Exact exchange

In principle, DFT calculations with an ideal exchange-correlation fiinctional should provide consistently accurate energetics. The catch is, of course, that the exact exchange-correlation fiinctional is not known. 

Equation (3.74) is the exact exchange energy (obtained from the Slater determinant the Kohn-Sham orbitals), is the exchange energy under the local spin densit) ... 

Pisani C and R Dovesi 1980. Exact-Exchange Hartree-Fock Calculations for Periodic Systems. I. Illustration of the Method. International Journal of Quantum Chemistry XVII 501-516. 

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. 

The calculated dipole moment is remarkably insensitive to the size of the basis set. Note that the SVWN value in this case is substantially better than BLYP and BPW91, i.e. this is a case where the theoretically poorer method provides better results than the more advanced gradient methods. Inclusion of exact exchange again improves the performance, and provides results very close to the experimental value, even with quite small basis sets. 

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