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arXiv:cond-mat/0701377 · Journal of Physics A Mathematical and General

An analytic expression for the electronic correlation term of the kinetic functional

Luigi Delle Site

Published Mar 8, 2006• 12 citations
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Abstract

We propose an analytic formula for the non-local Fisher information functional, or electronic kinetic correlation term, appearing in the expression of the kinetic density functional. Such an explicit formula is constructed on the basis of well-founded physical arguments and a rigorous mathematical prescription.
DOI
10.1088/0305-4470/39/12/013

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In a previous work (Ghiringhelli L. M. and Delle Site L., Phys. Rev. B , 77 (2008) 073104) we have proposed a methodological approach to determine the electron correlations contained in the kinetic functional. Its application to the test case of an almost uniform interacting electron gas led to a local density functional of the form ∫ρ( r )lnρ( r )d r . In this work we discuss the interpretation of such a result by performing an analysis of the formal and numerical properties of the functional under the process of coordinates' scaling. On the basis of such an analysis we propose a local analytic form of the kinetic functional of which the previous numerical result is a first-order approximation.
In a previous work [L. Delle Site, J. Phys. A: Math. Theor. 40, 2787 (2007)], the derivation of an analytic expression for the kinetic functional of a many-body electron system has been proposed. Though analytical, the formula is still nonlocal (multidimensional) and thus not ideal for numerical applications. In this work, by treating the test case of a uniform gas of interacting spinless electrons, we propose a computational protocol which combines the previous analytic results with the Monte Carlo sampling of electronic configurations in space. This, we show, leads to an internally consistent scheme to design well founded local kinetic functionals.