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Relativistic Density Functional Theory

Properties of the Exact Exchange and Construction of Pseudopotentials

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Theoretical Chemistry and Physics of Heavy and Superheavy Elements

Part of the book series: Progress in Theoretical Chemistry and Physics ((PTCP,volume 11))

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Abstract

An overview of relativistic density functional theory (RDFT) is given, including some illustrative results for atoms and molecules. Starting from quantum electrodynamics, the existence theorem of RDFT and the effective single-particle equations are outlined. In this formalism the ground state four current is the fundamental variable which allows the determination of all ground state observables. The crucial ingredient of the single-particle equations is the relativistic exchange-correlation (xc) potential, which is obtained as the functional derivative of the xcenergy functional with respect to the four current. As standard approximations for the xc-functional, the relativistic local density approximation (RLDA) and the relativistic generalized gradient approximation (RGGA) are reviewed. In particular, it is shown that the RLDA does not provide an adequate description of the relativistic xc-effects in finite systems, while the RGGA performs rather well over the complete periodic table. In contrast to the explicit density functionals RLDA and RGGA, the representation of implicit xc-functionals is not only based on the four current, but also on the effective single-particle spinors of RDFT. The most important implicit functional is the exact exchange. After a summary of the relativistic optimized potential method (ROPM), which is required for the evaluation of the xc-potential corresponding to implicit functionals, the properties of the exact exchange are investigated in detail, addressing in particular the role of the transverse corrections. As RDFT calculations frequently rely on a pseudopotential framework, the fully relativistic construction of normconserving pseudopotentials is presented, including the case of the highly nonlocal exact exchange. Finally, some molecular results are given, which illustrate the role of relativity in RDFT.

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  1. Institut fr Theoretische Physik, J. W. Goethe Universitt Frankfurt, D-60054, Frankfurt/Main, Germany

    E. Engel

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  1. School of Chemistry, Tel Aviv University, Tel Aviv, Israel

    U. Kaldor

  2. Rutherford Appleton Laboratory, Chilton, Oxfordshire, England

    S. Wilson

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Engel, E. (2003). Relativistic Density Functional Theory. In: Kaldor, U., Wilson, S. (eds) Theoretical Chemistry and Physics of Heavy and Superheavy Elements. Progress in Theoretical Chemistry and Physics, vol 11. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0105-1_11

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