Slater exchange approximation

The quest for various approximations for the exchange-correlation energy density/(p) has spanned decades in quantum chemistry and was recently reviewed [92]. Here, we will present the red line of its implementation, as it will be further used for the current applications. The benchmark density functional stands as the Slater exchange approximation, derived within the so-called Xa theory [179] ... 

Considerable improvement of molecular calculation was given by Becke s density gradient correction of the local spin density (or Slater exchange) approximation of the exchange energy [180] ... 

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. 

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... 

A density-functional molecular method with Slater s local exchange approximation, muffin-tin averaging of the potential, and a composite basis... 

The DV-Xa cluster method is a molecular orbital calculating method, assuming a Hartree-Fock-Slater (HFS) approximation. In this calculation, the exchange-correlation between electrons, is given by the following Slater s Xa potential. 

Here we use the self-consistent-charge (SCC) approximationto construct the coulomb potential Vc. The effective atomic charges are estimated by Mulliken population analysis and are spherically averaged around each nucleus. Then, they are superimposed to construct the molecular coulomb potential. For the exchange potential. Slater s approximation ... 

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... 

That Eq. (44) and Eq. (34) are different is due to the fact that GHF exchange is quadratic in the first-order density matrix, whereas Slater s approximation depends on the 4/3 power of the density. Only for the special case of a single determinantal wavefunction that has constant direction of S (i.e. for conventional but not generalized single determinants) can we regroup terms in Eq. (43) to yield Eq. (34). For this case N and S can be simplified as... 

The analysis of the results obtained showed the relevance of the inner shell polarization which was accounted for by the UHF calculations. Since a fully numerical four-component code including exchange was not at hand at that time the authors also had to analyze the impact of Slater s exchange approximation especially its transferability from the nonrelativistic to the relativistic realm. Shortly after these investigations Desclaux and Bessis presented fully numerical four-component calculations now substituting Slater s approximation by an explicit treatment of exchange and reported results for A and B values of Sc, Cu, Ga and Br [79]. 

When approximated or modelled, this potential is certain to be more complex than the simple Slater exchange potential Xa, LDA, LSD) and therefore will generate basis-function energy integrals... 

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