Vosko-Wilk-Nusair parametrization

We have used the basis set of the Linear-Muffin-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 the Vosko-Wilk-Nusair parametrization for the exchange-correlation energy density and potential. In conjunction with this we have treated the alloying effects for random and partially ordered phases with a multisublattice generalization of the coherent potential approximation (CPA). 

Calculations were done with a full-potential version of the LMTO method with nonoverlapping spheres. The contributions from the interstitial region were accounted for by expanding the products of Hankel functions in a series of atom-ce- -ered Hankels of three different kinetic energies. The corrected tetrahedron method was used for Brillouin zone integration. Electronic exchange and correlation contributions to the total energy were obtained from the local-density functional calculated by Ceperley and Alder " and parametrized by Vosko, Wilk, and Nusair. ... 

There are a number of model exchange-correlation functionals for the ground-state. How do they perform for ensemble states Recently, several local density functional approximations have been tested [24]. The Gunnarsson-Lundqvist-Wilkins (GLW) [26], the von Barth-Hedin (VBH)[25] and Ceperley-Alder [27] local density approximations parametrized by Perdew and Zunger [28] and Vosko, Wilk and Nusair (VWN) [29] are applied to calculate the first excitation energies of atoms. 

The Kohn-Sham-Gaspar potential derived from density-functional theory has a similar expression for V c with Xa = 2/3, and only took into account exchange [20],[40]. To include correlation, several forms were proposed for / , with parameters obtained from fits to RPA calculations or more accurate Monte Carlo simulations [41] and different spin interpolations. The current version of the DVM code contains altogether nine choices of Vje, the preferred form being the Vosko, Wilk and Nusair [42] parametrization of the Ceperley and Alder Monte Carlo simulations [43]. 

At the same time, the LDA gave an a posteriori justification of the old Xa method by Slater, because the latter is a special LDA variant without correlation. The corresponding spin-dependent version of the LDA is called a local spin-density approximation (LSDA or LSD or just spin-polarized LDA), and even now when people talk of LDA functionals, they always refer to its generalized form for systems with (potentially) unpaired spins. Among the most influential LDA parametrizations, the one of von Barth and Hedin (BH) [154] and the one of Vosko, Wilk and Nusair (VWN) [155] are certainly worth mentioning. The latter is based on the very accurate Monte Carlo-type calculations of Ceperley and Alder [156] for the uniform electron gas, as indicated above. 

LDA (local density approximation, in the parametrization of Slater for exchange and Vosko, Wilk and Nusair for correlation ),... 

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