Hartree-Fock theory, localized

What does this mean We have replaced the non-local and therefore fairly complicated exchange term of Hartree-Fock theory as given in equation (3-3) by a simple approximate expression which depends only on the local values of the electron density. Thus, this expression represents a density functional for the exchange energy. As noted above, this formula was originally explicitly derived as an approximation to the HF scheme, without any reference to density functional theory. To improve the quality of this approximation an adjustable, semiempirical parameter a was introduced into the pre-factor Cx which leads to the Xa or Hartree-Fock-Slater (HFS) method which enjoyed a significant amount of popularity among physicists, but never had much impact in chemistry,... 

Becke, A. D., 1993a, A New Mixing of Hartree-Fock and Local Density-Functional Theories , J. Chem. Phys., 98, 1372. 

Hartree-Fock and local density functional theory... 

In equation 6, pi r) is the electronic density of orbital i, having energy e . The formalism of Hartree-Fock theory (within the framework of which eqnation 6 was proposed) and Koopmans theorem provide support for interpreting 7(r) as the local ionization energy, which focuses upon the point in space rather than an orbital. 

Equations (3.20) and (3.21) represent an identity in Hartree-Fock theory. (The Hellmann-Feynman and virial theorems are satisfied by Hartree-Fock wavefunc-tions.) The particular interest offered by (3.21) lies in the fact that 7 = 1 appears to be the characteristic homogeneity of both Thomas-Fermi [62,75,76] and local density functional theory [77], in which case (3.20) gives the Ruedenberg approximation [78], E = v,e,-, while (3.21) gives the Politzer formula [79], E = Vne-... 

A. Kafafi and E. R. H. El-Gharkawy,/. Phys. Chem. A, 102,3202 (1998). A Simple Coupling Scheme Between Hartree-Fock and Local Spin-Density Functional Theories. 

In the present chapter, we review the pericyclic reactions studied with DFT methods to date. Local, nonlocal, and hybrid DFT methods have been used to study the parent systems of the most important pericyclic reactions. These results are compared with results of Hartree-Fock theory, post-Hartree-Fock calculations, and available experimental data. Our aim is to provide an overview... 

The development of the best method for constructing cluster models for solids has concerned many researchers. Gilbert (1972) and Adams (1962) independently developed a Hartree-Fock theory of localized or-... 

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