Diagrammatic many-body perturbation theory of atomic and molecular electronic structure

Abstract

The diagrammatic many-body perturbation theory of atomic and molecular electronic structure is reviewed. Attention is centred on the formulation of the method within the algebraic approximation (that is, using finite basis sets) which allows applications to be made to atoms and molecules within a unified framework. The second section is devoted to the basic formalism of the diagrammatic many-body perturbation theory of atoms and molecules. The diagrammatic expansion of both the energy and the wavefunction are considered, the latter being more compact than the former. Section 3 is concerned with aspects of the truncation of the perturbation expansion and the use of many-body perturbation theory in the analysis and comparison of many contemporary approaches to the correlation problem is briefly outlined. The fourth section is devoted to computational aspects of many-body perturbation theory calculations. Some applications are very briefly discussed in section 5.