Understanding the Relativistic Generalization of Density Functional Theory (DFT) and Completing It in Practice

Bagayoko, Diola

doi:10.4236/jmp.2016.79083

Cited by 11 publications

(14 citation statements)

References 36 publications

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“…Those values, along with occupied energies, are the only ones that belong to the spectrum of the Hamiltonian [25]. Both the Rayleigh theorem [25,43] for eigenvalues and the second corollary of the first DFT theorem [25,31,33,43,44] explain the spurious nature of unoccupied energies lowered from their values obtained with the optimal basis set. The noted unphysically lowering of unoccupied energies, including some of the lowest laying ones, while the occupied energies do not change, is a plausible explanation of the quasi-universal underestimation of band gaps in the literature.…”

Section: Discussionmentioning

confidence: 98%

First Principle Investigation of Electronic, Transport, and Bulk Properties of Zinc-Blende Magnesium Sulfide

et al. 2020

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We have studied electronic, structural, and transport properties of zinc-blende magnesium sulfide (zb-MgS). We employed a local density approximation (LDA) potential and the linear combination of atomic orbitals (LCAO) method. Our computational method is able to reach the ground state of a material, as dictated by the second theorem of density functional theory (DFT). Consequently, our findings have the physical content of DFT and agree with available, corresponding experimental ones. The calculated band gap of zb-MgS, a direct gap equal to 4.43 eV, obtained at the experimental lattice constant of 5.620 Å, completely agrees with the experimental band gap of 4.45 ± 0.2 eV. We also report total (DOS) and partial (pDOS) densities of states, electron and hole effective masses, the equilibrium lattice constant, and the bulk modulus. The calculated pDOS also agree with the experiment for the description of the states at the top and the bottom of the valence and conduction bands, respectively.

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Section: Discussionmentioning

confidence: 98%

First Principle Investigation of Electronic, Transport, and Bulk Properties of Zinc-Blende Magnesium Sulfide

et al. 2020

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“…We employed the Ceperley and Alder’s [ 20 ] local density approximation potential, which was parameterized by Vosko et al [ 21 ]. Based on DFT, it fully minimized the energy functional with the Bagayoko, Zhao, and Williams (BZW) method [ 22 , 23 , 24 ], as enhanced by Ekuma and Franklin (BZW-EF) [ 25 , 26 , 27 , 28 ], while implementing the linear combination of atomic orbitals (LCAO). We employed a program package developed at the Ames Laboratory of the U.S. Department of Energy, Ames, Iowa [ 29 , 30 ].…”

Section: Computational Methods and Related Detailsmentioning

confidence: 99%

“…The first of the above referenced three (3) consecutive calculations, with the smallest basis set, provides the true DFT description of the material. The occupied energies of these calculations are unaffected (i.e., they do not change), however, the unoccupied energies from these calculations are either lower than or equal to their corresponding values produced with the optimal basis set [ 25 , 27 , 31 ]. In the discussion section, we address this extra-lowering of some unoccupied energies while the occupied ones remain unchanged.…”

Section: Computational Methods and Related Detailsmentioning

confidence: 99%

Ground State Properties of the Wide Band Gap Semiconductor Beryllium Sulfide (BeS)

et al. 2021

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We report the results from self-consistent calculations of electronic, transport, and bulk properties of beryllium sulfide (BeS) in the zinc-blende phase, and employed an ab-initio local density approximation (LDA) potential and the linear combination of atomic orbitals (LCAO). We obtained the ground state properties of zb-BeS with the Bagayoko, Zhao, and Williams (BZW) computational method, as enhanced by Ekuma and Franklin (BZW-EF). Our findings include the electronic energy bands, the total (DOS) and partial (pDOS) densities of states, electron and hole effective masses, the equilibrium lattice constant, and the bulk modulus. The calculated band structure clearly shows that zb-BeS has an indirect energy band gap of 5.436 eV, from Γ to a point between Γ and X, for an experimental lattice constant of 4.863 Å. This is in excellent agreement with the experiment, unlike the findings of more than 15 previous density functional theory (DFT) calculations that did not perform the generalized minimization of the energy functional, required by the second DFT theorem, which is inherent to the implementation of our BZW-EF method.

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“…We succinctly provide below the essential features of our computational approach. Extensive details on it are available in the literature [34][35][36][37][38][39][40][41]. As with most other calculations, we employed a density functional theory (DFT) potential and the linear combination of atomic orbitals (LCAO).…”

Section: Methods and Computational Detailsmentioning

confidence: 99%

“…With just two (2) consecutive calculations leading to the same occupied energies, these energies could represent a local minima and not the absolute ones. The first of the referenced three (3) consecutive calculations [34] is the one providing the DFT description of the material. The basis set for this calculation is dubbed the optimal basis set, i.e., the smallest basis set leading to the ground state charge density and energies.…”

Section: Methods and Computational Detailsmentioning

confidence: 99%

Accurate Ground State Electronic and Related Properties of Hexagonal Boron Nitride (h-BN)

Malozovsky¹,

Bamba²,

Stewart³

et al. 2020

JMP

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We present an ab-initio, self-consistent density functional theory (DFT) description of ground state electronic and related properties of hexagonal boron nitride (h-BN). We used a local density approximation (LDA) potential and the linear combination of atomic orbitals (LCAO) formalism. We rigorously implemented the Bagayoko, Zhao, and Williams (BZW) method, as enhanced by Ekuma and Franklin (BZW-EF). The method ensures a generalized minimization of the energy that is far beyond what can be obtained with self-consistency iterations using a single basis set. The method leads to the ground state of the material, in a verifiable manner, without employing over-complete basis sets. We report the ground state band structure, band gap, total and partial densities of states, and electron and hole effective masses of hexagonal boron nitride (h-BN). Our calculated, indirect band gap of 4.37 eV, obtained with room temperature experimental lattice constants of a = 2.504 Å and c = 6.661 Å, is in agreement with the measured value of 4.3 eV. The valence band maximum is slightly to the left of the K point, while the conduction band minimum is at the M point. Our calculated, total width of the valence and total and partial densities of states are in agreement with corresponding, experimental findings.

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Understanding the Relativistic Generalization of Density Functional Theory (DFT) and Completing It in Practice

Cited by 11 publications

References 36 publications

First Principle Investigation of Electronic, Transport, and Bulk Properties of Zinc-Blende Magnesium Sulfide

First Principle Investigation of Electronic, Transport, and Bulk Properties of Zinc-Blende Magnesium Sulfide

Ground State Properties of the Wide Band Gap Semiconductor Beryllium Sulfide (BeS)

Accurate Ground State Electronic and Related Properties of Hexagonal Boron Nitride (h-BN)

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