Local-spin-density approximation

Here Vion(r) is the potential from the ions, and the atomic Rydberg units (e /2 = 2m = 5 = l) have been used in all the formulas. Since Eqs. (8) and (9) are explicitly defined in terms of the electron charge density, all approximations are applied to the last term in Eq. (7), the exchange and correlation energy. 

In the EDA, it is assumed that each point in space contributes additively to E.  

Modem functionals include more elaborate expressions for hom( ) (Vosko et al., 1980 Perdew and Zimger, 1981) relying on accurate Quantum Monte Carlo data for the homogeneous electron gas (Ceperley and Alder, 1980). Generalizing to magnetic solids, which is highly relevant for lanthanide materials, is straightforward as one merely has to consider two densities, one for spin-up and one for spin-down electrons, which corresponds to the LSD functional (von Barth and Hedin, 1972), Even more accurate calculations may be obtained by 

Spin-orbit interaction is only included in the density functional framework if the proper fully relativistic formalism is invoked (Strange, 1998). Often an approximate treatment of relativistic effects is implemented, by solving for the kinetic energy in the scalar-relativistic approximation (Skriver, 1983a), and adding to the total energy functional the spin-orbit term as a perturbation of the form 

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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. 

LORG (localized orbital-local origin) technique for removing dependence on the coordinate system when computing NMR chemical shifts LSDA (local spin-density approximation) approximation used in more approximate DFT methods for open-shell systems LSER (linear solvent energy relationships) method for computing solvation energy... 

In the more general case, where the a and p densities are not equal, LDA (where the sum of the a and p densities is raised to the 4/3 power) has been virtually abandoned and replaced by the Local Spin Density Approximation (LSDA) (which is given as the sum of die individual densities raised to the 4/3 power, eq. (6.17)). 

We have used the multisublattice generalization of the coherent potential approximation (CPA) in conjunction with the Linear-MufRn-Tin-Orbital (LMTO) method in the atomic sphere approximation (ASA). The LMTO-ASA is based on the work of Andersen and co-workers and the combined technique allows us to treat all phases on equal footing. To treat itinerant magnetism we have employed for the local spin density approximation (LSDA) the Vosko-Wilk-Nusair parameterization". 

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 muffin-tin potential around each atom in the unit cell has been calculated in the framework of the Local-Spin-Density-Approximation using the ASW method. The ASW method uses the atomic sphere approximation (ASA), i.e. for each atom a sphere radius is chosen such that the sum of the volumes of all the overlapping spheres equals the unit cell volume. The calculation yields the expected ferromagnetic coupling between Cr and Ni. From the self-consistent spin polarized DOS, partial and total magnetic moment per formula unit can be computed. The calculated total magnetic moment is 5.2 pg in agreement with the experimental value (5.3 0.1 e calculations presented here have been performed... 

Geometry optimization was performed on the discrete cluster unit to eliminate the effects of crystal packing and interactions with titanium ions. The calculations were carried out in local spin density approximation using a SPARTAN 5.0.3 package (Wavefanction, Inc., Irvine, CA 92612 USA). 

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.

The Local Density and Local Spin-Density Approximations... 

This is a very drastic approximation since, after all, the density in our actual system is certainly anything but constant and does not even come close to the situation characteristic of the uniform electron gas. As a consequence, one might wonder whether results obtained with such a crude model will be of any value at all. Somewhat surprisingly then, experience tells us that the local (spin) density approximation is actually not that bad, but rather deliv-... 

Proynov, E. I., A. Vela, and D. R. Salahub. 1994. Gradient-free exchange-correlation functional beyond the local-spin-density approximation. Phys. Rev. A 50, 2421. 

The initial implementation of DFT employed the so-called local density approximation, LDA (or, if we have separate a and [i spin, the local spin density approximation, LSDA). The basic assumption is that the density varies only slowly with distance -which it is locally constant. Another way of visualizing the concept of LDA is that we start with a homogeneous electron gas and subsequently localize the density around each external potential - each nucleus in a molecule or a solid. That the density is locally constant is indeed true for the intermediate densities, but not necessarily so in the high- and low-density regions. To correct for this, it was rec-... 

Various reasons have been advanced for the relative accuracy of spin-polarized Kohn-Sham calculations based on local (spin) density approximations for E c- However, two very favourable aspects of this procedure are clearly operative. First, the Kohn-Sham orbitals control the physical class of density functions which are allowed (in contrast, for example, to simpler Thomas-Fermi theories). Second, local density approximations for are mild-mannered,... 

LSDA Local spin density approximation Moruzzi el al. (1986)... 

Three types of exchange/correlation functionals are presently in use (i) functionals based on the local spin density approximation, (ii) functionals based on the generalized gradient approximation, and (iii) functionals which employ the exact Hartree-Fock exchange as a component. The first of these are referred to as local density models, while the second two are collectively referred to as non-local models or alternatively as gradient-corrected models. 

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