Relativistic electronic structure theory

C. B. Kellogg, An Introduction to Relativistic Electronic Structure Theory in Quantum Chemistry http //zopyros.ccqc.uga.edu/ kellogg/docs/rltvt/rltvt.html (1996). 

Schwerdtfeger, P. (ed.) (2002) Relativistic Electronic Structure Theory. Part 1 Fundamentals, Elsevier, Amsterdam. 

M. Dolg, in Relativistic Electronic Structure Theory - Part 1. Fundamentals (ed. P. Schwerdtfeger), Elsevier, Amsterdam, 2002, p. 523. 

Kaupp M In Schwerdtfeger P (ed.) Relativistic electronic structure theory, vol 2. Elsevier, Amsterdam (in press)... 

Relativistic Electronic Structure Theory, Part 1. Fundamentals... 

For the sake of brevity, we proceed in presenting a pragmatic approach to relativistic electronic structure theory, which is justified by its close analogy to the nonrelativistic theory and the fact that most of the finer relativistic aspects must be neglected for calculations on any atom or molecule with more than a few electrons. For a recent comprehensive account on the foundations of relativistic electronic structure theory we refer to Quiney et al. (1998b). 

Four-component theories for the calculation of electronic structures as described in detail in this review have become mature particularly in the last decade as a highly accurate tool for any kind of system be it an atom, molecule or solid. Theoretical as well as methodological understanding gave detailed insight into the foundations of relativistic electronic structure theory. Some fundamental questions are still open as we have explicated, especially in the first two sections of this review, and they will certainly be tackled and answered in the years to come. Methodological advances will also continue to be made. 

The modules for relativistic electronic structure theory were all integrated in the program Paragauss, which is a parallelized implementation of the LCGTO-FF-DFT method (Belling et al. 1999a,b). 

Needless to say, many-electron atoms and molecules are much more complicated than one-electron atoms, and the realization of the nonrelativistic limit is not easily accomplished in these cases because of the approximations needed for the description of a complicated many-particle system. However, the signature of relativistic effects (see, for example, Chapter 3 in this book) enables us to identify these effects even without calculation from experimental observation. Two mainly experimentally oriented chapters will report astounding examples of relativistic phenomenology, interpreted by means of the methods of relativistic electronic structure theory. These methods for the theoretical treatment of relativistic effects in many-electron atoms and molecules are the subject of most of the chapters in the present volume, and with the help of this theory relativistic effects can be characterized with high precision. 

Relativistic Electronic Structure Theory, Part I Fundamentals Theoretical and Computational Chemistry, Vol. 11 2002 Elsevier Science B.V. All rights reserved. 

Dirac s relativistic theory for the motion of electrons in molecules was introduced in the preceding chapters. The appearance of positron solutions and the four-component form of the wave function looks problematic at first sight but in practice it turns out that the real challenge is, like in non-relativistic electronic structure theory, the description of the correlation between the motion of electrons. The mean-field approximation that is made in the Dirac-Hartree-Fock (DHF) approach provides a good first step, but gives bond energies and structures that are often too inaccurate for chemical purposes. 

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