Tuning LDA+U for electron localization and structure at oxygen vacancies in ceria

We examine the real space structure and the electronic structure (particularly Ce4f electron localization) of oxygen vacancies in CeO(2) (ceria) as a function of U in density functional theory studies with the rotationally invariant forms of the LDA+U and GGA+U functionals. The four nearest neighbor Ce ions always relax outwards, with those not carrying localized Ce4f charge moving furthest. Several quantification schemes show that the charge starts to become localized at U approximately 3 eV and that the degree of localization reaches a maximum at approximately 6 eV for LDA+U or at approximately 5.5 eV for GGA+U. For higher U it decreases rapidly as charge is transferred onto second neighbor O ions and beyond. The localization is never into atomic corelike states; at maximum localization about 80-90% of the Ce4f charge is located on the two nearest neighboring Ce ions. However, if we look at the total atomic charge we find that the two ions only make a net gain of (0.2-0.4)e each, so localization is actually very incomplete, with localization of Ce4f electrons coming at the expense of moving other electrons off the Ce ions. We have also revisited some properties of defect-free ceria and find that with LDA+U the crystal structure is actually best described with U=3-4 eV, while the experimental band structure is obtained with U=7-8 eV. (For GGA+U the lattice parameters worsen for U>0 eV, but the band structure is similar to LDA+U.) The best overall choice is U approximately 6 eV with LDA+U and approximately 5.5 eV for GGA+U, since the localization is most important, but a consistent choice for both CeO(2) and Ce(2)O(3), with and without vacancies, is hard to find.     

First-principles study of lattice dynamics and thermodynamics of TiO2 polymorphs

The structural, phonon, and thermodynamic properties of six TiO(2) polymorphs, i.e., rutile, anatase, columbite, baddeleyite, orthorhombic I, and cotunnite, have been systematically investigated by density functional theory. The predicted volumes, bulk modulus, and Debye temperature are in good agreement with experiments. The phonon dispersions of the TiO(2) polymorphs were studied by the supercell approach, whereas the long-range dipole-dipole interactions were calculated by linear response theory to reproduce the LO-TO splitting, making accurate prediction of phonon frequencies for the polar material TiO(2). The calculated phonon dispersions show that all TiO(2) polymorphs are dynamically stable at ambient pressure, indicating the high-pressure phases might be quenched to ambient conditions as ultrahard materials. Furthermore, the finite temperature thermodynamic properties of TiO(2) polymorphs were predicted accurately from the obtained phonon density of states, which is critical in the future study of the pressure-temperature phase diagram of TiO(2). The calculated Gibbs energies reveal that rutile is more stable than anatase at ambient pressure. We derived the Gibbs energy and heat capacity functions for all TiO(2) polymorphs for use in thermodynamic modeling of phase equilibria.     

Critical Assessment of the DFT + U Approach for the Prediction of Vanadium Dioxide Properties

In a previous study (Stahl and Bredow, Chem. Phys. Lett. 2018, 695, 28–33), we have studied structural, energetic, and electronic properties of two vanadium dioxide VO₂ polymorphs with modified global and range-separated hybrid functionals. Since hybrid methods are computationally demanding, we evaluate the computationally more efficient DFT + U method in the present study. We assessed the widely used Dudarev PBE + U approach with a literature value of the effective Hubbard parameter U_eff = 3.4 eV. We compared the PBE + U results for the two VO₂ polymorphs with our previous results, a self-consistent hybrid functional sc-PBE0, and the meta-GGA functional SCAN. It was found that the PBE + U method yields a strongly distorted monoclinic phase and does not reproduce the metal-to-insulator transition of VO₂ correctly, even with modified values of U_eff. On the other hand, sc-PBE0 and SCAN describe the relative stability and the electronic structure of both polymorphs correctly and also provide reasonable lattice parameters. The functional SCAN yields the optimal balance between computational efficiency and accuracy. © 2019 The Authors. Journal of Computational Chemistry published by Wiley Periodicals, Inc.     

Characterization and optical properties of mechanochemically synthesized molybdenum-doped rutile nanoparticles and their electronic structure studies by density functional theory

The optical and electronic properties of molybdenum (Mo) doped rutile TiO₂ prepared by the mechanochemical method were studied both experimentally and using density functional theory (DFT). The synthesized nanoparticles were characterized by XRD, TEM, EDS-MAP, and XPS. The XRD results showed the successful incorporation of Mo in the rutile crystal lattice. High-resolution TEM images illustrated a decreasing trend in the (110) d-spacing for samples doped up to 3 at%. The shift toward higher binding energies in the XPS spectra was due to the higher oxidization tendencies of Mo⁵⁺ and Mo⁶⁺ substituted in Ti⁴⁺ sites. The optical behavior of samples was examined by UV–Vis and photoluminescence spectroscopy. The bandgap energy value of rutile was reduced from 3.0 eV to 2.4 eV by 2 at% Mo doping. The DFT calculations showed a reduction of bandgap energy value of rutile to 2.35 eV with 2 at% Mo, which is in harmony with the experimental results. The creation of energy states below the conduction band because of Mo doping was identified as the reason for reducing the bandgap energy and photoluminescence emission of rutile.     

Self-interaction artifacts on structural features of uranyl monohydroxide from Kohn�CSham calculations

Invoking a DFT?+?U approach, we explored self-interaction artifacts in results from Kohn?CSham (KS) density functional calculations on the geometry and the vibrational frequencies of uranyl monohydroxide and the corresponding tetra-aqua complex. Exchange?Ccorrelation functionals based on the local density approximation (LDA) and the generalized-gradient approximation (GGA) predict equilibrium geometries for [UO₂(OH)]⁺ that deviate from the results of hybrid DFT calculations and high-level wavefunction-based methods such as CCSD(T). LDA?+?U and GGA?+?U functionals with corrections for the insufficient localization of the U 5f shell yield better agreement, in particular for the angle U-O_h-H. At the LDA level, a linear coordination of the OH ligand results; with the +U correction, the angle U-O_h-H is reduced by ~35°, in good agreement with CCSD(T) results. At the GGA level, the bending angle is changed by ~20°. This relatively strong self-interaction artifact is traced back to a spurious ?? interaction between U 5f and O(p) orbitals which is less pronounced in the presence of further (aqua) ligands.     

Curious behaviors of photogenerated electrons and holes at the defects on anatase,rutile, and brookite TiO2 powders: A review

Photocatalytic reactions are governed by photogenerated charge carriers upon band gap excitation. Therefore, for better understanding of the mechanism, the dynamics of photocarriers should be studied. One of the attractive materials is TiO₂, which has been extensively investigated in the field of photocatalysis. This review article summarizes our recent works of time-resolved visible to mid-IR absorption measurements to elucidate the difference of anatase, rutile, and brookite TiO₂ powders. The distinctive photocatalytic activities of these polymorphs are determined by the electron-trapping processes at the defects on powders. Powders are rich in defects and these defects capture photogenerated electrons. The depth of the trap is crystal phase dependent, and they are estimated to be < 0.1 eV, ∼0.4 eV and ∼0.9 eV for anatase, brookite, and rutile, respectively. Electron trapping reduces probability to meet with holes and then elongate the lifetime of holes. Therefore, it works negatively for the reaction of electrons but positively works for the reaction of holes. In the steady-state reactions, both electrons and holes should be consumed. Hence, the balance between the positive and negative effects of defects determines the distinctive photocatalytic activities of anatase, rutile, and brookite TiO₂ powders.     

Theoretical study of CeO2 and Ce2O3 using a screened hybrid density functional

The predicted structures and electronic properties of CeO(2) and Ce(2)O(3) have been studied using conventional and hybrid density functional theory. The lattice constant and bulk modulus for CeO(2) from local (LSDA) functionals are in good agreement with experiment, while the lattice parameter from a generalized gradient approximation (GGA) is too long. This situation is reversed for Ce(2)O(3), where the LSDA lattice constant is much too short, while the GGA result is in reasonable agreement with experiment. Significantly, the screened hybrid HSE functional gives excellent agreement with experimental lattice constants for both CeO(2) and Ce(2)O(3). All methods give insulating ground states for CeO(2) with gaps for the 4f band lying between 1.7 eV (LSDA) and 3.3 eV (HSE) and 6-8 eV for the conduction band. For Ce(2)O(3) the local and GGA functionals predict a semimetallic ground state with small (0-0.3 eV) band gap but weak ferromagnetic coupling between the Ce(+3) centers. By contrast, the HSE functional gives an insulating ground state with a band gap of 3.2 eV and antiferromagnetic coupling. Overall, the hybrid HSE functional gives a consistent picture of both the structural and electronic properties of CeO(2) and Ce(2)O(3) while treating the 4f band consistently in both oxides.     

Band gap anomalies of the ZnM2(III)O4 (M(III)=Co, Rh, Ir) spinels

Development of high figure-of-merit p-type transparent conducting oxides has become a global research goal. ZnM(2)(III)O(4) (M(III) = Co, Rh, Ir) spinels have been identified as potential p-type materials, with ZnIr(2)O(4) reported to be a transparent conducting oxide. In this article the geometry and electronic structure of ZnM(2)(III)O(4) are studied using the Perdew-Purke-Ernzerhof generalized gradient approximation (PBE-GGA) to density functional theory and a hybrid density functional, HSE06. The valence band features of all the spinels indicate that they are not conducive to high p-type ability, as there is insufficient dispersion at the valence band maxima. The trend of increasing band-gap as the atomic number of the M(III) cation increases, as postulated from ligand field theory, is not reproduced by either level of theory, and indeed is not seen experimentally in the literature. GGA underestimates the band-gaps of these materials, while HSE06 severely overestimates the band-gaps. The underestimation (overestimation) of the band-gaps by GGA (HSE06) and the reported transparency of ZnIr(2)O(4) is discussed.     

Quantum mechanical modeling of Zn-based spinel oxides: Assessing the structural,vibrational, and electronic properties

The structural, electronic, and vibrational properties of two leading representatives of the Zn-based spinel oxides class, normal ZnX₂O₄ (X = Al, Ga, In) and inverse Zn₂MO₄ (M = Si, Ge, Sn) crystals, were investigated. In particular, density functional theory (DFT) was combined with different exchange-correlation functionals: B3LYP, HSE06, PBE0, and PBESol. Our calculations showed good agreement with the available experimental data, showing a mean percentage error close to 3% for structural parameters. For the electronic structure, the obtained HSE06 band-gap values overcome previous theoretical results, exhibiting a mean percentage error smaller than 10.0%. In particular, the vibrational properties identify the significant differences between normal and inverse spinel configurations, offering compelling evidence of a structure-property relationship for the investigated materials. Therefore, the combined results confirm that the range-separated HSE06 hybrid functional performs the best in spinel oxides. Despite some points that cannot be directly compared to experimental results, we expect that future experimental work can confirm our predictions, thus opening a new avenue for understanding the structural, electronic, and vibrational properties in spinel oxides.     

钛铁矿型六方相ZnTiO3的电子结构和光学性质

分别采用基于密度泛函理论(DFT)的局域密度近似(LDA)和广义梯度近似(GGA)方法对钛铁矿型六方相ZnTiO₃的电子结构进行了第一性原理计算, 并在局域密度近似下计算了六方相ZnTiO₃的光学性质, 并将计算结果与实验数据进行了对比. 结果表明, 在局域密度近似下计算得到的结构参数更接近实验数据. 理论预测六方相ZnTiO₃属于直接带隙半导体材料, 其禁带宽度(布里渊区Z 点)为3.11 eV. 电子态密度和Mulliken 电荷布居分析表明Zn―O键是典型的离子键而Ti―O键是类似于钙钛矿型ATiO₃ (A=Sr, Pb, Ba)的Ti―O共价键. 在50 eV的能量范围内研究了ZnTiO₃的介电函数、吸收光谱和折射率等光学性质, 并基于电子能带结构和态密度对光学性质进行了解释.     

Structure and Stability of TaON Polymorphs

The stabilities and electronic structures of several polymorphs of tantalum oxynitride, TaON, were studied quantum‐chemically at density‐functional level. Results obtained by complementary quantum‐chemical techniques with wave‐functions either expanded in atom‐centered functions or in plane waves were compared. Close agreement was obtained for the relative stabilities of the baddeleyite, anatase, rutile, and fluorite phases of TaON. The effect of anion distribution on the structural parameters and the lattice energies of the anatase and rutile polymorphs was investigated. The calculated band structure of the polymorphs is compared with available experimental information.     

一种超硬新材料BeP2N4的电子结构和力学性质及本征硬度

基于密度泛函理论,采用局域密度近似(LDA)和广义梯度近似(GGA)泛函研究了硅铍石、尖晶石结构的 BeP₂N₄ 材料的晶格参数、能带结构、态密度、分态密度、Mulliken布居值和弹性性质, 计算结果与已有的实验值和理论值符合很好. 能带结构和态密度表明两种结构的BeP₂N₄材料是宽的直接带隙的绝缘体材料. 尖晶石结构BeP₂N₄的体弹性模量、剪切模量和弹性模量比硅铍石结构的相应的力学量大得多. 利用Sung等提出的硬度经验判据和Gao等提出的基于Mulliken轨道重叠布居数的共价固体本征硬度计算方法, 预测了两种结构的本征硬度值. 计算结果表明硅铍石结构BeP₂N₄虽然体弹模量小, 但是它并不是一种软的材料, 而是一种易脆的硬度较硬的材料, 随着压力增加硅铍石结构BeP₂N₄的脆性逐渐过渡到延性. 尖晶石结构BeP₂N₄是一种易脆的超硬材料. 采用GGA计算得到的硅铍石BeP₂N₄向尖晶石相转变压力为14 GPa, 与理论预测值(24 GPa)相比偏小.     

Density functional theory calculations of dense TiO2 polymorphs: implication for visible-light-responsive photocatalysts

Structural parameters and electronic band gaps of dense TiO(2) polymorphs, i.e., alpha-PbO(2), baddeleyite, fluorite, and cotunnite types of structures, were calculated using a first-principles density functional method with local-density approximation. The ambient phases, i.e., rutile and anatase, with known theoretical and experimental data were used to ensure the validity of the calculations. The fluorite-type TiO(2) turned out to have the narrowest band gap, 1.08 or 2.18 eV after applying a very approximate band gap correction, due to highly symmetrical TiO(8) polyhedra with Ti(3d) and O(2p) orbitals in the most mixed state. Ti with eight coordinated oxygens, as feasible under high pressure or residual stress, may have potential applications as a visible-light-responsive photocatalyst.     

Structural, optoelectronic, infrared and Raman spectra of orthorhombic SrSnO3 from DFT calculations

Orthorhombic SrSnO₃ was investigated using density functional theory (DFT) considering both the local density and generalized gradient approximations, LDA and GGA, respectively. The electronic band structure, density of states, complex dielectric function, optical absorption, and the infrared and Raman spectra were computed. Calculated lattice parameters are close to the experimental measurements, and an indirect band gap (2.27 eV) was obtained within the GGA (LDA) level of calculation. Effective masses for holes and electrons were estimated, being very anisotropic in comparison with similar results for orthorhombic CaSnO₃. The complex dielectric function and the optical absorption of SrSnO₃ were shown to be sensitive to the plane of polarization of the incident light. The infrared spectrum between 100 and 600 cm⁻¹ was obtained, with its main peaks being assigned, and a nice agreement between experimental and theoretical peaks of the Raman spectrum of orthorhombic SrSnO₃ was achieved.     

A DFT+U study of acetylene selective hydrogenation on oxygen defective anatase (101) and rutile (110) TiO2 supported Pd4 cluster

The reaction mechanisms for selective acetylene hydrogenation on three different supports, Pd(4) cluster, oxygen defective anatase (101), and rutile (110) titania supported Pd(4), cluster are studied using the density functional theory calculations with a Hubbard U correction (DFT+U). The present calculations show that the defect anatase support binds Pd(4) cluster more strongly than that of rutile titania due to the existence of Ti(3+) in anatase titania. Consequently, the binding energies of adsorbed species such as acetylene and ethylene on Pd(4) cluster become weaker on anatase supported catalysts compared to the rutile supported Pd(4) cluster. Anatase catalyst has higher selectivity of acetylene hydrogenation than rutile catalyst. On the one hand, the activation energies of ethylene formation are similar on the two catalysts, while they vary a lot on ethyl formation. The rutile supported Pd catalyst with lower activation energy is preferable for further hydrogenation. On the other hand, the relatively weak adsorption energy of ethylene is gained on anatase surface, which means it is easier for ethylene desorption, hence getting higher selectivity. For further understanding, the energy decomposition method and micro-kinetic analysis are also introduced.