Chapter 241 The Dual, Localized or Band‐Like, Character of the 4f‐States

Abstract

Abstract The correct treatment of the 4f electrons in lanthanides is a great challenge to any modern electronic structure theory. On the one hand, when considering the spatial extent of their atomic orbitals, the 4f electrons are confined to the region close to the nuclei, that is they are very core‐like. On the other hand, with respect to their position in energy, they should rather be classified as valence or conduction electrons. Unfortunately, the most common implementations of DFT, such as LDA or GGA, have not proven very successful in describing localized f‐electron systems. In this chapter, we show the predictive capability of the SIC‐LSD approach when applied to 4f electron systems, in particular as far as the cohesive properties are concerned. The SIC‐LSD provides an ab initio computational scheme that allows the differentiation between band‐like and core‐like f‐electrons. To determine the number of localized 4f electrons in a particular 4f‐solid, we are guided by the minimization of the SIC‐LSD total energy functional over all possible configurations of co‐existing localized (SIC) and itinerant 4f‐states. This chapter elaborates on these issues, naturally leading to the dual character of the 4f electron: either localized (after applying the SIC) or band‐like (LSD) and contributing to the Fermi surface. From this, the notion of nominal valence is developed defining the number of remaining band‐like states as the valence of the lanthanide ion. These band‐like states determine the bonding properties. This definition of valence turns out to be extremely useful and we give numerous examples of how this notion of valence contributed to a better understanding of the physical properties of the lanthanides and their compounds. In particular, the bonding properties of the lanthanides, such as the lattice constants, and their pressure behaviour can be studied without using adjustable parameters. Local magnetic moments and spectroscopic investigations provide a study of some of the properties of the localized f‐states. Specifically, we find the degree of 4f localization to be similar in the light and heavy lanthanides. The one‐electron SIC‐LSD is shown to be an ab initio computational scheme consistent with all three Hund's rules. A finite temperature generalization based on the local SIC‐LSD method leads to the first‐principles study of the phase diagrams of the lanthanides. The study of a magnetic phase diagram for the heavy lanthanides leads to the discovery of the role played by the lanthanide contraction in determining the magnetic structure of heavy lanthanides. Also, the importance of the Fermi surface webbing features in driving the magnetic order is explained. Calculating the phase diagram of the α‐/γ‐phase transition in elemental Ce allows us to identify the entropy as the driving force in this transition. These finite temperature studies incorporate thermal fluctuations only. Finally, an outline is given on how to include dynamical, quantum fluctuations in the present methodology.