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Elsevier, Handbook of Numerical Analysis, p. 453-483

DOI: 10.1016/s1570-8659(03)10006-3

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Computational approaches of relativistic models in quantum chemistry

Journal article published in 2003 by Jean-Paul Desclaux, Jean Dolbeault ORCID, Maria J. Esteban, Paul Indelicato, Eric Séré
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Abstract

This chapter is a review of some methods used for the computation of relativistic atomic and molecular models based on the Dirac equation. In the linear case, we briefly describe finite basis set approaches, including ones that are generated numerically, perturbation theory and effective Hamiltonians procedures, direct variational methods based on nonlinear transformations, min-max formulations and constrained minimizations. In the atomic case, we describe the MCDF method and some ways to solve numerically the homogeneous and inhomogeneous Dirac-Fock equations. Finally, we describe also some numerical methods relevant to the case of molecules.