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Title: Enhanced von Weizsäcker Wang-Govind-Carter kinetic energy density functional for semiconductors

Abstract

We propose a new form of orbital-free (OF) kinetic energy density functional (KEDF) for semiconductors that is based on the Wang-Govind-Carter (WGC99) nonlocal KEDF. We enhance within the latter the semi-local 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 Kohn-Sham density functional theory (KSDFT) by comparing predicted energy differences between phases, equilibrium volumes, and bulk moduli for various semiconductors, along with metal-insulator 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 non-interacting 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 III-V semiconductors without parameter adjustment. Overall, this KEDF is more accurate than previously proposed OF KEDFs (e.g., the Huang-Carter (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 » KEDF holds considerable promise for large-scale OFDFT simulations of metallic through semiconducting materials.« less

Authors:
 [1];  [2]
  1. Department of Chemistry, Princeton University, Princeton, New Jersey 08544-1009 (United States)
  2. 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 08544-5263 (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., E-mail: eac@princeton.edu. Enhanced von Weizsäcker Wang-Govind-Carter kinetic energy density functional for semiconductors. United States: N. p., 2014. Web. doi:10.1063/1.4869867.
Shin, Ilgyou, & Carter, Emily A., E-mail: eac@princeton.edu. Enhanced von Weizsäcker Wang-Govind-Carter kinetic energy density functional for semiconductors. United States. doi:10.1063/1.4869867.
Shin, Ilgyou, and Carter, Emily A., E-mail: eac@princeton.edu. Wed . "Enhanced von Weizsäcker Wang-Govind-Carter kinetic energy density functional for semiconductors". United States. doi:10.1063/1.4869867.
@article{osti_22253115,
title = {Enhanced von Weizsäcker Wang-Govind-Carter kinetic energy density functional for semiconductors},
author = {Shin, Ilgyou and Carter, Emily A., E-mail: eac@princeton.edu},
abstractNote = {We propose a new form of orbital-free (OF) kinetic energy density functional (KEDF) for semiconductors that is based on the Wang-Govind-Carter (WGC99) nonlocal KEDF. We enhance within the latter the semi-local 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 Kohn-Sham density functional theory (KSDFT) by comparing predicted energy differences between phases, equilibrium volumes, and bulk moduli for various semiconductors, along with metal-insulator 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 non-interacting 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 III-V semiconductors without parameter adjustment. Overall, this KEDF is more accurate than previously proposed OF KEDFs (e.g., the Huang-Carter (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 large-scale 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 Thomas-Fermi 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 » means a step ahead in the field of fully nonlocal kinetic energy functionals, because they are capable of giving better local behavior than the semilocal functionals, yielding at the same time accurate results for total kinetic energies. Moreover, the functionals enjoy the possibility of being evaluated as a single integral in momentum space if an adequate reference density is defined, and then quasilinear scaling for the computational cost can be achieved.« less
  • Proofs from different theoretical frameworks, namely, the Hohenbergh-Kohn theorems, the Kohn-Sham scheme, and the first-order 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 Kohn-Sham effective potential, arbitrary only to an additive orbital-independent constant. Key points leading to the current result as well as confusion about the quantity in the literature are briefly discussed.
  • We present a nonlocal kinetic-energy 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 » calculations. Discussion of the chemical potential and the first ionization potential in atoms is included. The functional is also extended to spin-polarized systems. {copyright} {ital 1996 The American Physical Society.}« less
  • The gradient expansion of the molecular kinetic-energy functional is assessed through numerical results for fourteen diatomic and polyatomic molecules. The correlation of the dissociation energies (D/sub e/) of molecules with the Weizsacker contribution to the kinetic energy (T/sub W/) is established through a plot of D/sub e//N/sup 2/ against T/sub W/ where N is the number of electrons. The conclusions support and extend the observations of Allan, et al. (J. Chem. Phys. 83, 4562 (1985)).
  • 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 ground-state density functional for the kinetic energy, T{sub s}[{rho}], of an N-electron system implies the existence of a density-functional 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 » his different view of this derivative, which undermined the foundations of density-functional theory, can be discounted.« less