LDA and GGA Correlation Functionals

As a result, this functional is in a form containing the kinetic energy density, 

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 VWN EDA correlation functional has 12 parameters in total xo , at, bt, ct for / = 1 — 3. Notice that there are five combinations for these parameters (ver. 5 is usually employed. For the parameter values, see Vosko et al. 1980). 

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 

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