Slater exchange

This expression is not orbitally dependent. As such, a solution of the Hartree-Fock equation (equation (Al.3.18) is much easier to implement. Although Slater exchange was not rigorously justified for non-unifonn electron gases, it was quite successfiil in replicating the essential features of atomic and molecular systems as detennined by Hartree-Fock calculations. 

Kohn-Sham or Slater exchange was more accurate for realistic systems [H]. Slater suggested that a parameter be introduced that would allow one to vary the exchange between the Slater and Kolm-Sham values [19]. The parameter, a, was often... 

Inserting equation (6-14) into equation (6-12) retrieves the p4/3 dependence of the exchange energy indicated in equation (3-5). This exchange functional is frequently called Slater exchange and is abbreviated by S. No such explicit expression is known for the correlation part, ec. However, highly accurate numerical quantum Monte-Carlo simulations of the homogeneous electron gas are available from the work of Ceperly and Alder, 1980. 

Tschinke, V., andT. Ziegler. 1991. Gradient corrections to the Hartree-Fock-Slater exchange and their influence on bond energy calculations. Theor. Chim. Acta 81, 81. 

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... 

The integral of the first term in square brackets gives the non-relativistic Dirac-Slater exchange energy, the second giving the relativistic correction ... 

Within Slater s derivation, the value for the constant a is 1, and Eq. (8.7) defines so-called Slater exchange . 

The energy density Cxc is always treated as a sum of individual exchange and correlation contributions. Note that there is some potential for nomenclature confusion here because two different kinds of densities are involved the electron density is a per unit volume density, while tlie energy density is a per particle density. In any case, within this formalism, it is clear from inspection of Eq. (8.7) that the Slater exchange energy density, for example, is... 

Density functional theory, 21, 31, 245-246 B3LYP functional, 246 Hartree-Fock-Slater exchange, 246 Kohn-Sham equations, 245 local density approximation, 246 nonlocal corrections, 246 Density matrix, 232 Determinantal wave function, 23 Dewar benzene, 290 from acetylene + cyclobutadiene, 290 interaction diagram, 297 rearrangement to benzene, 290, 296-297 DFT, see Density functional theory... 

The non-relativistic DV-Xa calculation [21] was performed with the Slater exchange parameter, a = 0.7, for all atoms and with 50,000 DV sampling points, which provided a precision of less than 0.1 eV for valence electron energy eigenvalues. We employed the basis functions of the central nickel atom ls-4p orbitals, while those of the nitrogen and carbon atoms were used ls-2p orbitals. The calculations were carried out self-consistently until the difference in the orbital populations between the initial and final states of the iteration was less... 

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