Local spin-density approximations Vosko-Wilk-Nusair

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. 

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". 

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... 

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-... 

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. 

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]. 

---