Electronic structure local spin-density approximation

The simplest approximation to the complete problem is one based only on the electron density, called a local density approximation (LDA). For high-spin systems, this is called the local spin density approximation (LSDA). LDA calculations have been widely used for band structure calculations. Their performance is less impressive for molecular calculations, where both qualitative and quantitative errors are encountered. For example, bonds tend to be too short and too strong. In recent years, LDA, LSDA, and VWN (the Vosko, Wilks, and Nusair functional) have become synonymous in the literature. 

In order to perform the calculation., of the conductivity shown here we first performed a calculation of the electronic structure of the material using first-principles techniques. The problem of many electrons interacting with each other was treated in a mean field approximation using the Local Spin Density Approximation (LSDA) which has been shown to be quite accurate for determining electronic densities and interatomic distances and forces. It is also known to reliably describe the magnetic structure of transition metal systems. 

The LDA and the Local Spin Density approximation (LSD), when spin is considered, have been successful in determining molecular structure and many one-electron properties or expectation values. It is very well known now that the LDA and LSD underbind core electrons and overbind atoms in a molecule. Energies are not as good as those obtained by correlated ab initio methods, although the relative energies of isomers and activation barriers which do not involve bond-breaking can be quite accurate. It was observed,... 

As most of the electronic structure simulation methods, we start with the Born-Oppenheimer approximation to decouple the ionic and electronic degrees of freedom. The ions are treated classically, while the electrons are described by quantum mechanics. The electronic wavefunctions are solved in the instantaneous potential created by the ions, and are assumed to evolve adiabatically during the ionic dynamics, so as to remain on the Born-Oppenheimer surface. Beyond this, the most basic approximations of the method concern the treatment of exchange and correlation (XC) and the use of pseudopotentials. XC is treated within Kohn-Sham DFT [3]. Both the local (spin) density approximation (LDA/LSDA) [16] and the generalized gradients approximation (GGA) [17] are implemented. The pseudopotentials are standard norm-conserving [18, 19], treated in the fully non-local form proposed by Kleinman and Bylander [20]. 

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 local spin density approximation (LSD) for the exchange-correlation energy, (1.11), was proposed in the original work of Kohn and Sham [6], and has proved to be remarkably accurate, useful, and hard to improve upon. The generalized gradient approximation (GGA) of (1.12), a kind of simple extension of LSD, is now more widely used in quantum chemistry, but LSD remains the most popular way to do electronic-structure calculations in solid state physics. Tables 1.1 and 1.2 provide a summary of typical errors for LSD and GGA, while Tables 1.3 and 1.4 make this comparison for a few specific atoms and molecules. The LSD is parametrized as in Sect. 1.5, while the GGA is the non-empirical one of Perdew, Burke, and Ernzerhof [20], to be presented later. 

The determination of electron correlation effects, cluster geometry and their interplay is a difficult problem. Most theoretical studies performed so far have attempted to deal with one of these aspects at a time [4-11, 43-46]. For example, in Refs [4-7, 10, 11] the electron interactions were treated in mean-field approximations (X a, local spin density, unrestricted Hartree-Fock) and only a few, mostly highly symmetric structures were considered. Optimizations of the cluster geometry were performed in Ref. [8] for... 

In (1) the Coulomb interaction between the conduction states is neglected. These states are rather extended (see fig. 1) and the Coulomb integrals are not very large. For such states the local spin density (LSD) approximation of the spin density functional formalism (Kohn and Sham 1965) has been rather successful (von Barth and Williams 1983). In this scheme the electrons are formally treated as independent and correlation effects are included in an effective one-particle potential. By using 6fc s in (1) which are obtained from a LSD approximation or deduced from experiment, we may incorporate some interaction effects implicitly in the Hamiltonian (1). In this way chemical information about the compound considered may also be incorporated. Relativistic effects on the band structure are also included in this approach. 

In this section, the ground state properties of the lanthanides are studied with a first principles all-electron total energy band structure method. The LMTO method is employed within the local density (LDA) and local spin density (LSD) functional approximations (Hohenberg and Kohn 1964, Kohn and Sham 1965, Gunnarsson and Lundqvist 1976). The von Barth-Hedin (1972) interpolation formula is used for the exchange and correlation potential with the parameters of Hedin and Lundqvist (1971) and RPA scaling (Janak 1978). 

Most calculations of the electronic structure of solids, including those performed for f electron metals, are based on density functional theory within the Kohn-Sham ansatz to which, in turn, a local density (LDA) or local spin density (LSDA) approximation is applied. Each part of this characterization has it own implications and it is important to understand which is relevant when judging the validity of results. 

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