Slater local-exchange approximation

Density-functional theory has its conceptual roots in the Thomas-Fermi model of a uniform electron gas [325,326] and the Slater local exchange approximation [327]. A formalistic proof for the correctness of the Thomas-Fermi model was provided by Hohenberg-Kohn theorems, [328]. DFT has been very popular for calculations in sohd-state physics since the 1970s. In many cases DFT with the local-density approximation and plane waves as basis functions gives quite satisfactory results, for sohd-state calculations, in comparison to experimental data at relatively low computational costs when compared to other ways of solving the quantum-mechanical many-body problem. 

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

Improved calculational schemes were originally developed by the American physicists John C. Slater and Conyers Herring, using plane waves as basis sets. Slater used a muffin-tin potential, where the atomic wave functions inside the atomic spheres were fit to the plane waves. He was also the first person to use a viable local exchange approximation, which he called the Xa model. 

The following relatively simple expression is commonly used for the exchange-only energy under the local density approximation [Slater 1974] ... 

The application of density functional theory to isolated, organic molecules is still in relative infancy compared with the use of Hartree-Fock methods. There continues to be a steady stream of publications designed to assess the performance of the various approaches to DFT. As we have discussed there is a plethora of ways in which density functional theory can be implemented with different functional forms for the basis set (Gaussians, Slater type orbitals, or numerical), different expressions for the exchange and correlation contributions within the local density approximation, different expressions for the gradient corrections and different ways to solve the Kohn-Sham equations to achieve self-consistency. This contrasts with the situation for Hartree-Fock calculations, wlrich mostly use one of a series of tried and tested Gaussian basis sets and where there is a substantial body of literature to help choose the most appropriate method for incorporating post-Hartree-Fock methods, should that be desired. 

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... 

Local density approximation (LDA) with Slater s Xa functional for exchange (Ref. 57) and the functional of Vosko, Wilk, and Nusair (Ref. 109) for correlation. 

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... 

Approximate DFT approaches have been available for many decades. The most well known method to inorganic chemists is probably the Xa method first introduced by Slater and Johnson [15]. The Xa scheme utilises only the exchange part of the Local Density Approximation (9). 

Table 3 Calculated and experimental distances for Pa tf-CsHs)2 in A. HFS denotes Hartree-Fock with Slater Xa for exchange effects, whereas LDA is a local-density approximation, andBLYP, BP86, and PW91 are three different generalized-gradient approximations. Finally, X marks the center of the CgHg rings. The results are all taken from ref. 32...

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