LSDA, 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 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. 

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 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-... 

The LDA (or, in the case of radicals, the local spin density approximation, LSDA) exchange-correlation energy is generally expressed as... 

The LDA has been adopted in most DFT electronic stmcture calculations on sohds since the 1970s but was not considered accurate enough for quantum chemistry until the 1990s when refinements were made. Thus, even though the DFT formahsm is, in principle, exact, the many-body problem is stiU only solved approximately in the LDA scheme The LDA works best for metals. Band gaps tend to be underestimated. The local spin-density approximation (LSDA) is a generahzation of the LDA to account for electron spin ... 

This can be extended to the local spin density approximation (LSDA) for those cases where the a and p densities are not equal. Slater s X method is a scaled form of Eq. (1.52), and often the terms LSDA and Slater are used interchangeably. 

The earliest class of DFT methods is known as local (electron) density approximation (LDA) methods in the case that the total electron density is decomposed into individual spin densities for +1 /2 and -1/2 spin we refer to these methods as local spin density approximation (LSDA) methods. In these methods the total molecular XC energy is evaluated by integration on a numerical grid of the electron density, and the energy is a function of only the specific value of the density at each point, hence the local density ... 

The simplest approximation, employed for very many years until the most recent developments, is known as Local Spin Density Approximation (LSDA) and does not depend on the gradients of the electronic density but only on the electronic density itself. One of the variants of LSDA, commonly employed in the applications to molecular systems in the last years, is the one called SVWN. In this exchange-correlation functional, the exchange is provided by Slater s formula (3) for the uniform electron gas, whereas the correlation is evaluated according to the expression derived by Vosko, Wilk and Nusair (4) from an interpolation of previous Monte-Carlo results for the spin-polarized homogeneous electron gas... 

Another problem is that for fee Fe, the Generalized Gradient Approximation (GGA) is assumed to be the most accurate approximation for the exchange-correlation potential, but most of the studies on the FeNi alloys have been made using the Local Spin Density Approximation (LSDA). Therefore, it was of some importance to perform an exhaustive study of FeNi alloys using the GGA, and this was done in Paper VIII, where we have investigated the FeNi alloys from pure Fe to alloys with a Ni concentration of 50%. 

Better results than with the LDA are obtained by an elaboration of the LDA in which electrons of a and spin in the uniform electron gas are assigned different spatial KS orbitals and from which different electron density functions and follow. This unrestricted LDA method (cf. UHF, section 5.2.3.6e) is called the local spin density approximation, LSDA, and has the advantages that it can handle systems with one or more unpaired electrons, like radicals, and systems in which electrons are becoming unpaired, such as molecules far from their equilibrium geometries even for ordinary molecules it appears to be more forgiving toward the use of (necessarily) inexact xcfunctionals [37], For species in which all the electrons are securely paired, the LSDA is equivalent to the LDA. Like and its functional derivative... 

---