Beyond local density approximation

Perdew JP (1991b) Unified theory of exchange and correlation beyond local density approximation, in P.Ziesche and H.Eschrig (eds)., Electronic Structure of Solids 91, Akademie Verlag, Berlin, pll... 

T. Grabo, T. Kreibich, S. Kurth, and E. K.U. Gross, in The Strong Cotdomb Correlations and Electronic Structure Calculations Beyond Local Density Approximations, edited by V. Anisimov (Gordon and Breach, Amsterdam, 2000). 

Perdew, J. P., 1991, Unified Theory of Exchange and Correlation Beyond the Local Density Approximation , in Electronic Structure of Solids, P. Ziesche, H. Eschrig (eds.), Akademie Verlag, Berlin. 

Beyond the local-density approximation in calculations of Compton profiles... 

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. 

The time-dependent density functional theory [38] for electronic systems is usually implemented at adiabatic local density approximation (ALDA) when density and single-particle potential are supposed to vary slowly both in time and space. Last years, the current-dependent Kohn-Sham functionals with a current density as a basic variable were introduced to treat the collective motion beyond ALDA (see e.g. [13]). These functionals are robust for a time-dependent linear response problem where the ordinary density functionals become strongly nonlocal. The theory is reformulated in terms of a vector potential for exchange and correlations, depending on the induced current density. So, T-odd variables appear in electronic functionals as well. 

The simplest approximation to Fxc[p(r)L the bottom rung of the DFT Jacob s ladder, results from the local density approximation, LDA. In mathematics a local property of a function at a point on the surface (line, or two-dimensional surface, or hypersurface) that is defined by the function is a property that depends on the behavior of the function only in the immediate vicinity of the point [49]. Immediate vicinity can be taken to mean the region within an infinitesimal distance beyond the point. Consider the derivative at some point P on the line defined by plotting y = fix) against x. This property, the derivative or gradient, is the limit... 

Anisimov VI (ed.) (1999) Strong Coulomb Correlatins in Electronic Structure Calculations Beyond the Local Density Approximation. Gordon Breach, New York... 

Beyond the Local Density Approximation Gradient-corrected Functionals... 

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