LSDA theory

The search for additional LSDAs over the past 10 years has been extensive and the results are both stimulating and rewarding. New formulations, containing a variety of LSDAs, such as amphoteric sulfobetaines, polymers, and even nonionics, have been introduced. Thus, the older theories on the mechanism of lime soap dispersion require modification and supplementation by newer ones. This line of investigation becomes more significant as some of the LSDAs of this report become commercialized [38]. 

Table4.4 Spectroscopic properties for Au2 q= -1,0, + 1) using ab-initio (Hartree Fock, HF, second-order Moller-Plesset, MP2, and coupled cluster, CCSD(T)) and DFT (local spin-density approximation, LSDA, Perdew-Wang CCA, PW91, and Becke three-parameter Lee-Yang-Parr functional, B3LYP) methods at the RPPA level of theory.

In the LSDA and GGA approaches, the Coulomb integrals are calculated on the same footing as in HF theory, but using the Kohn-Sham orbitals. However, the exchange contribuhon is taken from a functional of the density and so the interplay of the Coulomb and exchange energies, which is clear under the HF approach, is not so well balanced in DFT. In particular, using Vxc based on the density in Equahon 8.12 implies that each electron contributes to its own potential, the so called self interaction problem. 

The density-functional theory (DFT) with spin polarization, even in the local approximations (LDA and LSDA with spin polarization) has been applied to describe many physical properties with good precision. The... 

A different approach to treat correlation effects which are not well described within the LSDA consists in incorporating self-interaction corrections (SIC) [111-114] in electron structure methods for solids, Svane et al. [115-120]. In the Hartree-Fock (HF) theory the electron-electron interactions are usually divided into two contributions, the Coulomb term and the exchange term although they both are Coulomb interactions. The separation though, is convenient because simplifications of self-consistent-field calculations can be obtained by including in both terms the interaction of the electron itself. In the HF theory this has no influence on the solutions because these selfinteractions in the Coulomb and exchange terms exactly cancel each other. However, when the exchange term is treated... 

Whether KS DFT should be classified as an ab initio method is a matter of debate. If the true were known and used, then KS DFT would be an ab initio method. However, the true is unknown and must be replaced by a model E sudi as the LSDA or the LSDA with gradient corrections. Some people would consider that use of disqualifies KS DFT as being an ab initio method, but others would not. Some of the gradient-corrected functionals contain empirical parameters, and in hybrid functionals, the mixing constant(s) are determined empirically. Use of functionals with empirically determined parameters clearly disqualifies a method as being ab initio, but the number of parameters used in these versions of DFT is far fewer than the number used in common semiempirical theories such as AMI or PM3 (Section 16.5), which use different parameters for each kind of atom, which is not true in DFT. The KS DFT method is usually considered in a category by itself, distinct from ab initio methods such as HF, Cl, MP, and CC. 

Independent electronic structure calculations on YbPtBi were performed by Oppeneer et al, (1997) on the basis of density-functional theory in the local-spin-density approximation (LSDA), generalized with additional intra-atomic Coulomb correlations between 4f electrons. These calculations show that the Yb 4f level is pinned at the Fermi energy. This pinning is a generic property. Furthermore the hybridized 4f level is split into two van Hove-like side maxima. 

The outline of the present chapter is as follows. Section 2 deals with the relevant physical, electronic, and magnetic properties of the lanthanides. Section 3 reviews briefly the above-mentioned theoretical methods, with the focus on the SIC-LSDA method, and, in particular, the full implementation of SIC, involving repeated transformations between Bloch and Wannier representations (Temmerman et al., 1998). This is then compared with the local-SIC, implemented in the multiple scattering theory (Liiders et al., 2005). Section 4 deals with the valence (Strange et al., 1999) and valence transitions of the lanthanides. Section 5 discusses the local magnetic moments of the lanthanides. Section 6 discusses two spectroscopies applied to lanthanides and some of their compoimds. Section 7 outlines a methodology of calculating the finite temperature (T) properties of the lanthanides and their... 

While these methods provide some useful insight into Gd and Ce, they yield unrealistic results for any other lanthanide material as the f-bands bimch at the Fermi level leading to unphysically large densities of states at the Fermi energy and disagreement with the de Haas van Alphen measurements. It is clear that a satisfactory theory of lanthanide electronic structures requires a method that treats all electrons on an equal footing and from which both localized and itinerant behaviour of electrons may be derived. SIC to the LSDA provide one such theory. 

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