Abstract:
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.

Abstract:
We report results from ab-initio, self-consistent density functional theory (DFT) calculations of electronic, transport, and related properties of chromium disilicide (CrSi_{2}) 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.

Abstract:
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.

Abstract:
An oversight of several previous results from local density approximation (LDA) calculations appear to have led to an incomplete, and hence misleading, characterization of the capability of density functional theory (DFT) to describe correctly the electronic properties of wurtzite GaN (w-GaN) and InN (w-InN) [Phys. Rev. B 82, 115102 (2010)]. These comments are aimed at presenting a different picture of the above capability for DFT calculations that solve self-consistently the system of equations of DFT. They also underscore, in light of the experimentally established Burstein-Moss effect, the need to specify the carrier density when citing a band gap for w-InN.

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.

Abstract:
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 Γ to a conduction band minimum between Г and X, for a room temperature lattice constant of 5.152 Å. 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 ±？1.8 GPa). Our predicted equilibrium lattice constant and band gap, at zero temperature, are 5.0438 Å and 5.4 eV, respectively.

Abstract:
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 Å and c = 4.3772 Å 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.

Abstract:
We utilized a simple, robust, first principle method, based on basis set optimization with the BZW-EF method, to study the electronic and related properties of transition metal mono-nitrides: ScN and YN. We solved the KS system of equations self-consistently within the linear combination of atomic orbitals (LCAO) formalism. It is shown that the band gap and low energy conduction bands, as well as elastic and structural properties, can be calculated with a reasonable accuracy when the LCAO formalism is used to obtain an optimal basis. Our calculated, indirect electronic band gap (EΓ Xg) is 0.79 (LDA) and 0.88 eV (GGA) for ScN. In the case of YN, we predict an indirect band gap (EΓ Xg) of 1.09 (LDA) and 1.15 eV (GGA). We also calculated the equilibrium lattice constants, the bulk moduli (Bo), effective masses, and elastic constants for both systems. Our calculated values are in excellent agreement with experimental ones where the latter are available.

Abstract:
We report self-consistent ab-initio electronic, structural, elastic, and optical properties of cubic SrTiO3 perovskite. Our non-relativistic calculations employed a generalized gradient approximation (GGA) potential and the linear combination of atomic orbitals (LCAO) formalism. The distinctive feature of our computations stem from solving self-consistently the system of equations describing the GGA, using the Bagayoko-Zhao-Williams (BZW) method. Our results are in agreement with experimental ones where the later are available. In particular, our theoretical, indirect band gap of 3.24 eV, at the experimental lattice constant of 3.91 , is in excellent agreement with experiment. Our predicted, equilibrium lattice constant is 3.92 , with a corresponding indirect band gap of 3.21 eV and bulk modulus of 183 GPa.

Abstract:
We report calculated, electronic and related properties of wurtzite and zinc blende gallium nitrides (w-GaN, zb-GaN). We employed a local density approximation (LDA) potential and the linear combination of atomic orbital (LCAO) formalism. The implementation of this formalism followed the Bagayoko, Zhao, and Williams (BZW) method, as enhanced by Ekuma and Franklin (BZW-EF). The calculated electronic and related properties, for both structures of GaN, are in good agreement with corresponding, experimental data, unlike results from most previous ab initio calculations utilizing a density functional theory (DFT) potential. These results include the electronic energy bands, the total and partial densities of states (DOS and pDOS), and effective masses for both structures. The calculated band gap of 3.29 eV, for w-GaN, is in agreement with experiment and is an average of 1.0 eV larger than most previous ab-initio DFT results. Similarly, the calculated band gap of zb-GaN of 2.9 eV, for a room temperature lattice constant, is the ab-initio DFT result closest to the experimental value.