Standard Local Density Approximation Research Articles

Empirical band-gap correction for LDA-derived atomic effective pseudopotentials

Atomic effective pseudopotentials enable atomistic calculations at the level of accuracy of density functional theory for semiconductor nanostructures with up to fifty thousand atoms. Since they are directly derived from ab-initio calculations performed in the local density approximation (LDA), they inherit the typical underestimated band gaps and effective masses. We propose an empirical correction based on the modification of the non-local part of the pseudopotential and demonstrate good performance for bulk binary materials (InP, ZnS, HgTe, GaAs) and quantum dots (InP, CdSe, GaAs) with diameters ranging from 1.0 nm to 4.45 nm. Additionally, we provide a simple analytic expression to obtain accurate quasiparticle and optical band gaps for InP, CdSe, and GaAs QDs, from standard LDA calculations.

Strongly constrained and appropriately normed density functional theory exchange-correlation functional applied to rare earth oxides

Density functional theory (DFT) is one of the main tools for studying the electronic structure of solids and molecules. Nevertheless, one of the main drawbacks of the implementation of DFT is the so-called self-interaction error (SIE) that can yield undesired delocalization errors and ultimately results in the prediction of metals instead of experimentally observed insulators. These SIEs can be amended by using more evolved exchange-correlation functionals than standard local density approximation such as the recent meta-generalized gradient approximation strongly constrained and appropriately normalized (SCAN) functional that is successful in describing electronic properties of $3d$ transition metal oxides. Nevertheless, the ability of such a functional to describe electronic properties of materials involving more localized states such as $4f$ orbitals is rather elusive. Here, we show that, even though SCAN can sometimes predict the insulating character of some compounds, it often fails in predicting the correct band edge orbital character of insulators. By comparing our SCAN results with benchmark simulations obtained with more accurate hybrid DFT calculations, we ascribe this failure to insufficiently amended SIEs by SCAN that results in an underestimation of Hund's splitting associated with $4f$ states. Thus, although appropriate for $3d$ transition metal elements, the SCAN functional is not yet a sufficient platform for studying electronic properties of materials involving rare-earth elements where $4f$ states play a key role in the properties.

Density profile of noninteracting fermions in a rotating two-dimensional trap at finite temperature

We study the average density of $N$ spinless noninteracting fermions in a $2d$ harmonic trap rotating with a constant frequency $\Omega$ and in the presence of an additional repulsive central potential $\gamma/r^2$. The average density at zero temperature was recently studied in Phys. Rev. A $\textbf{103}$, 033321 (2021) and an interesting multi-layered "wedding cake" structure with a "hole" at the center was found for the density in the large $N$ limit. In this paper, we study the average density at finite temperature. We demonstrate how this "wedding-cake" structure is modified at finite temperature. These large $N$ results warrant going much beyond the standard Local Density Approximation. We also generalize our results to a wide variety of trapping potentials and demonstrate the universality of the associated scaling functions both in the bulk and at the edges of the "wedding-cake".

Determining anisotropic reactive facet of ilmenite photocatalyst with Hubbard U assisted density functional theory

Findings on favorable charge-transfer pathways have been challenged for the enhancing catalytic reaction because electrical and optical efficiency are influenced by the interfacial/surface environment on the crystal structure. Herein, the electric and optical peculiarities of ATiO3 ilmenite catalyst are investigated for the anisotropic charge pathways by density functional theory framework with Hubbard U (DFT + U). The uncertainty for the best Hubbard U is simulated for the lattice parameters and band gaps in ATiO3. Our simulation corrected by Hubbard U = 10 eV shows the best reliability for ATiO3 involving 30 atoms as a basis at constant ilmenite structure and concluded that Perdew-Burke-Ernzerhof functional performance overcomes the deficiency of standard local density approximation functionals. Anisotropic carrier mobility in the Brillouin zone is compared with DFT + U on A-site cation effects. Among the representative three kinds of cations, our result shows that NiTiO3 exhibits a good optical absorption performance with the dielectric function and absorption coefficient in the visible light range, especially along the b3 direction which facilitates the separation of photogenerated electron-hole pairs at the top side of the shape. Our computational approach suggests a high reactive crystal facet of transition metal oxide contributing to the viable approach for the efficient catalytic reaction.

Comparative study of magnetic and electronic properties of room‐temperature polar magnets ScFeO3 and InFeO3

We performed calculations based on collinear and non‐collinear spin density functional theory to investigate magnetic and electronic properties of new room‐temperature polar magnetic compounds AFeO3 (A = Sc, In). Exchange and correlation effects were simulated by standard local spin density approximation and the generalized gradient approximation. We determined that the canted G‐type antiferromagnetic (G‐AFM) structure of the Fe spin moments is the most stable magnetic structure for both compounds, in accordance with experimental facts. The calculated Fe spin magnetic moments and resulting weak ferromagnetic components perpendicular to the c‐axis also agree well with the experiment. The magnitude of the Fe spin moment does not depend on the fact if the G‐AFM structure is collinear or canted. The energy difference between these two structures is found to be much larger for InFeO3, so as the exchange interaction constant Jnn between nearest‐neighbor magnetic Fe ions. The ScFeO3 and InFeO3 electronic structures, which reproduce well their magnetic properties are presented and discussed. By comparing them with the band structures of some typical multiferroics, we conclude that different electronic mechanisms should be responsible for their ferroelectric distortion. In ScFeO3, the cause of this distortion should be attributed to the hybridization between almost empty Sc 3d and occupied O 2p states along the hexagonal c‐axis. For InFeO3, however, the stereochemical activity of the In 5s localized electrons should be the principal driving force for ferroelectric distortion.

Shrinking Self-Interaction Errors with the Fermi–Löwdin Orbital Self-Interaction-Corrected Density Functional Approximation

The self-interaction error (SIE) is one of the major drawbacks of practical exchange-correlation functionals for Kohn-Sham density functional theory. Despite this, the use of methods that explicitly remove SIE from approximate density functionals is scarce in the literature due to their relatively high computational cost and lack of consistent improvement over standard modern functionals. In this article we assess the performance of a novel approach recently proposed by Pederson, Ruzsinszky, and Perdew [ J. Chem. Phys. 2014, 140, 121103] for performing self-interaction free calculations in density functional theory based on Fermi orbitals. To this end, we employ test sets consisting of reaction energies that are considered particularly sensitive to SIE. We found that the parameter-free Fermi-Löwdin orbital self-interaction correction method combined with the standard local spin density approximation (LSDA) and Perdew-Burke-Ernzerhof (PBE) functionals gives a much better estimate of reaction energies compared to their parent LSDA and PBE functionals for most of the reactions in these two sets. They also perform on par with the global PBE0 and range-separated LC-ωPBE hybrids, which partially eliminate the SIE by including Hartree-Fock exchange. This shows the potential of the Fermi-Löwdin orbital self-interaction correction (FLOSIC) method for practical density functional calculations without SIE.

Importance of van der Waals interaction on structural, vibrational, and thermodynamic properties of NaCl

Thermal equations of state (EOS) are essential in several scientific domains. However, experimental determination of EOS parameters may be limited at extreme conditions, therefore, ab initio calculations have become an important method to obtain them. Density functional theory (DFT) and its extensions with various degrees of approximations for the exchange and correlation (XC) energy is the method of choice, but large errors in the EOS parameters are still common. The alkali halides have been problematic from the onset of this field and the quest for appropriate DFT functionals for such ionic and relatively weakly bonded systems has remained an active topic of research. Here we use DFT + van der Waals functionals to calculate vibrational properties, thermal EOS, thermodynamic properties, and the B1 to B2 phase boundary of NaCl with high precision. Our results reveal a remarkable improvement over the performance of standard local density approximation and generalized gradient approximation functionals for all these properties and phase transition boundary, as well as great sensitivity of anharmonic effects on the choice of XC functional.

Better band gaps for wide-gap semiconductors from a locally corrected exchange-correlation potential that nearly eliminates self-interaction errors

This work constitutes a comprehensive and improved account of electronic-structure and mechanical properties of silicon-nitride () polymorphs via van Leeuwen and Baerends (LB) exchange-corrected local density approximation (LDA) that enforces the exact exchange potential asymptotic behavior. The calculated lattice constant, bulk modulus, and electronic band structure of polymorphs are in good agreement with experimental results. We also show that, for a single electron in a hydrogen atom, spherical well, or harmonic oscillator, the LB-corrected LDA reduces the (self-interaction) error to exact total energy to ∼10%, a factor of three to four lower than standard LDA, due to a dramatically improved representation of the exchange-potential.

Shape similarity of charge-transfer (CT) excitation energy curves in a series of donor-acceptor complexes and its description with a transferable energy of CT orbital

A simple nature of charge-transfer (CT) in the prototype complexes Dp-F2 (Dp=NH3, H2O) manifests itself in a very close shape of their CT excitation energy curves ωCT(R) along the donor-acceptor separation R. It affords a simple orbital description in terms of the CT orbitals (CTOs) obtained with a transformation of the virtual orbitals of the standard local density approximation (LDA). The transferable energy of the relevant CTO as a function of R closely approximates the common shape of ωCT(R), while the height of the individual curve is determined with the ionization potential of Dp.

DFT, L(S)DA, LDA+U, LDA+DMFT, …, whether we do approach to a proper description of optical response for strongly correlated systems?

I present a critical overview of so-called “ab initio” DFT (density fuctional theory) based calculation schemes for the description of the electronic structure, energy spectrum, and optical response for strongly correlated 3d oxides, in particular, crystal-field and charge transfer transitions as compared with an “old” cluster model that does generalize crystal-field and ligand-field theory. As a most instructive illustration of validity of numerous calculation techniques I address the prototypical 3d insulator NiO predicted to be a metal in frames of a standard LDA (local density approximation) band theory.

Electronic structure and optical properties of magnesium tetraborate: An ab initio study

The structural, electronic and optical properties of important dosimeter material MgB4O7 have been analyzed on the basis of the first-principles density functional theory calculations. Optimizations of the crystal structure have been performed using the standard local density approximation for the exchange-correlation (XC) functional whereas the electronic structure and linear optical properties were calculated using the semi-local XC potential of Tran and Blaha. The calculated lattice constants and atomic positions are found to be in good agreement with the experimental values. The calculated band gap is found to be direct (Г→Г), with the value of 9.58eV, consistent with the values which were determined or estimated for similar compounds. The top of the valence band is dominated by the O 2p-states, while the conduction band bottom consists predominantly of the 2p-states of the B ions with trigonal coordination with neighboring O’s. Optical absorption spectrum is characterized by two prominent peaks. The lower energy peak originates from electron transitions within the trigonal BO structural groups, while the higher energy peak is determined by electron transitions within the tetrahedral BO groups and polyhedral MgO structural motifs. All calculated optical properties are found to be anisotropic.

Calculated high-pressure structural properties, lattice dynamics and quasi particle band structures of perovskite fluorides KZnF3, CsCaF3 and BaLiF3

A detailed study of the high-pressure structural properties, lattice dynamics and band structures of perovskite structured fluorides KZnF3, CsCaF3 and BaLiF3 has been carried out by means of density functional theory. The calculated structural properties including elastic constants and equation of state agree well with available experimental information. The phonon dispersion curves are in good agreement with available experimental inelastic neutron scattering data. The electronic structures of these fluorides have been calculated using the quasi particle self-consistent approximation. The calculations reveal that all the fluorides studied are wide band gap insulators, and the band gaps are significantly larger than those obtained by the standard local density approximation, thus emphasizing the importance of quasi particle corrections in perovskite fluorides.

Ab initio calculations of fundamental properties of SrTe1−x O x alloys

Structural, electronic, optical and thermodynamic properties of the SrTe1−x O x alloys (0 ≤ x ≤ 1) in rock-salt phase are calculated using the full potential-linearized augmented plane wave (FP-LAPW) method within density functional theory. The exchange-correlation potential for structural properties was calculated by the standard local density approximation (LDA) and GGA (PBE) and the new form of GGA (WC) which is an improved form of the most popular Perdew–Burke–Ernzerhof (PBE), while for electronic properties, in addition to LDA, GGA corrections; Engel–Vosko GGA (EV-GGA) and modified Becke–Johnson (mBJ) schemes were also applied. The results show that the use of GGA (WC) in our calculations is more appropriate than GGA and LDA and gives a good description of structural properties such as lattice parameters and bulk modulus. Our investigation on the effect of composition on lattice constant, bulk modulus and band gap for ternary alloys shows almost nonlinear dependence on the composition. In addition to FP-LAPW method, the composition dependence of the refractive index and the dielectric constant was studied by different models. On the other hand, the thermodynamic stability of this alloy was investigated by calculating the excess enthalpy of mixing ΔH m as well as the phase diagram.

Structural, electronic and thermodynamic properties of SrxCa1‐xS: A first‐principles study

AbstractThe principal purpose of this work is to further the understanding of the structural, electronic, and thermodynamic properties of the SrxCa1–xS alloys (0≤x ≤1) in Rock‐salt phase using the full potential augmented plane wave (FP‐LAPW) method within density functional theory. The exchange‐correlation potential for structural properties was calculated by the standard local density approximation (LDA) and GGA (PBE) and the new form of GGA (WC) which is an improved form of the most popular Perdew‐Burke‐Ernzerhof (PBE), while for electronic properties, the alternative form of GGA modified by Becke‐Johnson exchange correlation potential (MBJ) was also applied. It is shown that investigation on the effect of composition on lattice constant, bulk modulus, and band gap for ternary alloys shows almost nonlinear dependence on the composition. On the other hand, the thermodynamic stability of these alloys was investigated by calculating the excess enthalpy of mixing ΔHm as well as the phase diagram. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A comparative study of the electronic properties of aluminum nitride compounds

Electronic properties of aluminum nitride in wurtzite, zinc-blende, and rock-salt phases are investigated by a full potential-linearized augmented plane waves method based on density functional theory within standard local density approximation and its four improved versions. Local density approximation corrected by the generalized gradient functional of Perdew-Wang-Engel-Vosko is found to be more successful than the other generalized gradient functional approximations considered in this work for providing reasonable lattice constants, energy gaps, effective electron and hole masses, and optical features for AlN phases. Although local density approximation corrected by modified Becke-Johnson potential underestimates the static dielectric constants, it provides the largest energy gaps of AlN phases very close to the available experimental and theoretical ones reported by high-cost calculations in the literature. Hence, this approach is decided to be the most accurate scheme among other approximations of this work for electronic band structure calculations of aluminum nitride phases.

Ab initio study of the p-hole magnetism at polar surfaces of ZnO: the role of correlations

A standard local density approximation and its self-interaction corrected version are applied to study spontaneous magnetization, promoted by localized p electron holes, of polar oxygen-terminated ZnO surfaces. The electronic properties and magnetic exchange interactions of three different facets are calculated. It is demonstrated that partially filled oxygen p orbitals of the polar surfaces exhibit magnetic moment formation and long range magnetic order leading to the occurrence of a ferromagnetic ground state. Monte Carlo simulations predict Curie temperatures above room temperature. In contrast to isolated defects in bulk materials, applying correlation corrections to the localized p-like surface states does not lead to a collapse of magnetic interaction: as the weakening of the magnetic interaction, caused by the reduced electronic overlap, is compensated by a strengthening due to an increase of the magnetic moments, the ferromagnetism can principally persist above room temperature, provided a large hole concentration exists.

Derivative discontinuity and exchange-correlation potential of meta-GGAs in density-functional theory.

We investigate fundamental properties of meta-generalized-gradient approximations (meta-GGAs) to the exchange-correlation energy functional, which have an implicit density dependence via the Kohn-Sham kinetic-energy density. To this purpose, we construct the most simple meta-GGA by expressing the local exchange-correlation energy per particle as a function of a fictitious density, which is obtained by inverting the Thomas-Fermi kinetic-energy functional. This simple functional considerably improves the total energy of atoms as compared to the standard local density approximation. The corresponding exchange-correlation potentials are then determined exactly through a solution of the optimized effective potential equation. These potentials support an additional bound state and exhibit a derivative discontinuity at integer particle numbers. We further demonstrate that through the kinetic-energy density any meta-GGA incorporates a derivative discontinuity. However, we also find that for commonly used meta-GGAs the discontinuity is largely underestimated and in some cases even negative.

Momentum space anisotropy of electronic correlations in Fe and Ni: An analysis of magnetic Compton profiles

The total and magnetically resolved Compton profiles are analyzed within the combined density functional and dynamical mean field theory for the transition metal elements Fe and Ni. A rather good agreement between the measured and computed magnetic Compton profiles (MCPs) of Fe and Ni is obtained with the standard Local Spin Density Approximation (LSDA). By including local but dynamic many-body correlations captured by Dynamical Mean Field Theory (DMFT), the calculated magnetic Compton profile is further improved when compared with experiment. The second moment of the difference of the total Compton profiles between LSDA and DMFT, along the same momentum direction, has been used to discuss the strength of electronic correlations in Fe and Ni.

A first principle study of pressure-induced effects on phase transitions, band structures and elasticity of zinc oxide

Using the first-principles projector-augmented wave (PAW) method, the pressure induced effects on solid–solid phase transition, electronic band structures and elasticity of zinc oxide are investigated. The four possible structures are considered here, including rocksalt (B1), CsCl (B2), zinc blende (B3), and wurtzite (B4). It is found that structural properties and phase transition points by the PBEsol method are better than those computed using the standard local density approximation and Perdew, Burke and Ernzerhof functionals. Moreover, using the hybrid HSE06 functional, the band structures around phase transition points are displayed. The predicted fundamental gaps of the four considered structures provide improvements over directly density functional theory calculations. Meanwhile, the effective masses for the electrons in the conduction band and the holes in the valence band are derived. Furthermore, the elastic abnormal behavior is achieved around the phase transition points. For B4, B1 and B2 structures, the longitudinal and transverse sound velocities are evaluated along significant symmetry directions with pressure, and it still awaits experimental confirmation.

Kohn-Sham band gaps and potentials of solids from the optimised effective potential method within the random phase approximation

We present an implementation of the optimised effective potential (OEP) scheme for the exact-exchange (EXX) and random phase approximation (RPA) energy functionals and apply these methods to a range of bulk materials. We calculate the Kohn-Sham (KS) potentials and the corresponding band gaps and compare them to the potentials obtained by standard local density approximation (LDA) calculations. The KS gaps increase upon going from the LDA to the OEP in the RPA and finally to the OEP for EXX. This can be explained by the different depth of the potentials in the bonding and interstitial regions. To obtain the true quasi-particle gaps the derivative discontinuities or G0W0 corrections need to be added to the RPA-OEP KS gaps. The predicted G0W0@RPA-OEP quasi-particle gaps are about 5% too large compared to the experimental values. However, compared to G0W0 calculations based on local or semi-local functionals, where the errors vary between different materials, we obtain a rather consistent description among all the materials.