Vosko-Wilk-Nusair correlation functional

VWN5 A Vosko, Wilk, Nusair correlation functional... 

The one-electron Kohn-Sham equations were solved using the Vosko-Wilk-Nusair (VWN) functional [27] to obtain the local potential. Gradient correlations for the exchange (Becke fimctional) [28] and correlation (Perdew functional) [29] energy terms were included self-consistently. ADF represents molecular orbitals as linear combinations of Slater-type atomic orbitals. The double- basis set was employed and all calculations were spin unrestricted. Integration accuracies of 10 -10 and 10 were used during the single-point and vibrational frequency calculations, respectively. The cluster size chosen for Ag or any bimetallic was... 

Hedin- Lundqvist, HL, exchange-correlation potential [37], which is equivalent to our earlier use [130] of the von Barth-Hedin potential, vBH, [38] with parameter values as used by Hedin and Lundqvist. Calculations were also performed using the Xa form, with a = 0.7 [4] and the Vosko-Wilk-Nusair form of Vxc [41]. A somewhat lower total energy was obtained by inclusion of the 3d, and in particular the 3p and 3d, basis functions, compared with the results obtained using the minimal basis set. 

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... 

GGA functionals. Slater (S) exchange [68] and Vosko-Wilk-Nusair (VWN) correlation [74] LDA functionals, and the HF exchange integral with three parameters ... 

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... 

Any exchange functional can be combined with any correlation functional. For example, the notation BLYP/6-31G denotes a DF calculation done with the Becke 1988 exchange functional and the Lee-Yang-Parr correlation functional, with the KS orbitals expanded in a 6-31G basis set. The letter S (which acknowledges Slater s Xa method) denotes the LSDA exchange functional (15.140). VWN denotes the Vosko-Wilk-Nusair expression for the LSDA correlation functional (actually, these workers gave two differ-... 

Kafafi devised the hybrid K2-BVWN (standing for Kafafi 2-parameter, Becke, Vosko-Wilk-Nusair) exchange-correlation functional [S. A. Kafafi, /. Phys. Chem. A, 102,10404 (1998)]. K2-BVWN/6-311+G(2df) calculations of of 350 species had... 

The Xa method is an example of LDA in which the correlation energy is neglected and the exchange energy expression is multiplied by a parameter a. A fairly accurate expression for the correlation energy of the uniform electron gas, the VWN (Vosko, Wilk, Nusair) functional, was derived by fitting it to Monte Carlo results. 

From Reference 13, triple-J + polarization basis set for heavy atoms, double- + polarization basis set for hydrogen atoms. Vosko-Wilk-Nusair LSDA XC functional. Gradient-corrected Perdew— ng exchange and Perdew correlation functionals. 

Gradient-corrected Becke exchange and Perdew correlation functionals used perturbatively with self-consistent Vosko—Wilk—Nusair LSDA densities. 

Correlation functional due to Wilk, Vosko and Nusair Zero differential overlap... 

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. 

Which is very closely related to Vosko, Wilk and Nusair s local correlation functional (VWN). 

Accurate values of the correlation functional are available thanks to the quantum Monte Carlo calculations of Ceperley and Alder (1980). These values have been interpolated in order to give an analytic form to the correlation potential (Vosko, Wilk and Nusair, 1980). 

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. 

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. ... 

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