LDA correlation functional

The LDA correlation functional used in these calculations was not the VWN parameterization of the Ceperly and Alder reference data for the uniform electron gas but that of Perdew and Wang.18... 

At the beginning of this decade, the Xa methods, i.e. without explicit correlation, were still used in Chemistry. MS-Xa was used for the study of large systems, in particular for magnetic properties [95-101], and LCAO-Xa (also called HFS) for electronic stmcture investigations of small metallic systems [102-106]. A big improvement was reached when the correlation energies of the spin-paired and spin-polarized uniform electron gas, calculated accurately by Ceperley and Alder [76], were incorporated in the LDA correlation functionals. 

The VWN LDA correlation functional (Vosko et al. 1980) was developed to make the RPA expression converge to the high and low density limits. This functional was inductively derived on the basis of the Pad6 interpolation by fitting parameters to the exact correlation energy of a uniform density gas given by the quantum Monte... 

The PW LDA correlation functional (Perdew and Wang 1992) reforms the VWN LDA correlation functional to simplify it, to reduce the number of parameters, and to satisfy more fundamental physical conditions. The functional form is... 

These LDA correlation functionals have been used in various property calculations, especially in solid state calculations. However, we should recall that these LDA correlation functionals are not exact functionals but are inductively derived approximative functionals. Actually, even though the exact correlation energy of a uniform electron gas in a quanmm Monte Carlo calculation has (9(p) and density dependences at the high and low density limits, respectively... 

Ceperley and Alder 1980), these LDA correlation functionals have been proven to violate at least one of these limits (Tsuneda et al. 2001). 

The PW91 correlation functional (Perdew and Wang 1992) augments the PW LDA correlation functional with a GGA term using parameters fitted to satisfy as many fundamental physical conditions of the correlation energy as possible. The resulting functional has a very complicated form,... 

The B3LYP hybrid functional (Becke 1993), the first hybrid functional, is the most frequently used functional (or method) in all functionals (or all theories) in quantum chemistry calculations. This functional uses three parameters as the mixing ratios to form the adiabatic connections between the Hartree-Fock exchange integral and the LDA exchange functional and between the LYP-GGA correlation functional and the LDA correlation functional, and to combine with the attenuated GGA term of the B88 exchange functional. 

On the basis of these results, it can be concluded that the DFT/SCRF calculations lead usually to similar results to the ones from the MP2/SCRF calculations, provided the post-LDA exchange-correlation functionals are used. Energetic effects exceeding 2 kcal/mol compare well with experiment in most systems investigated. In cases, where DFT/SCRF and experimental results differ more than 1-2 kcal/mol, the cause of the discrepancy is clouded by a diversity of approximations and simplifications within the DFT/SCRF framework. 

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