LDA functional

The exchange-correlation functional for the uniform electron gas is known to high precision for all values of the electron density, n. For some regimes, these results were determined from careful quantum Monte Carlo calculations, a computationally intensive technique that can converge to the exact solution of the Schrodinger equation. Practical LDA functionals use a continuous function that accurately fits the known values of gas(/i). Several different... 

Nonempirical GGA functionals satisfy the uniform density limit. In addition, they satisfy several known, exact properties of the exchange-correlation hole. Two widely used nonempirical functionals that satisfy these properties are the Perdew-Wang 91 (PW91) functional and the Perdew-Burke-Ernzerhof (PBE) functional. Because GGA functionals include more physical ingredients than the LDA functional, it is often assumed that nonempirical GGA functionals should be more accurate than the LDA. This is quite often true, but there are exceptions. One example is in the calculation of the surface energy of transition metals and oxides. 

Most gradient corrected functionals are constructed with the correction being a term added to the LDA functional, i.e.. 

FLAPW GGA study of the structure and optical properties of AgFe02 and CuFe02 has been carried out by Blaha s group. " Ogata has reviewed band models of Na cCo02. This solid has also been the subject of a study by the recently-developed dynamic mean field theory (DMFT). This study used VASP with an LDA functional, a value of U = 3 eV for Co and an on-site potential for Na. It was found that the Na potential was the key to explaining the stronger correlation for X = 0.7 than for x = 0.3. 

Ab initio methods as well as looking at the structure can of course consider band structure. In the first rush of excitement following the discovery of high Tc superconductors, a number of studies on the band structure of cuprates were undertaken. The results of these up to 1989 are reviewed in detail by Pickett. These calculations established that the bands that crossed the Fermi level were antibonding Cu 3d /O 2p bands. Most of them used an LDA functional but these compounds are expected to be strongly correlated and there is experimental evidence for local Coulomb repulsion on Cu(ii) sites. Larbaoui et found that using a GGA functional... 

We see that the first two terms simply give the expansion of the LDA functional around the constant density 0, i.e.,... 

GGA functionals. Slater (S) exchange [68] and Vosko-Wilk-Nusair (VWN) correlation [74] LDA functionals, and the HF exchange integral with three parameters ... 

Local density approximations (EDA). This group includes functionals derived in the analytic theory of a UEG and applied, directly or with empirical modifications, to nonuniform densities. AU LDA functionals have the form... 

Emzerhof and Scuseria [107] suggested approximating using the LDA functional in which the actual p(r) is replaced by a fictitious density p r) defined by T(r) = Cfp ( (r), where r(r) is the kinetic energy density of the actual nonuniform system. This leads to the local T-approximation (LTA)... 

Despite the great variety of calculational schemes employed, relativistic band structure codes have by now achieved a high level of accuracy. While for example the calculated lattice constant of fcc-Th in early publications covered a broad range of values (Fig. 1), a number of state-of-the-art relativistic full potential methods give reliable values very close to each other, about 2.5 percent below the experimental lattice constant (which is the systematic error of the LDA functional used in the calculations). Moreover, the most accurate schemes coincide in their total energies within a few mHartree per atom, a level of accuracy almost comparable to non-relativistic band structure schemes. 

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