Local spin-density approximations exchange-correlation

Table 9.1 presents excitation energies for a few atoms and ions. Calculations were performed with the generalized KLI approximation [69,74], For comparison, experimental data and the results obtained with the local-spin-density (LSD) exchange-correlation potential [75] are shown. The KLI method contains only the exchange. 

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. 

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. 

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

HJ point out that in the detailed work on H2 by Kolos and Wolniewicz,114 the first excited state 3 2 was found to have a very weak minimum at a large separation. This binding presumably arises from a van der Waals force which is not included in the density functional theory when a local approximation to exchange and correlation is employed. Nevertheless, as HJ point out, their study of the corresponding state of the dimers Li2-Cs2 revealed a weak, but definite maximum in each case. Rough estimates of binding energy and equilibrium separation are shown in Table 16. It is, of course, possible that these results are a consequence of the local spin-density approximation, so that further work will... 

Iron-series Dimers.—Harris and Jones96 have in addition calculated binding energy curves for low-lying states of the 3density functional formalism with a local spin-density approximation for the exchange and correlation energy. 

Source Zeller, R. (2006) and the spin-polarized exchange-correlation integral, I c, calculated by the local spin density approximation. The Stoner parameter is, to a first approximation, element-specific and independent of the atom s local environment. 

Here, V [p] is the potential energy in the field of the nuclei plus any external perturbation, T [p] is the kinetic energy of a set of n independent electrons, moving in an effective one-electron potential which leads to the density p(r), and J p] is the total Coulomb interaction [1]. [p] is the remainder, usually described as the exchange-correlation energy. This term represents the key-problem in DFT, since the exact E c is unknown, and approximations must be used. The simplest approach is the local spin density approximation (LSD), in which the functional for the uniform electron gas of density p is integrated over the whole space ... 

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%. 

Thus we have shown that the short wavelength hypothesis is not exact in general. Even if it were, it would not provide a strong explanation for the success of the local spin density approximation, because the k 6 tail of the exchange-correlation energy... 

For the calculations we used the Munich version of the linear combination of Gaussian-type orbital density functional (LCGTO-DF) code. ° The computationally economic local spin-density approximation (LSDA) to the exchange-correlation functional has been successfully used in chemical applications since the seventies. This functional (employed here in the parameterization suggested by Vosko, Wilk, and Nusair, has been shown to describe accurately impor-... 

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]. 

Hartree-Fock (HF) and a variety of exchange, correlation, and hybrid functionals were considered in this study. The local spin density approximation is represented by the exchange functional S (Slater and Dirac 1930) [72] together with the correlation functionals VWN (Vosko, Wilk, and Nusair) [73], PZ81 (Perdew and Zunger) [74], and PW92 (Perdew and Wang 1992) [75]. 

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