Exchange potential Slater

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 ... 

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. 

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... 

The exchange potential of Equation 7.31 is called the Slater potential [12], because it was Slater who had proposed [18] that the nonlocal exchange potential of HF theory can be replaced by the potential... 

The key to understanding the difference between the Slater potential and the exact exchange potential lies in the explicit dependence of the Fermi hole pjr, r ) on... 

Here ip is an orbital of an electron with Mg = 1/2(t), e is its one-electron energy, is the classical Coulomb potential (including electron self-interaction terms), and represents the effects of electron exchange. In Slater s model, this is related to p h, the local density of electrons of the same spin... 

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... 

The main difficulty in solving the Hartree-Fock equation is caused by the non-local character of the potential in which an electron is orbiting. This causes, in turn, a complicated dependence of the potential, particularly of its exchange part, on the wave functions of electronic shells. There have been a number of attempts to replace it by a local potential, often having an analytical expression (e.g. universal Gaspar potential, Slater approximation for its exchange part, etc.). These forms of potential are usually employed to find wave functions when the requirements for their accuracy are not high or when they serve as the initial functions. 

This formula was used by Slater [385] to define an effective local exchange potential. The generally unsatisfactory results obtained in calculations with this potential indicate that the locality hypothesis fails for the density functional derivative of the exchange energy Ex [294],... 

For the self-consistent orbitals, we have determined1"4 the exact analytical asymptotic structure in the classically forbidden vacuum region of (i) the Slater potential VJ (r), (u) the functional derivative (exchange potential)... 

To determine the correlation-kinetic field and potential we assume the KS exchange-potential vx(r) to bejthat derived6,7 by restricted differentiation of the exchange energy functional Ex [p]. The resulting expression for the potential which is in terms of the density p(r) and Slater potential Vx (r) is... 

The three terms represent nuclear, coulomb and exchange-correlation potentials respectively. The third, problematic, term is written as a functional of the density. The same problem which occured in the Hartree-Fock simulation of atomic structure was overcome by defining the one-electron exchange potential with the Slater approximation for a uniform electron gas ... 

The DV-Xx cluster method [11], which is one of the first principle molecular orbital calculation methods, was used for the calculation of the electronic state of the Li3N crystal. In this method, Slater s exchange potential was used [12],... 

Another reason for the choice of the title is the above-mentioned introduction of the Xa-method and the MS-Xa method by Slater and coworkers. There are, however, in particular two other reasons for choosing the title. The first is the formulation of the Density Functional Theory by Hohenberg and Kohn in 1964 [19], which today is probably one of the most quoted papers in electronic structure calculations. This basic work was followed by another important paper in 1965 by Kohn and Sham [20], where they showed how one could use the method for practical calculations and introduced the Kohn-Sham, KS, exchange potential. Exactly the same expression for the exchange potential had previously been derived by Caspar [21], This exchange potential is therefore often known as the Caspar-Kohn-Sham, GKS, potential. Another very important reason for choice of the title is the introduction of the three dimensional numerical integration method by Ellis and Painter in 1968-1970 [22-24]. This... 

The calculation of x-ray emission spectra of molecules or solids are one of the most successful applications of the discrete variational (DV) Hartree-Fock-Slater (Xa) MO method using cluster approximation [8-10], which was originally coded by Ellis and his CO workers [11-14] based on Slater s Xa exchange potential [15]. The DV-Xa method has several advantages for the calculation of x-ray transition process as follows. 

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