Exchange and correlation potential

The local density approximation is highly successful and has been used in density functional calculations for many years now. There were several difficulties in implementing better approximations, but in 1991 Perdew et al. successfully parametrised a potential known as the generalised gradient approximation (GGA) which expresses the exchange and correlation potential as a function of both the local density and its gradient ... 

Note that the operator fKS differs from the Fock operator f that we introduced in Section 1.3 in connection with the Hartree-Fock scheme only in the way the exchange and correlation potentials are treated. In the former, the non-classical contributions are expressed via the - in its exact form unknown - exchange-correlation potential Vxc, the functional derivative of Exc with respect to the charge density. In the latter, correlation is neglected... 

Density-functional theory, developed 25 years ago (Hohenberg and Kohn, 1964 Kohn and Sham, 1965) has proven very successful for the study of a wide variety of problems in solid state physics (for a review, see Martin, 1985). Interactions (beyond the Hartree potential) between electrons are described with an exchange and correlation potential, which is expressed as a functional of the charge density. For practical purposes, this functional needs to be approximated. The local-density approximation (LDA), in which the exchange and correlation potential at a particular point is only a function of the charge density at that same point, has been extensively tested and found to provide a reliable description of a wide variety of solid-state properties. Choices of numerical cutoff parameters or integration schemes that have to be made at various points in the density-functional calculations are all amenable to explicit covergence tests. 

An electron transferring across the metal surface first sustains the electrostatic coulomb potential due to the sinface potential, x, and then enters into the exchange and correlation potential field,, caused by the ion-electron and electron-electron... 

Levy M, March NH, Line-integral formulas for exchange and correlation potentials separately, submitted to Phys. Rev. A. 

Exchange and Correlation Potentials in a Line-Integral Form. 84... 

Determination of the Exchange and Correlation Potentials from Accurate Many-Body Wave Functions... 

The exchange and correlation potentials and are defined the functional derivatives with respect to the electron density of the corresponding functionals ... 

In this section we shall investigate the asymptotic form of the exchange and correlation potentials. It will be shown that Vi r) and ux a(r) approach each other exponentially fast for r —t oo, and that the difference between Fctr(r) and Ucjv r) decays exponentially as well. Using the notation of the last section the detailed statements read as follows ... 

In this section we shall demonstrate that the above rigorous properties of the full OEP discussed above are preserved by the KLI approximation. As for the OEP equation, we first write the KLI approximation (99) separately for the exchange and correlation potentials ... 

DF schemes in which the exchange and correlation potential is a function of the local electron density (or spin density)... 

At present the most frequently used parameterization for exchange and correlation are those of Perdew and Zunger [40] or Vosko, Wilk and Nusalr [41]. These two functionals which are based on the Monte Carlo simulations by Ceperly and Adler [42] give rather similar results. There are deficiencies in the LDA schemes which are due to the wrong asymptotic behaviour of the exchange and correlation potential since it falls off exponentially and not as... 

Table I. ASCF and STS core-level binding energies ( E and lei, respectively ) for free A1 atom, using various exchange and correlation potentials, (all energies are in eV) in comparison witli reference data.

The Local Density Approximation (LDA) replaces the exchange and correlation potential 14c > which is by essence non-local, by a local potential built from the properties of the homogeneous electron gas (HEG). At each point f of the inhomogeneous system, the exchange correlation energy is... 

It is also of relevance in the present context to note that the perturbation theory of Gorling and Levy [61] has been applied by Holas and March [62] to provide a calculational scheme for exact exchange and correlation potentials based on the equation of motion for the density matrix. 

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