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Relativistic Self-Consistent Fields

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Handbook of Relativistic Quantum Chemistry

Abstract

The simplest relativistic computational methods for many-electron systems involve the solution of one-particle Dirac equations for an electron moving in some effective (“mean-field”) potential. This potential depends on the one-particle solutions which describe the electron charge distribution; therefore, such mean-field problems are solved iteratively until self-consistency. The two most important relativistic self-consistent field methods are the relativistic variants of the Hartree-Fock and Kohn-Sham methods, whose computational frameworks have large overlap. In this chapter, the development of these methods for atoms and molecules is sketched. While atomic calculations are usually performed solving differential variational equations, molecular calculations rely on basis set expansion methods. These seemed to be problematic initially, but with kinetically balanced basis sets, smooth convergence is obtained. Most relativistic Kohn-Sham calculations performed today combine relativistic kinematics (the use of Dirac spinors) with nonrelativistic exchange-correlation functionals.

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Authors and Affiliations

  1. Fachbereich Chemie, Technische Universität Kaiserslautern, Erwin-Schrödinger-Str. 52, D-67663, Kaiserslautern, Germany

    Christoph van Wüllen

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  1. Christoph van Wüllen
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Correspondence to Christoph van Wüllen .

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Editors and Affiliations

  1. Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, State Key Laboratory of Rare Earth Materials Chemistry and Applications, College of Chemistry and Molecular Engineering and Center for Computational Science and Engineering, Peking University, Beijing, China

    Wenjian Liu

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van Wüllen, C. (2017). Relativistic Self-Consistent Fields. In: Liu, W. (eds) Handbook of Relativistic Quantum Chemistry. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40766-6_24

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