Fock exchange functional

In this section we will approach the question which is at the very heart of density functional theory can we possibly replace the complicated N-electron wave function with its dependence on 3N spatial plus N spin variables by a simpler quantity, such as the electron density After using plausibility arguments to demonstrate that this seems to be a sensible thing to do, we introduce two early realizations of this idea, the Thomas-Fermi model and Slater s approximation of Hartree-Fock exchange defining the X(/ method. The discussion in this chapter will prepare us for the next steps, where we will encounter physically sound reasons why the density is really all we need. 

Barone, V., 1994, Inclusion of Hartree-Fock Exchange in Density Functional Methods. Hyperfine Structure of Second Row Atoms and Hydrides , J. Chem. Phys., 101, 6834. 

Buhl, M., 1997, Density Functional Calculations of Transition Metal NMR Chemical Shifts Dramatic Effects of Hartree-Fock Exchange , Chem. Phys. Lett., 267, 251. 

BH HLYP Exchange functional with equal-weighted contributions of Hartree-Fock, local spin density, and Becke functionals and Lee, Yang, and Parr s correlation functionals... 

Laming, G. J., N. C. Handy, and W. H. Miller. 1995. Comparison of the Gaussian and Bessel Function Exchange Functionals with the Hartree-Fock Exchange for Molecules. J. Phys. Chem. 99, 1880. 

Lelj, F., C. Adamo, and V. Barone. 1994. Role of Hartree-Fock exchange in density functional theory. Some aspects of the conformational potential energy surface of glycine in the gas phase. Chem. Phys. Lett. 230, 189. 

These preliminary results indicate that the possibility of finding explicit functionals of the one-particle density for arbitrary systems is not too far away. Clearly, these constructive functionals are both symmetry as well as system-size dependent. In this sense, our constructive approach leads to energy density functionals which are not universal. Nevertheless, Eqs. (184) and (196) show (for the Hartree-Fock case) a remarkable structure for the kinetic energy and exchange functionals. A considerable part of these functionals is common to all systems, regardless of their symmetry or size. This property, can perhaps be favorably exploited in the construction of approximate energy density functionals. 

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