Slater-Dirac exchange potential

This result was rediscovered by Slater (1951) with a slightly different numerical coefficient of C. Authors often refer to a term Vx which is proportional to the one-third power of the electron density as a Slater-Dirac exchange potential. 

While Dirac [3] chose to solve Eq. (4) as a quadratic equation for in terms of the Hartree potential yHC "), it was Slater in 1951 ([6] see also [4]) who chose an alternative, and more fruitful, route by regarding Eq. (4) as demonstrating that it could be viewed as a modified Hartree equation, with the Hartree potential Unfr) now supplemented by the exchange n -potential (the so-called Dirac-Slater (DS) exchange potential), to yield a total one-body potential energy... 

Just to remind you, the electron density and therefore the exchange potential are both scalar fields they vary depending on the position in space r. We often refer to models that make use of such exchange potentials as local density models. The disagreement between Slater s and Dirac s numerical coefficients was quickly resolved, and authors began to write the exchange potential as... 

This began with a landmark paper by Slater in which he proposed that the effects of exchange in the wave function could be replaced by an exchange potential, proportional to p where p is the electron density function. This followed earlier work by Dirac, in which he showed how to add the exchange energy to the Thomas-Fermi theory of the atom. The exchange potential is also dependent on a factor, cv, which is allowed to vary somewhat from its value in a uniform electron gas. The method is called the Xa method and involves solving a series of one-electron wave equations in a self-consistent manner. 

Electronic structure methods that use the electron density as the basic variable trace their origin to the Thomas-Permi [2], Thomas-Permi-Dirac [3], and related models [4-7] developed in the early years of quanmm mechanics. Many similarities with the present day DPT can be also found in Caspar s exchange potential [8] and Slater s Xa-methods [9-11]. By the 1960s, these precursors of DPT were fuUy developed and used extensively for the calculations of atoms and solids, but their impact on molecular quanmm chemistry remained insignificant. The Thomas-Permi and Thomas-Permi-Dirac models proved to be of little use in chemistry because they can never yield a lower... 

The atomic potentials for the heavy atoms were calculated by Liberman and coworkers using the Dirac Hamiltonian and statistical exchange potential somewhat smaller than that suggested by Slater. (D. Liberman, J. T. Waber, and D. T. Cromer, Phys, Rev, 1965, 137, A27 R. D. Cowan, A. C. Larson, D. Liberman,. B. Mann, and J. Waber, ibid., 1966, 144, 5). 

The two relativistic four-component methods most widely used in calculations of superheavy elements are the no-(virtual)pair DF (Coulomb-Breit) coupled cluster technique (RCC) of Eliav, Kaldor, and Ishikawa for atoms (equation 3), and the Dirac-Slater discrete variational method (DS/DVM) by Fricke for atoms and molecules. " Fricke s DS/DVM code uses the Dirac equation (3) approximated by a Slater exchange potential (DFS), numerical relativistic atomic DS wavefunctions, and finite extension of the nuclei. DFS calculations for the superheavy elements from Z = 100 to Z = 173 have been tabulated by Fricke and Soff. A review on various local density functional methods applied in superheavy chemistry has been given by Pershina. ... 

The so-called Hartree-Fock-Slater method is much more widely utilized, and is a hybrid of the Hartree and Thomas-Fermi-Dirac methods. In this method the direct part of the potential is calculated using the Hartree-Fock approach, whereas the exchange part is approximated by some statistical expression of the model of free electrons. The Slater potential is given by ... 

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