Relativistic many-body perturbation theory methods

Since the Dirac equation is written for one electron, the real problem of ah initio methods for a many-electron system is an accurate treatment of the instantaneous electron-electron interaction, called electron correlation. The latter is of the order of magnitude of relativistic effects and may contribute to a very large extent to the binding energy and other properties. The DCB Hamiltonian (Equation 3) accounts for the correlation effects in the first order via the Vy term. Some higher order of magnitude correlation effects are taken into account by the configuration interaction (Cl), the many-body perturbation theory (MBPT) and by the presently most accurate coupled cluster (CC) technique. 

The perturbation theory of relativistic QED, see for example [47,65], is the source of widely used methods of nonrelativistic many-body perturbation theory (MBPT) [66]. We demonstrate how it can also be used to formulate the theory of relativistic self-consistent fields as the first step in a more elaborate theory of MBPT incorporating radiative corrections. 

The all-orders relativistic many-body perturbation theory approach [82], [83], the combination of this approach with the multiconfiguration Dirac - Fock method [84] or the relativistic coupled-cluster approach [85] allow for the evaluation of the energy levels for valence electrons with accuracy of the order of... 

The relativistic many-body perturbation theory of atomic and molecular electronic structure can be formulated within the algebraic approximation in a manner analogous to the non-relativistic formulation. A detailed discussion of the method, which is still under development, lies outside the scope of this chapter but the technique s potential will be illustrated by displaying some results for the relativistic version of the model problem considered in Section V.B, a hydrogenic atom with nuclear charge Z perturbed by the potential — Z lrP The exact energy of the perturbed problem in its ground state is... 

Quiney, H.M., 1988, Relativistic many-body perturbation theory, in Relativistic Effects in Atoms and Molecules, Methods in Computational Chemistry, Vol. 2, ed. S. Wilson (Plenum, New York). 

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