Abstract
This chapter gives an overview of relativistic density functional theory. Both its foundations, the existence theorem and the Kohn–Sham equations, and its core quantity, the exchange–correlation (xc) energy functional, are discussed. It is first outlined how a workable relativistic Kohn–Sham scheme can be obtained within the framework of quantum electrodynamics and which alternatives for its implementation are available. Particular emphasis is then placed on the relativistic corrections to the xc-functional. The modification of its functional form due to the relativistic motion of the electrons and their retarded interaction via exchange of photons is distinguished from the effect resulting from insertion of a relativistic density into the functional. The difference between the relativistic xc-functional and its nonrelativistic form is studied in detail for the case of the exchange functional (which can be handled exactly via the optimized effective potential method). This analysis is complemented by some first-principles results for the correlation functional, relying on a perturbative approach. Finally, the accuracy of approximate relativistic xc-functionals, the local density and the generalized gradient approximation, is assessed on the basis of the exact results.
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Acknowledgements
I am very grateful to R. M. Dreizler and D. Ködderitzsch for many valuable discussions on the topics of this contribution.
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Engel, E. (2015). Relativistic Density Functional Theory. In: Liu, W. (eds) Handbook of Relativistic Quantum Chemistry. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41611-8_18-1
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DOI: https://doi.org/10.1007/978-3-642-41611-8_18-1
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