The crystal structure of A-Ce2O3

Density Functional Theory Plus Dynamical Mean Field Theory within the Framework of Linear Combination of Numerical Atomic Orbitals: Formulation and Benchmarks

The combination of density functional theory with dynamical mean-field theory (DFT+DMFT) has become a powerful first-principles approach to tackle strongly correlated materials in condensed matter physics. The wide use of this approach relies on robust and easy-to-use implementations, and its implementation in various numerical frameworks will increase its applicability on the one hand and help crosscheck the validity of the obtained results on the other. In this work, we develop a formalism within the linear combination of numerical atomic orbital (NAO) basis set framework, which allows for merging of NAO-based DFT codes with DMFT quantum impurity solvers. The formalism is implemented by interfacing two NAO-based DFT codes with three DMFT impurity solvers, and its validity is testified by benchmark calculations for a wide range of strongly correlated materials, including 3d transition metal compounds, lanthanides, and actinides. Our work not only enables DFT+DMFT calculations using popular and rapidly developing NAO-based DFT code packages but also facilitates the combination of more advanced beyond-DFT methodologies available in these codes with the DMFT machinery.

An Insight into Geometries and Catalytic Applications of CeO2 from a DFT Outlook

Rare earth metal oxides (REMOs) have gained considerable attention in recent years owing to their distinctive properties and potential applications in electronic devices and catalysts. Particularly, cerium dioxide (CeO2), also known as ceria, has emerged as an interesting material in a wide variety of industrial, technological, and medical applications. Ceria can be synthesized with various morphologies, including rods, cubes, wires, tubes, and spheres. This comprehensive review offers valuable perceptions into the crystal structure, fundamental properties, and reaction mechanisms that govern the well-established surface-assisted reactions over ceria. The activity, selectivity, and stability of ceria, either as a stand-alone catalyst or as supports for other metals, are frequently ascribed to its strong interactions with the adsorbates and its facile redox cycle. Doping of ceria with transition metals is a common strategy to modify the characteristics and to fine-tune its reactive properties. DFT-derived chemical mechanisms are surveyed and presented in light of pertinent experimental findings. Finally, the effect of surface termination on catalysis by ceria is also highlighted.

Electronic excitation spectra of cerium oxides: from ab initio dielectric response functions to Monte Carlo electron transport simulations

Nanomaterials made of cerium oxides CeO₂ and Ce₂O₃ have a broad range of applications, from catalysts in automotive, industrial or energy operations to promising materials to enhance hadrontherapy effectiveness in oncological treatments. To elucidate the physico-chemical mechanisms involved in these processes, it is of paramount importance to know the electronic excitation spectra of these oxides, which are obtained here through high-accuracy linear-response time-dependent density functional theory calculations. In particular, the macroscopic dielectric response functions  of both bulk CeO₂ and Ce₂O₃ are derived, which compare remarkably well with the available experimental data. These results stress the importance of appropriately accounting for local field effects to model the dielectric function of metal oxides. Furthermore, we reckon the energy loss functions Im(-1/) of the materials, including the accurate evaluation of the momentum transfer dispersion from first-principles calculations. In this respect, by using Mermin-type parametrization we are able to model the contribution of different electronic excitations to the dielectric loss function. Finally, from the knowledge of the electron inelastic mean free path, together with the elastic mean free path provided by the relativistic Mott theory, we carry out statistical Monte Carlo (MC) electron transport simulations to reproduce the major features of the reported experimental reflection electron energy loss (REEL) spectra of cerium oxides. The good agreement with REEL experimental data strongly supports our approach based on MC modelling, whose main inputs were obtained using ab initio calculated electronic excitation spectra in a broad range of momentum and energy transfers.

Comparative study of HSOA-/SOA2- versus H3-BPO4B- functionalities anchored on TiO2-supported antimony oxide-vanadium oxide-cerium oxide composites for low-temperature NOX activation

TiO₂-supported antimony oxide-vanadium oxide-cerium oxide (SVC) imparts Lewis acidic (L)/Brönsted acidic (B) sites, labile (O_α)/mobile oxygens (O_M), and oxygen vacancies (O_V) for selective catalytic NO_X reduction (SCR). However, these species are harmonious occasionally, readily poisoned by H₂O/sulfur/phosphorus/carbon, thus limiting SCR performance of SVC. Herein, a synthetic means is reported for immobilizing HSO_A^-/SO_A^2- (A= 3-4) or H_3-BPO₄^B- (B= 1-3) on the L sites of SVC to form SVC-S and SVC-P. HSO_A^-/SO_A^2-/H_3-BPO₄^B- acted as additional B sites with distinct characteristics, altered the properties of O_α/O_M/O_V species, thereby affecting the SCR activities and performance of SVC-S and SVC-P. SVC-P activated Langmuir-Hinshelwood-typed SCR better than SVC-S, as demonstrated by a greater O_α-directed pre-factor and smaller binding energy between O_α and NO. Meanwhile, SVC-S provided a larger B-directed pre-factor, thereby outperforming SVC-P in activating Eley-Rideal-typed SCR that dictated the overall SCR activities. Compared with SVC-S, SVC-P contained fewer O_V species, yet, had higher O_M mobility, thus enhancing the overall redox cycling feature, while providing greater Brönsted acidity. Consequently, the resistance of SVC-P to H₂O or soot were greater than or similar to that of SVC-S. Conversely, SVC-S revealed greater tolerance to hydro-thermal aging and SO₂ than SVC-P. This study highlights the pros and cons of HSO_A^-/SO_A^2-/H_3-BPO₄^B- functionalities in tailoring the properties of metal oxides in use as SCR catalysts.

Development and Application of a ReaxFF Reactive Force Field for Cerium Oxide/Water Interfaces

Ceria (CeO₂) is a well-known catalytic oxide with many environmental, energy production, and industrial applications, most of them involving water as a reactant, byproduct, solvent, or simple spectator. In this work, we parameterized a Ce/O/H ReaxFF for the study of ceria and ceria/water interfaces. The parameters were fitted to an ab initio training set obtained at the DFT/PBE0 level, including the structures, cohesive energies, and elastic properties of the crystalline phases Ce, CeO₂, and Ce₂O₃; the O-defective structures and energies of vacancy formation on CeO₂ bulk and CeO₂ (111) surface, as well as the absorption and reaction energies of H₂ and H₂O molecules on CeO₂ (111). The new potential reproduced reasonably well all the fitted properties as well as the relative stabilities of the different ceria surfaces, the oxygen vacancies formation, and the energies and structures of associative and dissociative water molecules on them. Molecular dynamics simulations of the liquid water on the CeO₂ (111) and CeO₂ (100) surfaces were carried out to study the coverage and the mechanism of water dissociation. After equilibration, on average, 35% of surface sites of CeO₂ (111) are hydroxylated whereas 15% of them are saturated with molecular water associatively adsorbed. As for the CeO₂ (100) surface, we observed that water preferentially dissociates covering 90% of the available surface sites in excellent agreement with recent experimental findings.

Preferential Oxidation of CO over CoFe2O4 and M/CoFe2O4 (M = Ce, Co, Cu or Zr) Catalysts

CoFe2O4 prepared by sol-gel has been examined with respect to its catalytic performance for preferential CO oxidation in a H2-rich stream. In turn, the promoting effects of incorporation of Ce, Co, Cu, and Zr by impregnation on the surface of CoFe2O4 on the process are examined as well. The catalysts have been characterized by N2 adsorption, X-ray diffraction (XRD), high resolution transmission electron microscopy (HRTEM), temperature programmed reduction (TPR), and X-ray photoelectron spectra (XPS), as well as diffuse reflectance infrared DRIFTS under reaction conditions with the aim of establishing structure/activity relationships for the mentioned catalyst/process. It is shown that while the presence of the various metals on CoFe2O4 hinders a low temperature CO oxidation process, it appreciably enhances the activity above 125 °C. This is basically attributed to the surface modifications, i.e. cobalt oxidation, induced in CoFe2O4 upon introduction of the metals. In turn, no methanation activity is observed in any case except for the copper-containing catalyst, in which achievement of reduced states of cobalt appears most favored.

Assessment of PBE+U and HSE06 methods and determination of optimal parameter U for the structural and energetic properties of rare earth oxides

Rare earth oxides are attracting increasing interest as a relatively unexplored group of materials with potential applications in heterogeneous catalysis and electrocatalysis; therefore, a credible and universal computational approach is needed for modeling their reactivity. In this work, we systematically assessed the performance of the PBE+U method against the results of the hybrid HSE06 method with respect to the description of structural parameters and energetic properties of the selected hexagonal lanthanide sesquioxides and the cubic fluorite-type cerium dioxide. In addition, we evaluated the performance of PBE+U in describing the electronic structure and adsorption properties of the CeO₂(111) and Nd₂O₃(0001) surfaces. The HSE06 method reproduces rather well the lattice parameters and selected energetic properties with respect to the experimental values. The PBE+U method is able to reproduce the results of HSE06 or the experimental values only if the U parameter is selected from an appropriate range of values. The U value around 3 eV gives the best description of the lattice parameters of most bulk oxides. 2 eV-3 eV is also found to be the optimal range of U for the reaction energies of bulk La₂O₃, Ce₂O₃, Nd₂O₃, Er₂O₃, and Ho₂O₃. U = 1 eV gives the best results for Pr₂O₃, Pm₂O₃, Eu₂O₃, Tm₂O₃, and Lu₂O₃, whereas Gd₂O₃ could not be accurately described by the PBE+U method. The U values (∼3 eV) found optimal for most bulk oxides also work well in the calculations of adsorption of small molecules on Nd₂O₃(0001) and CeO₂(111), although larger U values are required to obtain sufficient localization of 4f electrons.

Black Current: Structure, Characterization, and Optoelectronic Properties of Ce3 Cl3 [MoO6 ]

The admixture of CeO₂ , Ce, CeCl₃ , and MoO₃ with an excess of LiCl as flux in evacuated silica ampules leads to large black single crystals as well as a black microcrystalline powder of Ce₃ Cl₃ [MoO₆ ] after tempering at 850 °C for three days. The title compound crystallizes in the hexagonal space group P6₃ /m (a=934.93(4), c=538.86(2) pm) with two formula units per unit cell. The crystal structure consists of rather unusual trigonal-prismatic [MoO₆ ]^6- units besides Ce³⁺ ions in a tetra-capped trigonal-prismatic coordination, formed by four Cl^- and six O^2- ions. The black color is related to an optical band gap of 1.35(2) eV, which was determined by diffuse reflectance spectroscopy and confirmed by theoretical calculations. The low band gap between the 4f¹ state of cerium (HOMO) and the 5d⁰ state of molybdenum (LUMO) gave rise to the idea of electronic excitation between these two states by IR irradiation, creating a drop in the resistivity of the material, which was detected by appropriate measurements.

Assessment of Density Functional Approximations for Highly Correlated Oxides: The Case of CeO2 and Ce2O3

CeO₂ based materials are very attractive as catalytic components for industrial processes and environmentally friendly technologies; therefore, a reliable and computationally affordable theoretical description of the main properties of ceria is needed. In particular, the description of the interconversion between the Ce(IV) and Ce(III) oxidation states, on which lies the main chemical features of the cerium oxide, results in quite a challenge at the Density Functional Theory level. Here, we tested several density functional approximations, spanning from GGA to hybrid (Global, Meta-Global, and Range Separated Corrected) functionals, on the structural, vibrational, electronic, and thermochemical properties of bulk CeO₂ and Ce₂O₃. GGA and Meta-GGA xc best predict the thermochemical data, while the discrepancies increase with the introduction of the exact exchange in hybrid functionals. Overall, the Short Range Corrected and Global Hybrid functionals with a percentage of Exact Exchange between 16 and 25 give the best description of the crystal properties. Then, a group of the best performing functionals has been tested on the formation energy of an oxygen vacancy at the (111) CeO₂ surface. In general, increasing the amount of exact exchange in the hybrid functionals leads to a better description of the localized Ce 4 f states, while the energy of formation of the O vacancy decreases, worsening compared to the experiment.

Reinvestigation of the crystal structure of Ca2Ce8(SiO4)6O2 apatite by Rietveld refinement

The lattice parameters of apatite-type Ca₂Ca₈(SiO₄)₆O₂ determined from X-ray powder diffraction data are inconsistent with those found in the literature for the same type of material. Hence the structure was redetermined and compared with previously published data.

Ca₂Ln₈(SiO₄)₆O₂ apatites with Ln = La, Ce, Pr, Nd, Sm, Eu, Gd and Tb crystallize in space group P6₃/m. The crystal structure of apatite-type Ca₂Ce₈(SiO₄)₆O₂ [dicalcium octa­cerium hexa­kis­(silicate) dioxide], which has been synthesized by calcination, was refined from powder X-ray diffraction data using the Rietveld method. A database survey shows that contrary to the previously published Ca₂Ce₈(SiO₄)₆O₂ structure [Skakle et al. (2000 ▸). Powder Diffr.15, 234–238], the cell volume of the structure reported here is consistent with those of other Ln apatites.

Assessing Hubbard-corrected AM05+U and PBEsol+U density functionals for strongly correlated oxides CeO2 and Ce2O3

The structure–property relationships of bulk CeO₂ and Ce₂O₃ have been investigated within the DFT+U framework. AM05+U and PBEsol+U reproduce experimental crystalline parameters and properties with superior accuracy compared to conventional Hubbard-corrected exchange–correlation functionals.

Evidence for 5d-σ and 5d-π covalency in lanthanide sesquioxides from oxygen K-edge X-ray absorption spectroscopy

The electronic structure in the complete series of stable lanthanide sesquioxides, Ln₂O₃ (Ln = La to Lu, except radioactive Pm), has been evaluated using oxygen K-edge X-ray absorption spectroscopy with a scanning transmission X-ray microscope (STXM).

Real-space multiple-scattering Hubbard model calculations for d- and f-state materials

Calculations are presented of the electronic structure and X-ray spectra of materials with correlated d- and f-electron states based on the Hubbard model, a real-space multiple-scattering formalism and a rotationally invariant local density approximation. Values of the Hubbard parameter are calculated ab initio using the constrained random-phase approximation. The combination of the real-space Green's function with Hubbard model corrections provides an efficient approach to describe localized correlated electron states in these systems, and their effect on core-level X-ray spectra. Results are presented for the projected density of states and X-ray absorption spectra for transition metal- and lanthanide-oxides. Results are found to be in good agreement with experiment.

Reduced ceria nanofilms from structure prediction

Experimentally, Ce2O3 films are used to study cerium oxide in its fully or partially reduced state, as present in many applications. We have explored the space of low energy Ce2O3 nanofilms using structure prediction and density functional calculations, yielding more than 30 distinct nanofilm structures. First, our results help to rationalize the roles of thermodynamics and kinetics in the preparation of reduced ceria nanofilms with different bulk crystalline structures (e.g. A-type or bixbyite) depending on the support used. Second, we predict a novel, as yet experimentally unresolved, nanofilm which has a structure that does not correspond to any previously reported bulk A2B3 phase and which has an energetic stability between that of A-type and bixbyite. To assist identification and fabrication of this new Ce2O3 nanofilm we calculate some observable properties and propose supports for its epitaxial growth.

Aqueous medium induced optical transitions in cerium oxide nanoparticles

Experimental and theoretical investigations were performed to investigate the effect of water on optical properties of nanoceria as a function of Ce³⁺ concentration.

On the structure of Ce-containing silicophosphate glasses: a core–shell molecular dynamics investigation

New Ce³⁺–O and Ce⁴⁺–O parameters for a force-field based on the core–shell model were developed and applied to get insights into the structure of five silicophosphate glasses with increasing Ce₂O₃ and P₂O₅ content.

Epitaxial Cubic Ce2O3 Films via Ce-CeO2 Interfacial Reaction

Thin films of reduced ceria supported on metals are often applied as substrates in model studies of the chemical reactivity of ceria based catalysts. Of special interest are the properties of oxygen vacancies in ceria. However, thin films of ceria prepared by established methods become increasingly disordered as the concentration of vacancies increases. Here, we propose an alternative method for preparing ordered reduced ceria films based on the physical vapor deposition and interfacial reaction of Ce with CeO2 films. The method yields bulk-truncated layers of cubic c-Ce2O3. Compared to CeO2 these layers contain 25% of perfectly ordered vacancies in the surface and subsurface allowing well-defined measurements of the properties of ceria in the limit of extreme reduction. Experimentally, c-Ce2O3(111) layers are easily identified by a characteristic 4 × 4 surface reconstruction with respect to CeO2(111). In addition, c-Ce2O3 layers represent an experimental realization of a normally unstable polymorph of Ce2O3. During interfacial reaction, c-Ce2O3 nucleates on the interface between CeO2 buffer and Ce overlayer and is further stabilized most likely by the tetragonal distortion of the ceria layers on Cu. The characteristic kinetics of the metal-oxide interfacial reactions may represent a vehicle for making other metastable oxide structures experimentally available.

A self-consistent DFT + DMFT scheme in the projector augmented wave method: applications to cerium, Ce2O3 and Pu2O3 with the Hubbard I solver and comparison to DFT + U

An implementation of full self-consistency over the electronic density in the DFT + DMFT framework on the basis of a plane wave–projector augmented wave (PAW) DFT code is presented. It allows for an accurate calculation of the total energy in DFT + DMFT within a plane wave approach. In contrast to frameworks based on the maximally localized Wannier function, the method is easily applied to f electron systems, such as cerium, cerium oxide (Ce2O3) and plutonium oxide (Pu2O3). In order to have a correct and physical calculation of the energy terms, we find that the calculation of the self-consistent density is mandatory. The formalism is general and does not depend on the method used to solve the impurity model. Calculations are carried out within the Hubbard I approximation, which is fast to solve, and gives a good description of strongly correlated insulators. We compare the DFT + DMFT and DFT + U solutions, and underline the qualitative differences of their converged densities. We emphasize that in contrast to DFT + U, DFT + DMFT does not break the spin and orbital symmetry. As a consequence, DFT + DMFT implies, on top of a better physical description of correlated metals and insulators, a reduced occurrence of unphysical metastable solutions in correlated insulators in comparison to DFT + U.

Density functional study of oxygen vacancy formation and spin density distribution in octahedral ceria nanoparticles

We report plane wave basis density functional theory (DFT) calculations of the oxygen vacancies formation energy in nanocrystalline CeO2-x in comparison with corresponding results for bulk and (111) CeO2 surface. Effects of strong electronic correlation of Ce4f states are taken into account through the use of an effective on-site Coulomb repulsive interaction within DFT+U approach. Different combinations of exchange-correlation functionals and corresponding U values reported in the literature are tested and the obtained results compared with experimental data. We found that both absolute values and trends in oxygen vacancy formation energy depend on the value of U and associated with degree of localization of Ce4f states. Effect of oxygen vacancy and geometry optimization method on spatial spin distribution in model ceria nanoparticles is also discussed.

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.