On the minimizer of the Thomas-Fermi-Dirac-von Weizsäcker model

Wahyuni, Siti; Dwandaru, Wipsar Sunu Brams; Rosyid, Muhammad Farchani

doi:10.1088/1742-6596/539/1/012015

Cited by 1 publication

(3 citation statements)

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“…Wahyuni et.al. [8] have found the estimate of the minimizer for TFDW model of electrons in the influence of an external potential, without "touching" the associate Euler-Lagrange equation, the so-called direct method.…”

Section: Introductionmentioning

confidence: 99%

“…[8] have shown that this minimizer function is bounded from above by the "umbrella" function b(x) which depends on the external potential V (x). This function is given by…”

Section: Introductionmentioning

confidence: 99%

“…This current work is a part of our continued work as in [8]. We want to find out the application of this direct methods to crystal physics by making use of the umbrella function to estimate the minimizer of the TFDW functional of NaCl crystal lattice.…”

Section: Introductionmentioning

confidence: 99%

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Estimation of the Minimizer of the Thomas-Fermi-Dirac-von Weizsäcker Functional of NaCl Crystal Lattice

Wahyuni

Dwandaru

Rosyid

2016

J. Phys.: Conf. Ser.

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Abstract. Estimation of the minimizer of the Thomas-Fermi-Dirac-von Weizsäcker functional of NaCl crystal lattice is calculated by making use of a direct method we have developed recently. The method is referred to as direct method for the reason that in the course of the calculation of the estimation, we do not derive the Euler-Lagrange equation at all. By using the graph of the umbrella functions, the estimation of the minimizer function is represented. The minimizer is bounded from above by the umbrella functions. IntroductionThe Thomas-Fermi (TF) theory was proposed by Thomas and Fermi independently in 1927. Dirac introduced the exchange correction to the theory in 1930, so that the corrected model is called the Thomas-Fermi-Dirac (TFD). Then the gradient correction of the kinetic energy was added by von Weizsäcker in 1935, so that it is called the Thomas-Fermi-von Weizsäcker (TFW) model. Those theories were placed on a firm mathematical footing by Lieb [1]. Although the Thomas-Fermi-Dirac-von Weizsäcker (TFDW) theory has not been studied as extensively as other theories, some authors studied it, such as Engel and Dreizler [2], who presented an accurate numerical solution of the variational equation resulting from the standard TFDW energy functional plus fourth-order gradient terms of the kinetic energy.Chan et.al.[3] perform a numerical study of the TFDW theory in finite systems to gain an understanding of the variational behavior of kinetic energy functionals. Their findings indicate that the TFDW theory can give an approximate description of matter, with atomic energies, binding energies, and bond lengths of the correct order of magnitude, though not to the accuracy required of a qualitative chemical theory.Zhuravlev et.al.[4] calculate valence electron densities in series of crystal substances MA (M = Li, Na, K, Rb, Ag, Mg, Ca; A = F, Cl, Br, O, S) with a NaCl lattice using the ab initio local DFT method combined with the ab initio pseudopotential technique. They found that systematic variations of valence electron density are depending on the atomic number of anion and cation.

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Section: Introductionmentioning

confidence: 99%

“…[8] have shown that this minimizer function is bounded from above by the "umbrella" function b(x) which depends on the external potential V (x). This function is given by…”

Section: Introductionmentioning

confidence: 99%