Investigating Polaron Formation in Anatase and Brookite TiO2 by Density Functional Theory with Hybrid-Functional and DFT + U Methods

s valence electrons in cations of metal oxides serving as descriptors for electron and hole polarons

In some metal oxides, an excess electron can give rise to the formation of a small polaron localized on a single site. However, there are still some metal oxides that exhibit the formation of a large polaron. The underlying mechanism behind this phenomenon remains unclear. In this study, we investigate polaron formation in metal oxides favorable for polaron formation using different functionals and through a review of the literature. Our findings indicate that the s valence electrons in cations could serve as a descriptor to classify the polarons in materials. In metal oxides with cations having ns (n ⩾ 5) valence electrons, excess charges trend to localize on several sites or form a two-dimensional shape, and even a large polaron, as these s electrons are delocalized in nature and have a large effect on p or d state polarons. The delocalized nature of ns (n ⩽ 4) valence electrons in cations is relatively small and does not affect the localization condition of p or d state polarons. Therefore, the excess charges in these metal oxides with ns (n ⩽ 4) valence electrons prefer to form a small polaron localizing on a single site. This work unveils the impact of the s valence in cations on polaron formation and provides a fundamental understanding of various types of polarons in metal oxides.

Polymorphs of Titanium Dioxide: An Assessment of the Variants of Projector Augmented Wave Potential of Titanium on Their Geometric and Dielectric Properties

Titanium dioxide (TiO₂) is one of the important functional materials owing to its diverse applications in many fields of chemistry, physics, nanoscience, and technology. Hundreds of studies on its physicochemical properties, including its various phases, have been reported experimentally and theoretically, but the controversial nature of relative dielectric permittivity of TiO₂ is yet to be understood. Toward this end, this study was undertaken to rationalize the effects of three commonly used projector augmented wave (PAW) potentials on the lattice geometries, phonon vibrations, and dielectric constants of rutile (R-)TiO₂ and four of its other phases (anatase, brookite, pyrite, and fluorite). Density functional theory calculations within the PBE and PBEsol levels, as well as their reinforced versions PBE+U and PBEsol+U (U = 3.0 eV), were performed. It was found that PBEsol in combination with the standard PAW potential centered on Ti is adequate to reproduce the experimental lattice parameters, optical phonon modes, and the ionic and electronic contributions of the relative dielectric permittivity of R-TiO₂ and four other phases. The origin of failure of the two soft potentials, namely, Ti_pv and Ti_sv, in predicting the correct nature of low-frequency optical phonon modes and ion-clamped dielectric constant of R-TiO₂ is discussed. It is shown that the hybrid functionals (HSEsol and HSE06) slightly improve the accuracy of the above characteristics at the cost of a significant increase in computation time. Finally, we have highlighted the influence of external hydrostatic pressure on the R-TiO₂ lattice, leading to the manifestation of ferroelectric modes that play a role in the determination of large and strongly pressure-dependent dielectric constant.

Polaron formation and transport in Bi2WO6 studied by DFT+U and hybrid PBE0 functional approaches

Bi₂WO₆ (BWO) is considered as a promising material for photocatalytic water splitting. Its unique layered structure leads the charge separation, and transport is different from other materials. However, the charge transport mechanisms in BWO are not well understood. In this work, we investigated polaron formation and transport in BWO using the DFT+U and hybrid PBE0 functional approaches. We found that the electron will form 2-dimensional (2D)-shaped polarons among W sites in the ab plane of BWO with approximately 55% polaron density state on the central W site. This type of polaron is similar to the electron polarons in WO₃. For other W-based materials, the electrons may also form a 2D-shaped polaron. We found that the W 6s orbital plays an important role in these 2D-shaped electron polarons. The calculated mobility of electron polarons in BWO was consistent with experimental findings. For the hole state, it could form a small hole polaron on the O site with O 2p in character. However, it will not form a polaron on the Bi site, which is quite different from BiVO₄. This study provides insight for understanding polaron formation and transport in materials with W and Bi ions. It also provides understanding regarding charge separation and transport for materials with layered structures.

Detection and Correction of Delocalization Errors for Electron and Hole Polarons Using Density-Corrected DFT

Modeling polaron defects is an important aspect of computational materials science, but the description of unpaired spins in density functional theory (DFT) often suffers from delocalization error. To diagnose and correct the overdelocalization of spin defects, we report an implementation of density-corrected (DC-)DFT and its analytic energy gradient. In DC-DFT, an exchange-correlation functional is evaluated using a Hartree-Fock density, thus incorporating electron correlation while avoiding self-interaction error. Results for an electron polaron in models of titania and a hole polaron in Al-doped silica demonstrate that geometry optimization with semilocal functionals drives significant structural distortion, including the elongation of several bonds, such that subsequent single-point calculations with hybrid functionals fail to afford a localized defect even in cases where geometry optimization with the hybrid functional does localize the polaron. This has significant implications for traditional workflows in computational materials science, where semilocal functionals are often used for structure relaxation. DC-DFT calculations provide a mechanism to detect situations where delocalization error is likely to affect the results.

Hole Polaron Migration in Bulk Phases of TiO2 Using Hybrid Density Functional Theory

Understanding charge-carrier transport in semiconductors is vital to the improvement of material performance for various applications in optoelectronics and photochemistry. Here, we use hybrid density functional theory to model small hole polaron transport in the anatase, brookite, and TiO₂-B phases of titanium dioxide and determine the rates of site-to-site hopping as well as thermal ionization into the valance band and retrapping. We find that the hole polaron mobility increases in the order TiO₂-B < anatase < brookite and there are distinct differences in the character of hole polaron migration in each phase. As well as having fundamental interest, these results have implications for applications of TiO₂ in photocatalysis and photoelectrochemistry, which we discuss.

Experimental and theoretical investigation of the enhancement of the photo-oxidation of Hg0 by CeO2-modified morphology-controlled anatase TiO2

This study aims to investigate the coeffects of predominantly exposed anatase TiO₂{001} and {101} and CeO₂ loading on the photo-oxidation of Hg⁰ to relieve the adverse effects caused by higher temperatures of 50-250 °C. The effect of loading CeO₂ on the photocatalytic activity of morphology-controlled TiO₂ was not only investigated using DFT with U correction but also experimentally analyzed by characterizing the electrochemical properties and the formation of free radicals. The theoretical calculation showed that CeO₂ loading on TiO₂{101} was more stable than that on TiO₂{001}. Accordingly, a larger portion of CeO₂ was observed to anchor to the (101) plane than to the (001) plane. CeO₂ loading is more beneficial for increasing the distribution of photo-induced electrons and holes on the surface of 7%CeTi than on the surface of TiO₂ and increases the energy difference between the conduction band edge of 7%CeTi and the standard redox potential of O₂/·O₂^-. Correspondingly, the photocatalytic removal efficiencies (PREs) of Hg⁰ by 7%CeTi were significantly enhanced compared with those of pristine TiO₂. The effect of CeO₂ was highly morphologically dependent on the photocatalytic activity. This study provides valuable insight into surface engineering strategies for morphology-controlled photocatalysts for air pollution control technology.

Density Functional Theory Study of Optical and Electronic Properties of (TiO2)n=5,8,68 Clusters for Application in Solar Cells

A range of solution-processed organic and hybrid organic−inorganic solar cells, such as dye-sensitized and bulk heterojunction organic solar cells have been intensely developed recently. TiO₂ is widely employed as electron transporting material in nanostructured TiO₂ perovskite-sensitized solar cells and semiconductor in dye-sensitized solar cells. Understanding the optical and electronic mechanisms that govern charge separation, transport and recombination in these devices will enhance their current conversion efficiencies under illumination to sunlight. In this work, density functional theory with Perdew-Burke Ernzerhof (PBE) functional approach was used to explore the optical and electronic properties of three modeled TiO₂ brookite clusters, (TiO₂)_n=5,8,68. The simulated optical absorption spectra for (TiO₂)₅ and (TiO₂)₈ clusters show excitation around 200–400 nm, with (TiO₂)₈ cluster showing higher absorbance than the corresponding (TiO₂)₅ cluster. The density of states and the projected density of states of the clusters were computed using Grid-base Projector Augmented Wave (GPAW) and PBE exchange correlation functional in a bid to further understand their electronic structure. The density of states spectra reveal surface valence and conduction bands separated by a band gap of 1.10, 2.31, and 1.37 eV for (TiO₂)₅, (TiO₂)₈, and (TiO₂)₆₈ clusters, respectively. Adsorption of croconate dyes onto the cluster shifted the absorption peaks to higher wavelengths.

Formation and stability of small polarons at the lithium-terminated Li4Ti5O12 (LTO) (111) surface

Zero strain insertion, high cycling stability, and a stable charge/discharge plateau are promising properties rendering Lithium Titanium Oxide (LTO) a possible candidate for an anode material in solid state Li ion batteries. However, the use of pristine LTO in batteries is rather limited due to its electronically insulating nature. In contrast, reduced LTO shows an electronic conductivity several orders of magnitude higher. Studying bulk reduced LTO, we could show recently that the formation of polaronic states can play a major role in explaining this improved conductivity. In this work, we extend our study toward the lithium-terminated LTO (111) surface. We investigate the formation of polarons by applying Hubbard-corrected density functional theory. Analyzing their relative stabilities reveals that positions with Li ions close by have the highest stability among the different localization patterns.

Do HOMO-LUMO Energy Levels and Band Gaps Provide Sufficient Understanding of Dye-Sensitizer Activity Trends for Water Purification?

A dye-sensitized solar cell assembly can be used to harvest solar energy, while suitable dye sensitizers can be used to purify water. Here, we characterized the activity trends of four dye sensitizers, namely, PORPC-1, PORPC-2, PORPC-3, and PORPC-4, for water purification applications using density functional theory (DFT) with the Perdew-Burke-Ernzerhof (PBE), B3LYP, and PBE0 functionals, ΔSCF, time-dependent DFT (TD-DFT), and quasiparticle Green's function (GW) methods. The energy levels of the highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) were calculated using gas-phase and aqueous-phase methods in order to understand charge-injection abilities and the dye regeneration processes. PBE, B3LYP, PBE0, and TD-DFT methods failed to predict PORPC-4 to be the best sensitizer, while PORPC-2 and PORPC-4 were predicted to be the best sensitizers using ΔSCF coupled with the implicit solvation method, and HOMO-LUMO energies were corrected for the aqueous environment in the GW calculations. However, none of these methods accurately predicted the performance trend of all four dye sensitizers. Consequently, we used the aggregation assembly patterns of the dye molecules in an aqueous environment to further probe the activity trends and found that PORPC-3 and PORPC-4 prefer J-aggregated assembly patterns, whereas PROPC-1 and PORPC-2 prefer to be H-aggregated. Therefore, the performance of these dye molecules can be determined by combining HOMO-LUMO energy levels with aggregate-assembly patterns, with the activity trend predicted to be PORPC-4 > PORPC-2 > PORPC-3 > PORPC-1, which is in good agreement with experimental findings.

First-principles study of the effect of compressive strain on oxygen adsorption in Pd/Ni/Cu-alloy-core@Pd/Ir-alloy-shell catalysts

Through synergism between the ligand effect, the d-band center shift, and the surface alloying effect, the Pd₃CuNi@PdIr catalyst exhibits the poorest dioxygen adsorption and, consequently, the best catalytic ORR performance.