Relativistic methods within density functional theory

An interesting approach to the quantum mechanical description of many-electron systems such as atoms, molecules, and solids is based on the idea that it should be possible to find a quantum theory that refers solely to observable quantities. Instead of relying on a wave function, such a theory should be based on the electron density. In this section, we introduce the basic concepts of this density functional theory (DFT) from fundamental relativistic principles. The equations that need to be solved within DFT are similar in structure to the SCF one-electron equations. For this reason, the focus here is on selected conceptual issues of relativistic DFT. From a practical and algorithmic point of view, most contemporary DFT variants can be considered as an improved model compared to the Hartree-Fock method, which is the reason why this section is very brief on solution and implementation aspects for the underlying one-electron equations. For elaborate accounts on nonrelativistic DFT that also address the many formal difficulties arising in the context of DFT, we therefore refer the reader to excellent monographs devoted to the subject [383-385]. 

In this chapter we focus on methodological and computational aspects that are key to accurately modeling the spectroscopic and thermodynamic properties of molecular systems containing actinides within the density functional theory (DFT) framework. Our focus is on properties that require either an accurate relativistic all-electron description or an accurate description of the dynamical behavior of actinide species in an environment at finite temperature, or both. The implementation of the methods and the calculations discussed in this chapter were carried out with the NWChem software suite [1]. In the first two sections we discuss two methods that account for relativistic effects, the ZORA and the X2C Hamiltonian. Section 12.2.1 discusses the implementation of the approximate relativistic ZORA Hamiltonian and its extension to magnetic properties. Section 12.3 focuses on the exact X2C Hamiltonian and the application of this methodology to obtain accurate molecular properties. In Section 12.4 we examine the role of a dynamical environment at finite temperature as well as the presence of other ions on the thermodynamics of hydrolysis and exchange reaction mechanisms. Finally, Section 12.5 discusses the modeling of XAS... 

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