Exact exchange functionals

For this PP calculation the exact Ex has been combined with the LDA for Ec. In spite of the use of the exact exchange functional, FeO is predicted to be a metal, in contrast to experiment. At present, it is not clear whether this failure to reproduce the insulating ground state of FeO originates from the use of the LDA for Ec or from the technical limitations of the PP calculation (KLI approximation for vx, only three special it-points for the integration over the Brillouin zone, 3s elections in the core). It must be emphasized, however, that the band structure shown in Figure 4.6 is rather different from its LDA counterpart (Dufek et al. 1994), which emphasizes the importance of the exact vx for this system. 

Neither the LDA nor the GGA can mediate the long-range force generated by virtual excitations. Not only the exact exchange functional is very nonlocal, but also the exact correlation functional. 

This statement has to be taken with care, for it certainly depends on the approximation for the exchange-correlation potential. For example, it holds when using the local-density approximation or any of the generalized gradient approximations. However, if we use the exact exchange functional, the calculations are at least as computationally demanding as in Hartree-Fock. 

A. D. Becke, Density-functional thermochemistry. III. The role of exact exchange, /. Chem. Phys., 98, 5648 (1993). 

Models which include exact exchange are often called hybrid methods, the names Adiabatic Connection Model (ACM) and Becke 3 parameter functional (B3) are examples of such hybrid models defined by eq. (6.35). The <, d and parameters are determined by fitting to experimental data and depend on the form chosen for typical values are a 0.2, d 0.7 and c 0.8. Owing to the substantially better performance of such parameterized functionals the Half-and-Half model is rarely used anymore. The B3 procedure has been generalized to include more filling parameters, however, the improvement is rather small. 

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