Kohn-Sham Band Gaps Research Articles

First-principles calculations to investigate the elastic, electronic, dynamical, and optical properties of cubic ZrCoAs half-Heusler semiconductor for photovoltaic applications

The electronic, mechanical, elastic, dynamical, and optical properties of the ZrCoAs half-Heusler compound have been systematically investigated using the plane wave self-consistent field approach with the Perdew-Burke-Erzerhof generalized gradient approximation (GGA-PBE) exchange-correlation functional. The study includes examinations with and without spin orbit coupling (SOC) effects. Results indicate a decrease in the Kohn-Sham band gap with the inclusion of SOC effects. Electronic bandgap formation was attributed to Co 3d, Zr 3d, and As 2p for the conduction band, and Co 3d and As 2p for the valence band without SOC effects. With SOC, Co 5d, Zr 8d, and As 3p dominated the conduction band, while Co 3d and As 3p dominated the valence band. The lattice constant showed a 0. 063% decrease with the SOC effects, which is better aligned with the experimental observations. ZrCoAs demonstrated ductility, mechanical stability, and dynamical stability. The optical properties were found to be excellent for photovoltaic applications, suggesting its potential in solar energy conversion technology. This study provides valuable information on ZrCoAs and presents opportunities for its use in solar cells, optoelectronic devices, and thermoelectric applications. The material's versatility and suitability for practical applications make it a promising candidate for further exploration in renewable energy research.

The convexity condition of density-functional theory.

It has long been postulated that within density-functional theory (DFT), the total energy of a finite electronic system is convex with respect to electron count so that 2Ev[N0] ≤ Ev[N0 - 1] + Ev[N0 + 1]. Using the infinite-separation-limit technique, this Communication proves the convexity condition for any formulation of DFT that is (1) exact for all v-representable densities, (2) size-consistent, and (3) translationally invariant. An analogous result is also proven for one-body reduced density matrix functional theory. While there are known DFT formulations in which the ground state is not always accessible, indicating that convexity does not hold in such cases, this proof, nonetheless, confirms a stringent constraint on the exact exchange-correlation functional. We also provide sufficient conditions for convexity in approximate DFT, which could aid in the development of density-functional approximations. This result lifts a standing assumption in the proof of the piecewise linearity condition with respect to electron count, which has proven central to understanding the Kohn-Sham bandgap and the exchange-correlation derivative discontinuity of DFT.

The diamond NV-center transition energies in the vicinity of an intrinsic stacking fault

The negatively charged nitrogen vacancy (NV−) center in a diamond is a nanometer-sized defect with very sensitive properties that can be manipulated, for example, for single-molecule photoluminescence and nuclear magnetic resonance sensing, as a single photon source for quantum cryptography and as a qubit in room temperature quantum computing. To have a minimal perturbation of its properties, it is important to isolate the NV-center from other defects. One type of the extended defects that can be common in diamonds is the intrinsic stacking fault (ISF) associated with dislocations. In this work, we use density functional theory simulations to investigate how the distance between the NV− center and an ISF affects its properties, including the transition energies, spin density, and energy eigenvalues in the Kohn–Sham bandgap. We have found that the NV-center properties are only slightly perturbed when placed in the vicinity of an ISF. Even for an interdistance of only 3.8 Å between the NV-center and the ISF, the decrease in its zero phonon line (ZPL) energy is less than 6.8%. To more significantly perturb the ZPL, the NV-center has to be placed inside the stacking fault glide plane (11.3% decrease). The changes in ZPL are in the majority of cases lower than the bulk value, which can be used to guide experimental observations. We find that the NV-center is only weakly interacting with ISFs, which in addition to a small bulk conversion depth of 5 Å to a diamond surface is important for their technological use.

Optimized effective potentials from the random-phase approximation: Accuracy of the quasiparticle approximation.

The optimized effective potential (OEP) method presents an unambiguous way to construct the Kohn-Sham potential corresponding to a given diagrammatic approximation for the exchange-correlation functional. The OEP from the random-phase approximation (RPA) has played an important role ever since the conception of the OEP formalism. However, the solution of the OEP equation is computationally fairly expensive and has to be done in a self-consistent way. So far, large scale solid state applications have, therefore, been performed only using the quasiparticle approximation (QPA), neglecting certain dynamical screening effects. We obtain the exact RPA-OEP for 15 semiconductors and insulators by direct solution of the linearized Sham-Schlüter equation. We investigate the accuracy of the QPA on Kohn-Sham bandgaps and dielectric constants, and comment on the issue of self-consistency.

Theoretical investigation of the structural, elastic, electronic, and dielectric properties of alkali-metal-based bismuth ternary chalcogenides

The past decade has witnessed the rapid introduction of organic-inorganic hybrid compounds in photovoltaic applications. Motivated by the strong demand for stable and nontoxic materials in this class, we report a theoretical study on the structural, elastic, electronic, thermodynamic and dielectric properties of alkali-metal-based bismuth ternary chalcogenides. In particular, we employ state-of-the-art density functional theory to explore the potential of $A\mathrm{Bi}{X}_{2}$ and $A\mathrm{Bi}{X}_{3}$ ($A=\mathrm{Na}$, K and $X=$ O, S) as light-absorbing media. All the compounds under investigation are found to be thermodynamically and mechanically stable, with a semiconductor band structure. The Kohn-Sham band gaps range between 0.80 eV and 1.80 eV, when calculated with semilocal functionals, values that increase to 1.24--2.47 eV with hybrid ones. Although all but ${\mathrm{NaBiO}}_{2}$ and ${\mathrm{KBiO}}_{2}$ are indirect band-gap semiconductors, the onset of the imaginary part of their dielectric functions, the optical gap, is only marginally larger than the quasiparticle gap. This is due to the generally flat nature of both the conduction and the valence bands. We then expect these compounds to absorb light in the upper part of the visible spectrum. In all cases the valence band is dominated by $\mathrm{O}\text{\ensuremath{-}}p$ and S-$p$ orbitals and the conduction one by Bi-$p$, suggesting the possibility of excitons with low binding energy. The only exceptions are ${\mathrm{NaBiO}}_{2}$ and ${\mathrm{KBiO}}_{2}$ for which the $\mathrm{O}\text{\ensuremath{-}}p$ states dominate the density of states at both sides of the band gap.

Band Gap of 3D Metal Oxides and Quasi-2D Materials from Hybrid Density Functional Theory: Are Dielectric-Dependent Functionals Superior?

Reproduction of the band gaps of semiconductors and insulators represents a well-known problem for standard DFT approaches based on semilocal functionals. The problem can be partly solved using hybrid functionals, in which a given portion of exact exchange is mixed with the DFT exchange. Recently, a new class of dielectric-dependent functionals has been introduced in which the amount of exact exchange is derived from the static dielectric function of a given compound. In this study we considered in a systematic way on an equal footing a set of 24 nonmagnetic three-dimensional (3D) bulk metal oxides and 24 quasi-two-dimensional (quasi-2D) semiconductors (oxides, hydroxides, chlorides, oxyhalides, nitrides, and transition metal dichalcogenides) and computed the corresponding Kohn-Sham band gaps with three global hybrid functionals and four range-separated hybrid functionals. These in turn were divided into standard (PBE0, B3LYP, HSE06, SC-BLYP) and dielectric-dependent (DD-B3LYP, DD-SC-BLYP, DD-CAM-B3LYP) functionals. We also performed a statistical analysis of the DFT data set along with structural parameters of these 2D and 3D materials. The surprising result is that overall there is no real improvement with the use of dielectric-dependent functionals compared to PBE0, HSE06, and B3LYP. Short-range DD-SC-BLYP gives a minor improvement in the band gaps for bulk metal oxides compared with standard SC-BLYP, but the mean absolute error is still 0.12 eV higher than with B3LYP. The use of dielectric-dependent standard or short-range functionals such as DD-B3LYP or DD-HSE06 worsens the situation. However, the dielectric-dependent version of the long-range-separated functional implemented with the Coulomb attenuating method (CAM), DD-CAM-B3LYP, leads to a clear improvement for band gaps of quasi-2D materials. On the basis of this analysis, the conclusion is that the use of a standard hybrid functional such as B3LYP or HSE06 is recommended for nonmagnetic bulk 3D metal oxides. On the other hand, the treatment of layered materials such as MoO3 or V2O5 benefits from the use of dielectric-dependent range-separated functionals.

Assessment of the GLLB-SC potential for solid-state properties and attempts for improvement

Based on the work of Gritsenko et al. (GLLB) [Phys. Rev. A 51, 1944 (1995)], the method of Kuisma et al. [Phys. Rev. B 82, 115106 (2010)] to calculate the band gap in solids was shown to be much more accurate than the common local density approximation (LDA) and generalized gradient approximation (GGA). The main feature of the GLLB-SC potential (SC stands for solid and correlation) is to lead to a nonzero derivative discontinuity that can be conveniently calculated and then added to the Kohn-Sham band gap for a comparison with the experimental band gap. In this work, a thorough comparison of GLLB-SC with other methods, e.g., the modified Becke-Johnson (mBJ) potential [F. Tran and P. Blaha, Phys. Rev. Lett. 102, 226401 (2009)], for electronic, magnetic, and density-related properties is presented. It is shown that for the band gap, GLLB-SC does not perform as well as mBJ for systems with a small band gap and strongly correlated systems, but is on average of similar accuracy as hybrid functionals. The results on itinerant metals indicate that GLLB-SC overestimates significantly the magnetic moment (much more than mBJ does), but leads to excellent results for the electric field gradient, for which mBJ is in general not recommended. In the aim of improving the results, variants of the GLLB-SC potential are also tested.

Predicting Ground-State Configurations and Electronic Properties of the Thermoelectric Clathrates Ba8AlxSi46–xand Sr8AlxSi46–x

The structural and electronic properties of the clathrate compounds Ba$_{8}$Al$_{x}$Si$_{46-x}$ and Sr$_{8}$Al$_{x}$Si$_{46-x}$ are studied from first principles, considering an Al content $x$ between 6 and 16. Due to the large number of possible substitutional configurations we make use of a special iterative cluster-expansion approach, to predict ground states and quasi-degenerate structures in a highly efficient way. These are found from a simulated annealing technique where millions of configurations are sampled. For both compounds, we find a linear increase of the lattice constant with the number of Al substituents, confirming experimental observations for Ba$_{8}$Al$_{x}$Si$_{46-x}$. Also the calculated bond distances between high-symmetry sites agree well with experiment for the full compositional range. For $x$ being below 16, all configurations are metallic for both materials. At the charge-balanced composition ($x=16$), the substitutional ordering leads to a metal-semiconductor transition, and the ground states of Ba$_{8}$Al$_{16}$Si$_{30}$ and Sr$_{8}$Al$_{16}$Si$_{30}$ exhibit indirect Kohn-Sham band gaps of 0.36 and 0.30 eV, respectively, while configurations higher in energy are metals. The finding of semiconducting behavior is a promising result in view of exploiting these materials in thermoelectric applications.

From the Kohn-Sham band gap to the fundamental gap in solids. An integer electron approach.

It is often stated that the Kohn-Sham occupied-unoccupied gap in both molecules and solids is "wrong". We argue that this is not a correct statement. The KS theory does not allow to interpret the exact KS HOMO-LUMO gap as the fundamental gap (difference (I - A) of electron affinity (A) and ionization energy (I), twice the chemical hardness), from which it indeed differs, strongly in molecules and moderately in solids. The exact Kohn-Sham HOMO-LUMO gap in molecules is much below the fundamental gap and very close to the much smaller optical gap (first excitation energy), and LDA/GGA yield very similar gaps. In solids the situation is different: the excitation energy to delocalized excited states and the fundamental gap (I - A) are very similar, not so disparate as in molecules. Again the Kohn-Sham and LDA/GGA band gaps do not represent (I - A) but are significantly smaller. However, the special properties of an extended system like a solid make it very easy to calculate the fundamental gap from the ground state (neutral system) band structure calculations entirely within a density functional framework. The correction Δ from the KS gap to the fundamental gap originates from the response part vresp of the exchange-correlation potential and can be calculated very simply using an approximation to vresp. This affords a calculation of the fundamental gap at the same level of accuracy as other properties of crystals at little extra cost beyond the ground state bandstructure calculation. The method is based on integer electron systems, fractional electron systems (an ensemble of N- and (N + 1)-electron systems) and the derivative discontinuity are not invoked.

A many-body GW + BSE investigation of electronic and optical properties of C2N

A recently synthesized layered material C2N was investigated based on many-body perturbation theory using the GW plus Bethe-Salpeter equation approach. The electronic band gap was determined to be ranging from 3.75 to 1.89 eV from the monolayer to the bulk. Significant GW quasiparticle corrections, of more than 0.9 eV, to the Kohn-Sham band gaps from the local density approximation calculations are found. Strong excitonic effects play a crucial role in optical properties. We found large binding energies of greater than 0.6 eV for bound excitons in few-layer C2N, while it is only 0.04 eV in bulk C2N. All the structures exhibit strong and broad optical absorption in the visible light region, which makes C2N a promising candidate for solar energy conversion, such as photocatalytic water splitting.

Prediction model of band gap for inorganic compounds by combination of density functional theory calculations and machine learning techniques

Machine learning techniques are applied to make prediction models of the G0W0 band-gaps for 156 AX binary compounds using Kohn-Sham band-gaps and other fundamental information of constituent elements and crystal structure as predictors. Ordinary least square regression (OLSR), least absolute shrinkage and selection operator (LASSO) and non-linear support vector regression (SVR) methods are applied with several levels of predictor sets. When the Kohn-Sham band-gap by GGA (PBE) or modified Becke-Johnson (mBJ) is used as a single predictor, OLSR model predicts the G0W0 band-gap of a randomly selected test data with the root mean square error (RMSE) of 0.54 eV. When Kohn-Sham band gap by PBE and mBJ methods are used together with a set of various forms of predictors representing constituent elements and crystal structures, RMSE decreases significantly. The best model by SVR yields the RMSE of 0.18 eV. A large set of band-gaps estimated in this way should be useful as predictors for materials exploration.

Strong excitonic effects in hydrogen-graphene-fluorine janus graphene

Abstractauthoren We present a first-principles many-body Green's function method (GW approximation and Bethe–Salpeter equation) of the electronic and optical properties of recently predicted hydrogen–graphene–fluorine janus graphene. Significant self-energy corrections, of more than 50%, to the Kohn–Sham bandgap from the local density approximation (LDA) calculations are found. Moreover, the optical absorption spectrum of this janus graphene is dominated by enhanced excitonic effects with formation of a bound exciton with considerable binding energy. The reduced spatial separation of excited electrons and holes gives rise to extremely short radiative lifetimes, preventing condensation.

Scaling correction approaches for reducing delocalization error in density functional approximations

Delocalization error associated with the presently used density functional approximations is one of the main sources of errors which plague density functional theory calculations. In this paper, we give a comprehensive review on scaling correction (SC) approaches developed recently for reducing the delocalization error. The global and local SC approaches impose the rigorous Perdew-Parr-Levy-Balduz condition that the total electronic energy should scale linearly between integer electron numbers, on systems involving global and local fractional electron distributions, respectively. After presenting the theoretical background and mathematical formulation of scaling corrections, we demonstrate that they lead to universal alleviation of delocalization error. This is exemplified by the substantial improvement for the prediction of a wide range of electronic properties, including Kohn-Sham frontier orbital energies and band gaps, dissociation behavior of molecules, reaction barriers, electric polarizabilities, and charge-transfer species. The encouraging performances of SC approaches highlight their practicality and usefulness, and also affirm that an explicit treatment of fractional electron distributions is essentially important for reducing the intrinsic delocalization error. The existing limitations, the remaining challenges, and the future perspectives of SC are also discussed. Moreover, the SC approaches are compared with some existing methods attempting to remove the self-interaction error, such as the Perdew-Zunger self-interaction correction, the local hybrid hyper-generalized gradient approximations, and the rangeseparated density functional approximations. The unique advantages of SC suggest that it could open a novel and potentially paradigm-changing route for advancing density functional theory methods towards chemical accuracy.

Surface polarization, rumpling, and domain ordering of strained ultrathinBaTiO3(001) films with in-plane and out-of-plane polarization

${\mathrm{BaTiO}}_{3}$ ultrathin films (thickness $\ensuremath{\approx}1.6$ nm) with in- and out-of-plane polarization are studied by first-principles calculations. Out-of-plane polarization is simulated using the method proposed by Shimada et al. [Phys. Rev. B 81, 144116 (2010)], which consists in building a supercell containing small domains with alternating up and down polarization. This allows one to investigate the properties of defect free ${\mathrm{BaTiO}}_{3}$ ultrathin films with polarization perpendicular to the surface, as a function of in-plane lattice constant, i.e., epitaxial strain. The configurations with polarization perpendicular to the surface $(c$ phase) are found stable under compressive strain, while under tensile strain, the polarization tends to lie in-plane ($aa$ phase), along [110]. In the $c$ phase, the most stable domain width is predicted to be 1 to 2 lattice constants, and the magnitude of the surface rumpling varies according to the direction of the polarization (upwards versus downwards), though its sign is unchanged, the oxygen anions pointing in all cases outwards. Finally, all the surfaces studied are found to be insulating. Analysis of the atom-projected electronic density of states gives insight into the surface contributions to the electronic structure. An important reduction of the Kohn-Sham band gap is predicted at ${\mathrm{TiO}}_{2}$ terminations in the $c$ phase ($\ensuremath{\approx}1$ eV with respect to the $aa$ phase). The Madelung potential at the surface plays the dominant role in modifications of the surface electronic structure.

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.

Assessing the Role of Water on the Electronic Structure and Vibrational Spectra of Monohydrated l-Aspartic Acid Crystals

In this work, we compare the calculated electronic and vibrational properties (infrared and Raman spectra) of anhydrous and monohydrated l-aspartic acid crystals to unveil the role of water in the later. This is accomplished through density functional theory (DFT) simulations within the Tkatchenko and Scheffler dispersion corrected generalized gradient approximation (GGA+TS). Both crystals are shown to have indirect band gaps and the simulations predict that water has a small effect on the Kohn–Sham band gap value (60 meV). Δ-sol corrected gaps, in contrast, exhibited a larger difference between the anhydrous and monohydrated crystals (main gap 0.30 eV larger for the latter). The conduction bands of the monohydrated species are much flatter because of structural changes produced by the presence of water, which leads to very large electron effective masses. However, the hole effective mass along the stacking direction of water molecules in the GGA+TS optimized monohydrated crystal is smaller than in other directions, suggesting that water stacking can improve on hole transport in similar bioorganic systems. These effects highlight the complex role of water on the carrier transport properties in monohydrated l-aspartic acid crystals, which is in contrast with the general belief that water simply increases the electrical conductance in molecular crystals. Finally, the calculated infrared and Raman spectra of the monohydrated phase exhibit molecular water vibrational signatures as well as water related peak shifts of as much as 100 cm–1 in comparison to those of the anhydrous structure. Remarkable water related Raman intensity peaks were obtained for the monohydrated crystal in the wavenumber ranges between 600 and 1000 cm–1 and between 2350 and 3450 cm–1, while for the infrared spectrum, a set of water absorption bands can be clearly identified in the 1550–1750 and 2800–3400 cm–1 wavenumber intervals.

Excitonic effects in the optical properties of a SiC sheet and nanotubes

The quasiparticle band structure and optical properties of single-walled zigzag and armchair SiC nanotubes (SiC-NTs) as well as single SiC sheet are investigated by ab initio many-body calculations using the GW and the GW plus Bethe-Salpeter equation (GW+BSE) approaches, respectively. Significant GW quasiparticle corrections of more than 1.0 eV to the Kohn-Sham band gaps from the local density approximation (LDA) calculations are found. The GW self-energy corrections transform the SiC sheet from a indirect LDA band gap to a direct band gap material. Furthermore, the quasiparticle band gaps of SiC-NTs with different chiralities behave very differently as a function of tube diameter, and this can be attributed to the difference in the curvature-induced orbital rehybridization between the different chiral nanotubes. The calculated optical absorption spectra are dominated by discrete exciton peaks due to exciton states with large binding energy up to 2.0 eV in the SiC sheet and SiC-NTs. The formation of strongly bound excitons is attributed to the enhanced electron-hole interaction in these low dimensional systems. Remarkably, the excited electron amplitude of the exciton wavefunction is found to peak on the Si atoms near the hole position (which is on the C site) in the zigzag SiC-NTs, indicating a charge transfer from an anion (hole) to its neighboring cations by photoexcitation. In contrast, this pronounced peak structure disappear in the exciton wavefunction in the armchair SiC-NTs. Furthermore, in the armchair SiC-NTs, the bound exciton wavefunctions are more localized and also strongly cylindrically asymmetric.

Electronic structure and lattice dynamical properties of different tetragonal phases ofBiFeO3

From first-principles calculations based on the plane-wave pseudopotential method within the density-functional $+U$ scheme, we have investigated the atomic geometry, electronic band-structure, and lattice dynamical properties of four tetragonal phases of the multiferroic ${\text{BiFeO}}_{3}$. In contrast to the indirect Kohn-Sham band gap of the rhombohedral phase, the most stable of the single-phase stable tetragonal structure is semiconducting with a smaller and direct band gap. It is found that the highest optical phonon branch is split from the rest of the phonon continuum by a small gap. The presently calculated zone-center optical modes have been compared and contrasted with the available polarized Raman-scattering studies and previous calculations based on a simple short-range force-constant method. The highest phonon mode with frequency $\ensuremath{\sim}662\text{ }{\text{cm}}^{\ensuremath{-}1}$ of ${A}_{1}$ representation in the tetragonal phase $(P4mm)$ can be readily distinguished from the frequency $\ensuremath{\sim}590\text{ }{\text{cm}}^{\ensuremath{-}1}$ of ${A}_{2}$ representation in the rhombohedral phase $(R3c)$.

Structure and band gaps of Ga-(V) semiconductors: The challenge of Ga pseudopotentials

Design of gallium pseudopotentials has been investigated for use in density functional calculations of zinc-blende-type cubic phases of GaAs, GaP, and GaN. A converged construction with respect to all-electron results is described. Computed lattice constants, bulk moduli, and band gaps vary significantly depending on pseudopotential construction or exchange-correlation functional. The Kohn-Sham band gap of the Ga-(V) semiconductors exhibits a distinctive and strong sensitivity to lattice constant, with near-linear dependence of gap on lattice constant for larger lattice constants and a $\ensuremath{\Gamma}\text{\ensuremath{-}}X$ crossover that changes the slope of the dependence. This crossover occurs at $\ensuremath{\approx}98$, 101, and 95% deviation from the equilibrium lattice constant for GaAs, GaP, and GaN, respectively.

Ab initio Structural, Electronic and Optical Properties of Orthorhombic CaGeO3.

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