Enhanced von Weizsäcker WangGovindCarter kinetic energy density functional for semiconductors
Abstract
We propose a new form of orbitalfree (OF) kinetic energy density functional (KEDF) for semiconductors that is based on the WangGovindCarter (WGC99) nonlocal KEDF. We enhance within the latter the semilocal von Weizsäcker KEDF term, which is exact for a single orbital. The enhancement factor we introduce is related to the extent to which the electron density is localized. The accuracy of the new KEDF is benchmarked against KohnSham density functional theory (KSDFT) by comparing predicted energy differences between phases, equilibrium volumes, and bulk moduli for various semiconductors, along with metalinsulator phase transition pressures. We also compare point defect and (100) surface energies in silicon for a broad test of its applicability. This new KEDF accurately reproduces the exact noninteracting kinetic energy of KSDFT with only one additional adjustable parameter beyond the three parameters in the WGC99 KEDF; it exhibits good transferability between semiconducting to metallic silicon phases and between various IIIV semiconductors without parameter adjustment. Overall, this KEDF is more accurate than previously proposed OF KEDFs (e.g., the HuangCarter (HC) KEDF) for semiconductors, while the computational efficiency remains at the level of the WGC99 KEDF (several hundred times faster than the HC KEDF). This accurate, fast, and transferable newmore »
 Authors:
 Department of Chemistry, Princeton University, Princeton, New Jersey 085441009 (United States)
 Department of Mechanical and Aerospace Engineering, Program in Applied and Computational Mathematics, and Andlinger Center for Energy and the Environment, Princeton University, Princeton, New Jersey 085445263 (United States)
 Publication Date:
 OSTI Identifier:
 22253115
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Chemical Physics; Journal Volume: 140; Journal Issue: 18; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; ACCURACY; DENSITY FUNCTIONAL METHOD; EFFICIENCY; ELECTRON DENSITY; KINETIC ENERGY; PHASE TRANSFORMATIONS; POINT DEFECTS; SEMICONDUCTOR MATERIALS; SILICON; SIMULATION; SURFACE ENERGY
Citation Formats
Shin, Ilgyou, and Carter, Emily A., Email: eac@princeton.edu. Enhanced von Weizsäcker WangGovindCarter kinetic energy density functional for semiconductors. United States: N. p., 2014.
Web. doi:10.1063/1.4869867.
Shin, Ilgyou, & Carter, Emily A., Email: eac@princeton.edu. Enhanced von Weizsäcker WangGovindCarter kinetic energy density functional for semiconductors. United States. doi:10.1063/1.4869867.
Shin, Ilgyou, and Carter, Emily A., Email: eac@princeton.edu. Wed .
"Enhanced von Weizsäcker WangGovindCarter kinetic energy density functional for semiconductors". United States.
doi:10.1063/1.4869867.
@article{osti_22253115,
title = {Enhanced von Weizsäcker WangGovindCarter kinetic energy density functional for semiconductors},
author = {Shin, Ilgyou and Carter, Emily A., Email: eac@princeton.edu},
abstractNote = {We propose a new form of orbitalfree (OF) kinetic energy density functional (KEDF) for semiconductors that is based on the WangGovindCarter (WGC99) nonlocal KEDF. We enhance within the latter the semilocal von Weizsäcker KEDF term, which is exact for a single orbital. The enhancement factor we introduce is related to the extent to which the electron density is localized. The accuracy of the new KEDF is benchmarked against KohnSham density functional theory (KSDFT) by comparing predicted energy differences between phases, equilibrium volumes, and bulk moduli for various semiconductors, along with metalinsulator phase transition pressures. We also compare point defect and (100) surface energies in silicon for a broad test of its applicability. This new KEDF accurately reproduces the exact noninteracting kinetic energy of KSDFT with only one additional adjustable parameter beyond the three parameters in the WGC99 KEDF; it exhibits good transferability between semiconducting to metallic silicon phases and between various IIIV semiconductors without parameter adjustment. Overall, this KEDF is more accurate than previously proposed OF KEDFs (e.g., the HuangCarter (HC) KEDF) for semiconductors, while the computational efficiency remains at the level of the WGC99 KEDF (several hundred times faster than the HC KEDF). This accurate, fast, and transferable new KEDF holds considerable promise for largescale OFDFT simulations of metallic through semiconducting materials.},
doi = {10.1063/1.4869867},
journal = {Journal of Chemical Physics},
number = 18,
volume = 140,
place = {United States},
year = {Wed May 14 00:00:00 EDT 2014},
month = {Wed May 14 00:00:00 EDT 2014}
}

We propose a kinetic energy density functional scheme with nonlocal terms based on the von Weizsaecker functional, instead of the more traditional approach where the nonlocal terms have the structure of the ThomasFermi functional. The proposed functionals recover the exact kinetic energy and reproduce the linear response function of homogeneous electron systems. In order to assess their quality, we have tested the total kinetic energies as well as the kinetic energy density for atoms. The results show that these nonlocal functionals give as good results as the most sophisticated functionals in the literature. The proposed scheme for constructing the functionalsmore »

Functional derivative of noninteracting kinetic energy density functional
Proofs from different theoretical frameworks, namely, the HohenberghKohn theorems, the KohnSham scheme, and the firstorder density matrix representation, have been presented in this paper to show that the functional derivative of the noninteracting kinetic energy density functional can uniquely be expressed as the negative of the KohnSham effective potential, arbitrary only to an additive orbitalindependent constant. Key points leading to the current result as well as confusion about the quantity in the literature are briefly discussed. 
Kineticenergy density functional: Atoms and shell structure
We present a nonlocal kineticenergy functional which includes an anisotropic average of the density through a symmetrization procedure. This functional allows a better description of the nonlocal effects of the electron system. The main consequence of the symmetrization is the appearance of a clear shell structure in the atomic density profiles, obtained after the minimization of the total energy. Although previous results with some of the nonlocal kinetic functionals have given incipient structures for heavy atoms, only our functional shows a clear shell structure for most of the atoms. The atomic total energies have a good agreement with the exactmore » 
Densitygradient expansion of the kineticenergy functional for molecules
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Comment on 'Kinetic energy as a density functional'
In a recent paper, Nesbet [Phys. Rev. A 65, 010502(R) (2001)] has proposed dropping ''the widespread but unjustified assumption that the existence of a groundstate density functional for the kinetic energy, T{sub s}[{rho}], of an Nelectron system implies the existence of a densityfunctional derivative, {delta}T{sub s}[{rho}]/{delta}{rho}(r), equivalent to a local potential function,'' because, according to his arguments, this derivative 'has the mathematical character of a linear operator that acts on orbital wave functions'. Our Comment demonstrates that the statement called by Nesbet an 'unjustified assumption' happens, in fact, to be a rigorously proven theorem. Therefore, his previous conclusions stemming frommore »