Vosko-Wilk-Nusair local correlation density functional

Three density functional theories (DFT), namely LDA, BLYP, and B3LYP, are included in this section. The simplest is the local spin density functional LDA (in the SVWN implementation), which uses the Slater exchange functional [59] and the Vosko, Wilk and Nusair [60] correlation functional. The BLYP functional uses the Becke 1988 exchange... 

To confirm the minimum point of the total energy profile with respect to the U=0 distance, other exchange - correlation potentials were also examined a local density functional by Vosko-Wilk-Nusair (VWN) (14) and a nonlocal... 

Theoretical work on the oxidation reactions of aromatic hydrocarbons is scarce. Bartolotti and Edney [10] used a simple density functional approach with the local exchange correlation functional developed by Vosko-Wilk-Nusair [11] to identify potential intermediates produced in the OH addition initiated atmospheric photooxidation of toluene. Although their energy results were acknowledgely preliminary in nature, their calculations were able to confirm certain aspects of the proposed reaction mechanism [2,3] and to predict the importance of carbonyl compounds containing... 

One approach, using a local density approximation for each part, has E - = Es -1- Evwn, where Eg is a Slater functional and Evwn is a correlation functional from Vosko, Wilk, and Nusair (1980). Both functionals in this treatment assume a homogeneous election density. The result is unsatisfactory, leading to enors of more than 50 kcal mol for simple hydrocarbons. 

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. 

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. ... 

Local density approximation (LDA) with Slater s Xa functional for exchange (Ref. 57) and the functional of Vosko, Wilk, and Nusair (Ref. 109) for correlation. 

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 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]. 

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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