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

In 2014, 50 years following the introduction of density functional theory (DFT), a rigorous understanding of it was published [AIP Advances, 4, 127,104 (2014)]. This understanding includes two features that complete the theory in practice, inasmuch as they are necessary for its correct application in electronic structure calculations;this understanding elucidates what appears to have been the crucial misunderstanding for 50 years, namely, the confusion between a stationary solution, attainable with most basis sets, following self-consistent iterations, with the ground state solution. The latter is obtained by a calculation that employs the well-defined optimal basis set for the system. The aim of this work is to review the above understanding and to extend it to the relativistic generalization of density functional theory by Rajagopal and Callaway [Phys. Rev. B7, 1912 (1973)]. This extension straightforwardly follows similar steps taken in the non-relativistic case, with the four-component current density, in the former, replacing the electronic charge density, in the latter. This new understanding, which completes relativistic DFT in practice, is expected to be needed for the study of heavy atoms and of materials (from molecules to solids) containing them—as is the case for some high temperature superconductors.

Accurate Electronic, Transport, and Bulk Properties of Zinc Blende Gallium Arsenide (Zb-GaAs)

We report accurate, calculated electronic, transport, and bulk properties of zinc blende gallium arsenide (GaAs). Our ab-initio, non-relativistic, self-con-sistent calculations employed a local density approximation (LDA) potential and the linear combination of atomic orbital (LCAO) formalism. We strictly followed the Bagayoko, Zhao, and William (BZW) method, as enhanced by Ekuma and Franklin (BZW-EF). Our calculated, direct band gap of 1.429 eV, at an experimental lattice constant of 5.65325 Å, is in excellent agreement with the experimental values. The calculated, total density of states data reproduced several experimentally determined peaks. We have predicted an equilibrium lattice constant, a bulk modulus, and a low temperature band gap of 5.632 Å, 75.49 GPa, and 1.520 eV, respectively. The latter two are in excellent agreement with corresponding, experimental values of 75.5 GPa (74.7 GPa) and 1.519 eV, respectively. This work underscores the capability of the local density approximation (LDA) to describe and to predict accurately properties of semiconductors, provided the calculations adhere to the conditions of validity of DFT.

Predictions of Electronic, Transport, and Structural Properties of Magnesium Sulfide (MgS) in the Rocksalt Structure

We report results from ab-initio, self-consistent density functional theory (DFT) calculations of electronic, transport and bulk properties of rock salt magnesium sulfide (MgS). In the absence of experimental data on these properties, except for the bulk modulus, these results are predictions. Our calculations utilized the Ceperley and Alder local density approximation (LDA) potential and the linear combination of Gaussian orbitals (LCGO). The key difference between our computations and other previous ab-initio DFT ones stems from our use of successively larger basis sets, in consecutive, self-consistent calculations, to attain the ground state of the material. We predicted an indirect (Γ-X) band gap of 3.278 eV for a room temperature lattice constant of 5.200Å. We obtained a predicted low temperature indirect (Γ-X) band gap of 3.512 eV, using the equilibrium lattice constant of 5.183Å. We found a theoretical value of 79.76 GPa for the bulk modulus;it agrees very well with the experimental finding of 78 ±3.7 GPa.

<i>Ab-Initio</i>Computations of Electronic, Transport, and Structural Properties of <i>zinc-blende</i>Beryllium Selenide (<i>zb</i>-BeSe)

We report results from several ab-initio computations of electronic, transport and bulk properties of zinc-blende beryllium selenide (zb-BeSe). Our nonrelativistic calculations utilized a local density approximation (LDA) potential and the linear combination of atomic orbitals (LCAO). The key distinction of our calculations from other DFT calculations is the implementation of the Bagayoko, Zhao and Williams (BZW) method, as enhanced by Ekuma and Franklin (BZW-EF), in the LCAO formalism. Our calculated, indirect band gap is 5.46 eV, from &Gamma;to a conduction band minimum between Г and X, for a room temperature lattice constant of 5.152 &Aring;. Available, room temperature experimental band gaps of 5.5 (direct) and 4 - 4.5 (unspecified) point to the need for additional measurements of this gap. Our calculated bulk modulus of 92.35 GPa is in excellent agreement with experiment (92.2 &plusmn;?1.8 GPa). Our predicted equilibrium lattice constant and band gap, at zero temperature, are 5.0438 &Aring;and 5.4 eV, respectively.

Accurate, First-Principle Study of Electronic and Related Properties of the Ground State of Li₂Se

We present results from ab-initio, self-consistent calculations of electronic and related properties for the ground state of cubic lithium selenide (Li2Se). We employed a local density approximation (LDA) potential and performed computations following the Bagayoko, Zhao, and Williams (BZW) method, as enhanced by Ekuma and Franklin (BZW-EF). This method verifiably leads to the ground state of materials without employing over-complete basis sets. We present the calculated electronic energies, total and partial densities of states, effective masses, and the bulk modulus. The present calculated band structures show clearly that cubic Li2Se has a direct fundamental energy band gap of 4.065 eV at the &Gamma;point for the room temperature experimental lattice constant of 6.017 &Aring;. This result is different from findings of previous density functional theory (DFT) calculations that uniformly reported an indirect band gap, from &Gamma;to X, for Li2Se. We predicted a direct band gap of 4.363 eV, at the computationally determined equilibrium lattice constant of 5.882 &Aring;, and a bulk modulus of 35.4 GPa. For the first time known to us, we report calculated electron and hole effective masses for Li2Se. The experimental confirmation of the large, direct gap we found will point to a potential importance of this material for ultraviolet technologies and applications. Due to a lack of experimental results, most of our calculated ones in this paper are predictions for Li2Se.

<i>Ab-Initio</i>Computations of Electronic, Transport, and Related Properties of Chromium Disilicide (CrSi₂)

We report results from ab-initio, self-consistent density functional theory (DFT) calculations of electronic, transport, and related properties of chromium disilicide (CrSi2) in the hexagonal C40 crystal structure. Our computations utilized the Ceperley and Alder local density approximation (LDA) potential and the linear combination of atomic orbitals (LCAO) formalism. As required by the second DFT theorem, our calculations minimized the occupied energies, far beyond the minimization obtained with self-consistency iterations with a single basis set. Our calculated, indirect band gap is 0.313 eV, at room temperature (using experimental lattice constants of a = 4.4276? and c = 6.368 ). We discuss the energy bands, total and partial densities of states, and electron and hole effective masses. This work was funded in part by the US Department of Energy, National Nuclear Security Administration (NNSA) (Award No. DE-NA0003679), the National Science Foundation (NSF) (Award No. HRD-1503226), LaSPACE, and LONI-SUBR.

Accurate Electronic, Transport, and Related Properties of Wurtzite Beryllium Oxide (w-BeO)

We report details of our ab-initio, self-consistent density functional theory (DFT) calculations of electronic and related properties of wurtzite beryllium oxide (w-BeO). Our calculations were performed using a local density approximation (LDA) potential and the linear combination of atomic orbitals (LCAO) formalism. Unlike previous DFT studies of BeO, the implementation of the Bagayoko, Zhao, and Williams (BZW) method, as enhanced by the work of Ekuma and Franklin (BZW-EF), ensures the full physical content of the results of our calculations, as per the derivation of DFT. We present our computed band gap, total and partial densities of states, and effective masses. Our direct band gap of 10.30 eV, reached by using the experimental lattice constants of a = 2.6979 &Aring;and c = 4.3772 &Aring;at room temperature, agrees very well the experimental values of 10.28 eV and 10.3 eV. The hybridization of O and Be p states in the upper valence bands, as per our calculated, partial densities of states, are in agreement with corresponding, experimental findings.

Energy Structure of Two-Dimensional Graphene-Semiconductor Quantum Dot

Graphene is a newly discovered material that possesses unique electronic properties. It is a two-dimensional singlelayered sheet in which the electrons are free and quasi-relativistic. These properties may open a door for many new electronic applications. In this paper we proposed a flat 2-dimensional circular graphene-semiconductor quantum dot. We have carried out theoretical studies including deriving the Dirac equation for the electrons inside the graphene-semiconductor quantum dot and solving the equation. We have established the energy structure as a function of the rotational quantum number and the size (radius) of the dot. The energy gap between the energy levels can be tuned with the radius of the quantum dot. It could be useful for quantum computation and single electron device application.

<i>Ab-Initio</i>Self-Consistent Density Functional Theory Description of Rock-Salt Magnesium Selenide (MgSe)

We report results on electronic, transport, and bulk properties of rock-salt magnesium selenide (MgSe), from density functional theory (DFT) calculations. We utilized a local density approximation (LDA) potential and the linear combination of atomic orbitals formalism (LCAO). We followed the Bagayoko, Zhao, and Williams (BZW) method, as enhanced by Ekuma and Franklin (BZW-EF), to perform a generalized minimization of the energy, down to the actual ground state of the material. We describe the successive, self-consistent calculations, with augmented basis sets, that are needed for this generalized minimization. Due to the generalized minimization, our results have the full, physical content of DFT, as per the second DFT theorem [AIP Advances, 4, 127104 (2014)]. Our calculated, indirect bandgap of 2.49 eV, for a room temperature lattice constant of 5.460 Å, agrees with experimental findings. We present the ground-state band structure, the related total and partial densities of states, DOS and PDOS, respectively, and electron and hole effective masses for the material. Our calculated bulk modulus of 63.1 GPa is in excellent agreement with the experimental value of 62.8 ± 1.6 GPa. Our predicted equilibrium lattice constant, at zero temperature, is 5.424 Å, with a corresponding indirect bandgap of 2.51 eV. We discuss the reasons for the agreements between our findings and available, corresponding, experimental ones, particularly for the band gap, unlike the previous DFT results obtained with ab-initio LDA or GGA potentials.

Ab Initio Calculation of Accurate Electronic and Transport Properties of Zinc Blende Gallium Antimonide (zb-GaSb)

This article reports the results of our investigations on electronic and transport properties of zinc blende gallium antimonide (zb-GaSb). Our ab-initio, self-consistent and non-relativistic calculations used a local density approximation potential (LDA) and the linear combination of atomic orbital formalism (LCAO). We have succeeded in performing a generalized minimization of the energy, using the Bagayoko, Zhao and Williams (BZW) method, to reach the ground state of the material while avoiding over-complete basis sets. Consequently, our results have the full physical content of density functional theory (DFT) and agree with available, corresponding experimental data. Using an experimental room temperature lattice constant of 6.09593?, we obtained a direct band gap of 0.751 eV, in good agreement with room temperature measurements. Our results reproduced the experimental locations of the peaks in the total density of valence states as well as the measured electron and hole effective masses. Hence, this work points to the capability of ab-initio DFT calculations to inform and to guide the design and the fabrication of semiconductor based devices—provided a generalized minimization of the energy is performed.