous and special relativity was ignored. Recent progress is described emphasizing three aspects: i) the representation of the positive and negative energy branches of the Dirac spectrum afforded by the algebraic approximation, and ii) the non-additivity of relativistic and correlation effects in calculations using the Dirac-Coulomb hamiltonian and the Dirac-Breit hamiltonian. Future directions of research are briefly described emphasizing particularly, i) improvements in the accuracy of matrix Dirac-Hartree-Fock-Breit calculations and in sum-over-states perturbative electron correlation calculations for molecules, and ii) the use of Bardeen-Cooper-Schrieffer reference models in calculations based on the diagrammatic many-body perturbation theory to afford a description of bond breaking processes.