Vosko, Wilk and Nusair VWN

Local exchange and correlation functionals involve only the values of the electron spin densities. Slater and Xa are well-known local exchange functionals, and the local spin density treatment of Vosko, Wilk and Nusair (VWN) is a widely-used local correlation functional. 

The correlation energy of a uniform electron gas has been determined by Monte Carlo methods for a number of different densities. In order to use these results in DFT calculations, it is desirable to have a suitable analytic interpolation formula. This has been constructed by Vosko, Wilk and Nusair (VWN) and is in general considered to be a very accurate fit. It interpolates between die unpolarized ( = 0) and spin polarized (C = 1) limits by the following functional. 

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. 

Later Vosko, Wilk and Nusair (VWN) [32] proposed a correlation functional that was obtained using Pade approximant interpolations of very accurate numerical calculations made by Ceperley and Alder, who used a quantum Monte Carlo method [33], The VWN correlation functional is,... 

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. 

Ihe correlation part Sc p) has been calculated and the results have been expressed as a very complicated function of p by Vosko, Wilk, and Nusair (VWN) see Parr and Yang, Appendix E S. H. Vosko, L. Wilk, and M. Nusair, Can. J. Phys., 58,1200 (1980). Thus... 

The local density approximation (LDA) which uses Dirac-Slater (S) expression for exchange and Vosko, Wilk and Nusair (VWN) expression for the correlation energy of uniform electron gas... 

As far as the correlation part is concerned, no such explicit expression for this term is known. However, there are highly accurate numerical quantum Monte-Carlo simulations of the uniform electron gas [21] from which several authors have derived analytical expressions by means of sophisticated interpolation schemes. One of the most widely used representations for this term is the one developed by Vosko, Wilk, and Nusair (VWN) [22]. 

The calculations were performed with the linear combination of Gaussian type orbital density functional theory (LCGTO-DFT) deMon2k (Koster et al. 2006) code. In O Fig. 16-1, the crosses refer to all-electron polarizabilities calculated with the local density approximation (LDA) employing the exchange functional from Dirac (1930) in combination with the correlation functional proposed by Vosko, Wilk and Nusair (VWN) (Vosko et al. 1980). The stars denote polarizabilities obtained with the gradient corrected exchange-correlation functional proposed by Perdew, Burke and Ernzerhof (PBE) (Perdew et al. 1996). 

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