LDA exchange functional

Becke formulated the following gradient-corrected exchange functional based on the LDA exchange functional in 1988, which is now in wide use ... 

This functional is found to be the exact LDA exchange functional. Furthermore, von Weizsacker proposed a correction term using the gradient of electron density for the Thomas-Fermi kinetic energy functional (von Weizsacker 1935),... 

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. 

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... 

In order to find a reasonable configuration for our calculation, we take test calculation to optimize the bulk structure of pyrite with GGA and LDA exchange-correlation functional. In the calculation, the plane wave cutoff energy set is 280 eV and the key point set is 4 x 4 x 4, the convergence tolerances set is 10 eV/atom. The optimized cell parameter of the two methods is 0.5415 nm and 0.5425 nm respectively, which is in good agreement with the experiment data (0.5417 nm) reported. It indicates that this configuration is sufficient to satisfy the request of accuracy. 

These are all dimensionless combinations of the density and the density gradients and Laplacians. This enables one to obtain the correct scaling properties of the exchange functional. We plot the quantities x and y for the krypton atom in Fig. 12. The exchange energy density within the LDA is given by... 

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