GGA Calculations Research Articles

Improved calculation of band gap of Sr2Bi2O5 crystal using modified Becke–Johnson exchange potential

The electronic structure of Sr2Bi2O5 is calculated by the scalar-relativistic full potential linearized augmented plane wave (FLAPW+lo) method using the modified Becke–Johnson potential combined with the local density approximation correlation (MBJ–LDA). Both the valence band maximum (VBM) and conduction band minimum (CBM) exist at the Γ-point, indicating that Sr2Bi2O5 is a direct-band-gap material. The band gap is calculated to be 3.17eV, which is very close to the experimental value. This result is in great contrast to the underestimation based on the GGA calculation. On the other hand, there is only a small difference in the effective masses of holes and electrons photogenerated near the VBM and CBM for the MBJ–LDA and GGA approaches. The optical properties of Sr2Bi2O5 are calculated from the complex dielectric function ε(ω)=ε1(ω)+iε2(ω). A highly polarized peak is observed at 3.5eV in the ε2(ω) function. Furthermore, the absorption coefficient estimated from the MBJ–LDA is very similar to that from the experimental result.

Metal-insulator transition at the LaAlO3/SrTiO3interface revisited: A hybrid functional study

We investigate the electronic properties of the ${\mathrm{LaAlO}}_{3}$/${\mathrm{SrTiO}}_{3}$ interface using density functional theory. In contrast to previous studies, which relied on (semi-)local functionals and the $\text{GGA}+U$ method, we here use a recently developed hybrid functional to determine the electronic structure. This approach offers the distinct advantage of accessing both the metallic and insulating multilayers on a parameter-free equal footing. As compared to calculations based on semilocal GGA functionals, our hybrid functional calculations lead to a considerably increased band gap for the insulating systems. The details of the electronic structure show substantial deviations from those obtained by GGA calculations. This casts severe doubts on all previous results based on semilocal functionals. In particular, corrections using rigid band shifts (``scissors operator'') cannot lead to valid results.

Structural, electronic properties, and chemical bonding in quaternary layered titanium pnictide-oxides Na2Ti2Pn2O and BaTi2Pn2O (Pn = As, Sb) from FLAPW–GGA calculations

By means of the first-principles FLAPW–GGA calculations, we have investigated the main trends in structural, electronic properties, and chemical bonding for a series of quaternary titanium pnictide-oxides: Na2Ti2As2O, Na2Ti2Sb2O, BaTi2As2O, and BaTi2Sb2O, which attracted now much attention as parent phases for a novel group of layered Fe-free superconducting materials. Our results cover the optimized lattice parameters and atomic positions, electronic bands, Fermi surface topology, total and partial density of electronic states. Besides, Bader analysis and the charge density maps are used to discuss the chemical bonding for the examined materials. We find that the atomic substitutions lead to anisotropic deformation of the crystal structure; this effect is related to strong anisotropy of inter-atomic bonds, which are of a mixed (covalent-ionic-metallic) type – in blocks [Ti2Pn2O], whereas the bonding between blocks [Ti2Pn2O] and atomic sheets of Na, Ba ions is of an ionic type. The actual effective atomic charges differ from the formal ionic charges due to covalency in blocks [Ti2Pn2O]. The near-Fermi electronic bands, which are responsible for metallic-like behavior of these materials and will be involved in the formation of superconducting state, arise mainly from the Ti 3dxy, dx2−y2, and dz2 states of the blocks [Ti2Pn2O], which define also the anisotropic character of conduction happening mainly in these blocks. The differences in the topology of the multi-sheet Fermi surfaces of these materials are discussed.

Implementation of the modified Becke–Johnson meta-GGA functional in Quantum Espresso

In this paper we present an implementation of the modified Becke–Johnson meta-GGA functional (TB09) in the PWSCF program of Quantum ESPRESSO package via the Libxc library. Using the functionals of TB09 we calculated the band gaps of some semiconductors and compared the results with previous calculations and experiments. We showed that combining GGA pseudo-potential with TB09 functionals would improve greatly the band gaps compared with the GGA calculations. The details of our implementation and code samples are also given.

First principle research of possible HM-AFM in double perovskites A2MoOsO6 and A2TcReO6 (A = Si, Ge, Sn, and Pb) with group IVA elements set on the A-site position

We calculated electronic structures of double perovskite structures of A2MoOsO6 and A2TcReO6 (A = Si, Ge, Sn, and Pb) based on the density functional theory which was carried out with a full structural optimization using generalized gradient approximation and taking into account the correlation effect (GGA + U). In GGA calculation, Pb2TcReO6 shows a half-metallic antiferromagnet (HM-AFM) characteristic, whereas Sn2MoOsO6, Pb2MoOsO6, and Sn2TcReO6 are nearly HM-AFMs. With GGA + U calculation, Sn2MoOsO6 and Pb2MoOsO6 become stable HM-AFM, but Sn2TcReO6 and Pb2TcReO6 changes HM-AFM into an antiferromagnetic insulator. The p–d hybridization between B(B′)d-Op and double exchange interaction is the mean reason to result in the half-metallic and compensated ferrimagnetic phase.

High-pressure experiments on phase transition boundaries between corundum, Rh2O3(II)-and CaIrO3-type structures in Al2O3

Phase transitions in Al 2 O 3 between corundum Rh 2 O 3 (II)-type and CaIrO 3 -type (post-perovskitetype) phases were examined at high pressure and high temperature in a laser-heated diamond-anvil cell (DAC) based on in situ X-ray diffraction measurements. The locations of corundum-Rh 2 O 3 (II) and Rh 2 O 3 (II)-CaIrO 3 boundaries were precisely determined by conducting both forward and backward reaction experiments. The results demonstrate that corundum undergoes a phase transition to Rh 2 O 3 (II)-type structure above 106 GPa at 1800 K with a negative Clapeyron slope of –6.5 ± 1.5 MPa/K, generally consistent with earlier experimental and theoretical works. The Rh 2 O 3 (II)-type phase further transforms into CaIrO 3 -type above 170 GPa at 2300 K, indicating the transition pressure much higher than earlier experimental work but in agreement with reported GGA calculations. The Clapeyron slope of this phase transition was found to be high negative (–20 ± 5 MPa/K).

Defect and impurity properties of hexagonal boron nitride: A first-principles calculation

In this paper, we have systematically studied the structural and electronic properties of vacancy defects and carbon impurity in hexagonal boron nitride ($h$-BN) by using both normal GGA calculations and advanced hybrid functional calculations. Our calculations show that the defect configurations and the local bond lengths around defects are sensitive to their charge states. The highest negative defect charge states are largely determined by the nearly-free-electron state at the conduction band minimum of BN. Generally, the in-gap defect levels obtained from hybrid functional calculations are much deeper than those obtained from normal GGA calculations. The formation energies of neutral defects calculated by hybrid functional and GGA are close to each other, but the defect transition energy levels are quite different between GGA and hybrid functional calculations. Finally, we show that the charged defect configurations as well as the transition energy levels exhibit interesting layer effects.

Rationale for switching to nonlocal functionals in density functional theory

Density functional theory (DFT) has been steadily improving over the past few decades, becoming the standard tool for electronic structure calculations. The early local functionals (LDA) were eventually replaced by more accurate semilocal functionals (GGA) which are in use today. A major persisting drawback is the lack of the nonlocal correlation which is at the core of dispersive (van der Waals) forces, so that a large and important class of systems remains outside the scope of DFT. The vdW-DF correlation functional of Langreth and Lundqvist, published in 2004, was the first nonlocal functional which could be easily implemented. Beyond expectations, the nonlocal functional has brought significant improvement to systems that were believed not to be sensitive to nonlocal correlations. In this paper, we use the example of graphene nanodomes growing on the Ir(111) surface, where with an increase of the size of the graphene islands the character of the bonding changes from strong chemisorption towards almost pure physisorption. We demonstrate how the seamless character of the vdW-DF functionals makes it possible to treat all regimes self-consistently, proving to be a systematic and consistent improvement of DFT regardless of the nature of bonding. We also discuss the typical surface science example of CO adsorption on (111) surfaces of metals, which shows that the nonlocal correlation may also be crucial for strongly chemisorbed systems. We briefly discuss open questions, in particular the choice of the most appropriate exchange part of the functional. As the vdW-DF begins to appear implemented self-consistently in a number of popular DFT codes, with numerical costs close to the GGA calculations, we draw the attention of the DFT community to the advantages and benefits of the adoption of this new class of functionals.

Pressure effects on band structures in dense lithium

We studied the change of the band structures in some structures of Li predicted at high pressures, using GGA and GW calculations. The width of the 1s band coming from the 1s electron of Li shows broadening by the pressurization, which is the normal behavior of bands at high pressure. The width of the band just below the Fermi level decreases by the pressurization, which is an opposite behavior to the normal bands. The character of this narrowing band is mostly p-like with a little s-like portion. The band gaps in some structures are really observed even by the GGA calculations. The gaps by the GW calculations increase to about 1.5 times the GGA values. Generally the one-shot GW calculation (diagonal only calculations) gives more reliable values than the GGA, but it may fail to predict band gaps for the case where band dispersion shows complex crossing near the Fermi level. There remains some structures for which GW calculations with off-diagonal elements taken into account are needed to identify the phase to be metallic or semiconducting.

The interaction mechanism of CO2 with CH3 and H on Cu (1 1 1) surface in synthesis of acetic acid from CH4/CO2: A DFT study

The interaction mechanisms of CO2 with CH3 and H on Cu(111) surface in synthesis of acetic acid from CH4/CO2 are systematically investigated by the first-principle DFT–GGA calculations. Four possible reaction pathways are proposed, and the detailed mechanisms and kinetics are discussed. Our results show that all products are formed by gaseous CO2 and adsorbed CH3 and H through the Eley–Rideal (E–R) mechanism. It is found that the values of the activation barrier for four different pathways are in the order of CH3COO-Cu<HCOO-Cu<HOOC-Cu<CH3OCO-Cu, suggesting that CO2 insertion into CuCH3 bond to form CH3COO-Cu is the most advantageous in dynamics among all four reaction pathways, and the corresponding activation barrier of the rate-controlled step is 85.2kJmol−1. The insertion of CO2 into CuH bond to form HCOO-Cu is secondly preferential pathway favored in dynamics. Therefore, H3CCOO is the main product, HCOO is a primary side product, and H3COCO are not obtained as it is inhibited by dynamics in comparison with other pathways. Above calculated results are in accordance with the experimental results, which can provide a new theoretical guidance for the direct synthesis of oxygenated compounds from CH4 and CO2.

Comparative study of defect transition energy calculation methods: The case of oxygen vacancy in In2O3and ZnO

Theoretical calculation of defect properties, especially transition energy levels, is typically done by first-principles density-functional theory calculation using supercells with finite size. So far, three approaches---band-filling corrections (BFC), band-edge corrections (BEC), and no corrections (NC)---have been applied to deal with the potential inaccuracy caused by the finite size. In this paper, we compare these three approaches by calculating the (0/2$+$ ionization energies of the oxygen vacancy (V${}_{\mathrm{O}}$) in In${}_{2}$O${}_{3}$ and ZnO. We find that a correction must be included whether or not the defect level is deep or shallow, especially when the defect band has a large dispersion. The BFC approach gives the best correction. The BEC approach works well in GGA calculations only for certain systems in which the band gap underestimation is partially corrected by choosing effective band edges.

Elastic stability and electronic structure of tantalum boride investigated via first-principles density functional calculations

The elastic properties, electronic structure and thermodynamic behavior of the TaB have been investigated for the first time in this work. Using first-principles plane-wave ultrasoft-pseudopotential density functional theory (DFT), the ground state properties and equation of state of TaB have been obtained. The average zero-pressure bulk modulus of TaB is 302GPa. By analyzing the elastically anisotropic behavior and the relative structure parameters of TaB, we found that the crystal cell along the b-axis was more compressible than along the a and c axes. The calculated ratio of bulk modulus and shear modulus (B/G) for TaB is 1.58, demonstrating that TaB is rather brittle. From the elastic stiffness constants, we found that TaB in the Cmcm phase is mechanically stable. The calculated hardness of TaB is 28.6GPa which is close to the previous data. Moreover, using the Gibbs 2 model, the thermodynamic properties such as the thermal expansion and Debye temperature of TaB have been obtained firstly. At the ambient temperature, the Debye temperatures of TaB are 792K and 845K from GGA calculation and LDA calculation, respectively.

Effect of Si substitution on electronic structure and magnetic properties of Heusler compounds Co2TiAl1−xSix

The electronic structures of Co-based Heusler compounds CoTiAl1−xSix (x=0, 0.25, 0.5, 0.75 and 1) are calculated by first-principles using the full potential linearized augmented plane wave (FP-LAPW) method within GGA and LSDA+U scheme. Particular emphasis was put on the role of the main group elements. In recent years, the GGA calculations of Co2TiAl (x=0) and Co2TiSi (x=1) indicated that they are half-metallic, but the electronic structure of this compound with x=0.25, 0.5 and 0.75 has not been reported yet, neither theoretically nor experimentally. The calculated results reveal that these are half-metallic and exhibit an energy gap in the minority spin state and also show 100% spin polarization. The substitution of Al by Si leads to an increase in the number of valence electrons, with increasing x. Our calculated results clearly show that with the Si doping, the lattice parameter linearly decreases; bulk modulus increases, and the total magnetic moment increases. The calculated energy gap in the minority spin state, using GGA scheme, was smaller than that obtained by using LSDA+U scheme. The outcomes of this research also show that the Co-3d DOS and therefore, the magnetic properties of compounds are dependent on electron concentration of the main group elements and it will affect the degree of p-d orbital occupation.

Correcting density functional theory for accurate predictions of compound enthalpies of formation: Fitted elemental-phase reference energies

Despite the great success that theoretical approaches based on density functional theory have in describing properties of solid compounds, accurate predictions of the enthalpies of formation ($\ensuremath{\Delta}{H}_{f}$) of insulating and semiconducting solids still remain a challenge. This is mainly due to incomplete error cancellation when computing the total energy differences between the compound total energy and the total energies of its elemental constituents. In this paper we present an approach based on GGA $+$ $U$ calculations, including the spin-orbit coupling, which involves fitted elemental-phase reference energies (FERE) and which significantly improves the error cancellation resulting in accurate values for the compound enthalpies of formation. We use an extensive set of 252 binary compounds with measured $\ensuremath{\Delta}{H}_{f}$ values (pnictides, chalcogenides, and halides) to obtain FERE energies and show that after the fitting, the 252 enthalpies of formation are reproduced with the mean absolute error $\text{MAE}=0.054$ eV/atom instead of $\text{MAE}\ensuremath{\approx}0.250$ eV/atom resulting from pure GGA calculations. When applied to a set of 55 ternary compounds that were not part of the fitting set the FERE method reproduces their enthalpies of formation with $\text{MAE}=0.048$ eV/atom. Furthermore, we find that contributions to the total energy differences coming from the spin-orbit coupling can be, to a good approximation, separated into purely atomic contributions which do not affect $\ensuremath{\Delta}{H}_{f}$. The FERE method, hence, represents a simple and general approach, as it is computationally equivalent to the cost of pure GGA calculations and applies to virtually all insulating and semiconducting compounds, for predicting compound $\ensuremath{\Delta}{H}_{f}$ values with chemical accuracy. We also show that by providing accurate $\ensuremath{\Delta}{H}_{f}$ the FERE approach can be applied for accurate predictions of the compound thermodynamic stability or for predictions of Li-ion battery voltages.

A Comparative First-Principles Study of Fe-, Co- and FeCo-Doped ZnO with Wurtzite and Zinc Blende Structures

First-principles study of the electronic and magnetic properties of zinc-blende and wurtzite structures of Fe-, Co-, and FeCo-doped ZnO is presented. It is found that after doping, this diamagnetic material becomes ferromagnetic and half-metallic. It is also shown that the half-metallicity may be obtained for ZnFeO, ZnCoO, and ZnFeCoO. The analysis of the spin density reveals that the ferromagnetic phase is due to the ferromagnetic coupling between the p–d states. The effects of Fe on the magnetic properties of ZB and WZ Fe-doped ZnO compound have been investigated with the GGA calculations. In order to understand the role of Fe atom in the ferromagnetism, the density of states both in the presence and absence of Co doping, were calculated. The obtained results show the presence of coupling between Co and Fe atoms through the spin-split impurity band exchange mechanism. More importantly, the calculations show that the magnetic moment changes sensitively with the type of structure of ZnO, zinc-blende, or wurtzite. A discussion by comparing the results obtained in this study and the experimental results reported in the literature of similar systems show a very good agreement.

Electrochemical properties of crystallized dilithium squarate: insight from dispersion-corrected density functional theory

The stacking parameters, lattice constants, and bond lengths of solvent-free dilithium squarate (Li(2)C(4)O(4)) crystals were investigated using density functional theory with and without dispersion corrections. The shortcoming of the GGA (PBE) calculation with respect to the dispersive forces appears in the form of an overestimation of the unit cell volume up to 5.8%. The original Grimme method for dispersion corrections has been tested together with modified versions of this scheme by changing the damping function. One of the modified dispersion-corrected DFT schemes, related to a rescaling of van der Waals radii, provides significant improvements for the description of intermolecular interactions in Li(2)C(4)O(4) crystals: the predicted unit cell volume lies then within 0.9% from experimental data. We applied this optimised approach to the screening of hypothetical framework structures for the delithiated (LiC(4)O(4)) and lithiated (Li(3)C(4)O(4)) phases, i.e. oxidized and reduced squarate forms. Their relative energies have been analysed in terms of dispersion and electrostatic contributions. The most stable phases among the hypothetical models for a given lithiation rate were selected in order to calculate the corresponding average voltages (either upon lithiation or delithiation of Li(2)C(4)O(4)). A first step towards energy partitioning in view of interpretating crystal phases relative stability in link with (de)-intercalation processes has been performed through the explicit evaluation of electrostatic components of lattice energy from atomic charges gained with the Atoms in Molecules (AIM) method.

Small Molecule Activation by Uranium Tris(aryloxides): Experimental and Computational Studies of Binding of N2, Coupling of CO, and Deoxygenation Insertion of CO2under Ambient Conditions

Previously unanticipated dinitrogen activation is exhibited by the well-known uranium tris(aryloxide) U(ODtbp)(3), U(OC(6)H(3)-Bu(t)(2)-2,6)(3), and the tri-tert-butyl analogue U(OTtbp)(3), U(OC(6)H(2)-Bu(t)(3)-2,4,6)(3), in the form of bridging, side-on dinitrogen complexes [U(OAr)(3)](2)(μ-η(2):η(2)-N(2)), for which the tri-tert-butyl N(2) complex is the most robust U(2)(N(2)) complex isolated to date. Attempted reduction of the tris(aryloxide) complex under N(2) gave only the potassium salt of the uranium(III) tetra(aryloxide) anion, K[U(OAr)(4)], as a result of ligand redistribution. The solid-state structure is a polymeric chain formed by each potassium cation bridging two arenes of adjacent anions in an η(6) fashion. The same uranium tris(aryloxides) were also found to couple carbon monoxide under ambient conditions to give exclusively the ynediolate [OCCO](2-) dianion in [U(OAr)(3)](2)(μ-η(1):η(1)-C(2)O(2)), in direct analogy with the reductive coupling recently shown to afford [U{N(SiMe(3))(2)}(3)](2)(μ-η(1):η(1)-C(2)O(2)). The related U(III) complexes U{N(SiPhMe(2))(2)}(3) and U{CH(SiMe(3))(2)}(3) however do not show CO coupling chemistry in our hands. Of the aryloxide complexes, only the U(OC(6)H(2)-Bu(t)(3)-2,4,6)(3) reacts with CO(2) to give an insertion product containing bridging oxo and aryl carbonate moieties, U(2)(OTtbp)(4)(μ-O)(μ-η(1):η(1)-O(2)COC(6)H(2)-Bu(t)(3)-2,4,6)(2), which has been structurally characterized. The presence of coordinated N(2) in [U(OTtbp)(3)](2)(N(2)) prevents the occurrence of any reaction with CO(2), underscoring the remarkable stability of the N(2) complex. The di-tert-butyl aryloxide does not insert CO(2), and only U(ODtbp)(4) was isolated. The silylamide also reacts with carbon dioxide to afford U(OSiMe(3))(4) as the only uranium-containing material. GGA and hybrid DFT calculations, in conjunction with topological analysis of the electron density, suggest that the U-N(2) bond is strongly polar, and that the only covalent U→N(2) interaction is π backbonding, leading to a formal (U(IV))(2)(N(2))(2-) description of the electronic structure. The N-N stretching wavenumber is preferred as a metric of N(2) reduction to the N-N bond length, as there is excellent agreement between theory and experiment for the former but poorer agreement for the latter due to X-ray crystallographic underestimation of r(N-N). Possible intermediates on the CO coupling pathway to [U(OAr)(3)](2)(μ-C(2)O(2)) are identified, and potential energy surface scans indicate that the ynediolate fragment is more weakly bound than the ancillary ligands, which may have implications in the development of low-temperature and pressure catalytic CO chemistry.

A comparative study for structural and electronic properties of single-crystal ScN

A comparative study by FP-LAPW calculations based on DFT within LDA, PBE-GGA, EV$_{ex}$-PW$_{co}$-GGA, and EV$_{ex}$-GGA-LDA$_{co}$ schemes is introduced for the structural and electronic properties of ScN in RS, ZB, WZ, and CsCl phases. According to all approximations used in this work, the RS phase is the stable ground state structure and makes a transition to CsCl phase at high transition pressure. While PBE-GGA and EV$_{ex}$-PW$_{co}$-GGA's have provided better structural features such as equilibrium lattice constant and bulk modulus, only EV$_{ex}$-PW$_{co}$-GGA and EV$_{ex}$-GGA-LDA$_{co}$'s have given the non zero, positive indirect energy gap for RS-ScN, comparable with the experimental ones. The indirect band gap of ScN in RS phase is enlarged to the corresponding measured value by EV$_{ex}$-PW$_{co}$-GGA+U$^{SIC}$ calculations in which the Coulomb self and exchange-correlation interactions of the localized d-orbitals of Sc have been corrected by the potential parameter of U. The EV$_{ex}$-PW$_{co}$-GGA calculations have also provided good results for the structural and electronic features of ScN in ZB, WZ, and CsCl phases comparable with the theoretical data available in the literature. EV$_{ex}$-PW$_{co}$-GGA and EV$_{ex}$-PW$_{co}$-GGA+U$^{SIC}$ schemes are considered to be the best ones among the others when the structural and electronic features of ScN are aimed to be calculated by the same exchange-correlation energy approximations.

Thermodynamic study of the Np–Zr system

A thermodynamic model of the Np–Zr system is developed using the CALPHAD method, and a review of previous work performed on this system is presented here. In general, results obtained are in good agreement with those proposed from experimental observations. It is found that the nature of reactivity of Np with Zr, is different from that of U and Pu: an expected elevation of melting point of Np–Zr alloys was not seen and a miscibility gap existed between the high-temperature bcc phases of Np and Zr. Formation enthalpy of the bcc phase obtained from the model is compared with results from KKR–ASA–CPA calculations. Lattice stabilities of various phases in the system are compared to values obtained from first-principles LDA and GGA calculations. The δ-NpZr 2 phase is modeled as a non-stoichiometric phase with a C32 structure, similar to what has been determined for the δ-phase in the U–Zr system. This phase is analogous to ω-phase in pure Zr, which is stabilized at high pressures. Two different possibilities for stability of the δ and ω phases have been proposed in the present work. Finally, calculated changes in enthalpy versus temperature are plotted for two alloys to guide future experimental work in resolving important issues in this system.

First-principle calculations of the bulk properties of 4 d transition metal carbides and nitrides in the rocksalt, zincblende and wurtzite structures

Bulk properties and stability of the entire series of group 4 d transition metal carbides and nitrides are reported in this work. The theoretical calculations were carried out within Local Density Approximation and Generalized Gradient Approximation using the Perdew, Burke and Ernzerhof exchange correlation functional. The generalized gradient approximation predictions were found to be closer to experimental values than the local density approximation predictions. In particular, LDA predictions were found to overestimate bulk moduli properties by as much as 5.6–11.5% while equilibrium lattice constants were found to be underestimated by as much as 0.2–5% compared to experimental values. On the other hand, GGA calculations were found to overestimate the lattice parameters by 0.2–6.9%, while underestimating the bulk moduli by as much as 0.07–5%. Out of the carbides considered, TcC and RuC were found to have the highest values of bulk moduli while YC and CdC had the lowest. Similarly, out of the nitrides, MoN and TcN were found to exhibit the largest bulk moduli, indicating that they were the hardest, while CdN had the lowest value and hence relatively softer. Overall, the nitrides presented higher values of bulk moduli than the carbides, an observation that is well supported by their correspondingly shorter bondlengths. The cohesive and structural properties of the 4 d transition metal carbides and nitrides are also reported.