Intricacies of DFT+U, Not Only in a Numeric Atom Centered Orbital Framework

Systematic Characterization of Electronic Metal-Support Interactions in Ceria-Supported Pt Particles

Electronic metal-support interactions affect the chemical and catalytic properties of metal particles supported on reducible metal oxides, but their characterization is challenging due to the complexity of the electronic structure of these systems. These interactions often involve different states with varying numbers and positions of strongly correlated d or f electrons and the corresponding polarons. In this work, we present an approach to characterize electronic metal-support interactions by means of computationally efficient density functional calculations within the projector augmented wave method. We describe Ce3+ cations with potentials that include a Ce4f electron in the frozen core, overcoming prevalent convergence and 4f electron localization issues. We systematically explore the stability and chemical properties of different electronic states for a Pt8/CeO2(111) model system, revealing the predominant effect of electronic metal-support interactions on Pt atoms located directly at the metal-oxide interface. Adsorption energies and the reactivity of these interface Pt atoms vary significantly upon donation of electrons to the oxide support, pointing to a strategy to selectively activate interfacial sites of metal particles supported on reducible metal oxides.

Low-spin state of Fe in Fe-doped NiOOH electrocatalysts

Doping with Fe boosts the electrocatalytic performance of NiOOH for the oxygen evolution reaction (OER). To understand this effect, we have employed state-of-the-art electronic structure calculations and thermodynamic modeling. Our study reveals that at low concentrations Fe exists in a low-spin state. Only this spin state explains the large solubility limit of Fe and similarity of Fe-O and Ni-O bond lengths measured in the Fe-doped NiOOH phase. The low-spin state renders the surface Fe sites highly active for the OER. The low-to-high spin transition at the Fe concentration of ~ 25% is consistent with the experimentally determined solubility limit of Fe in NiOOH. The thermodynamic overpotentials computed for doped and pure materials, η = 0.42 V and 0.77 V, agree well with the measured values. Our results indicate a key role of the low-spin state of Fe for the OER activity of Fe-doped NiOOH electrocatalysts.

Models of Polaron Transport in Inorganic and Hybrid Organic-Inorganic Titanium Oxides

Polarons are a type of localized excess charge in materials and often form in transition metal oxides. The large effective mass and confined nature of polarons make them of fundamental interest for photochemical and electrochemical reactions. The most studied polaronic system is rutile TiO₂ where electron addition results in small polaron formation through the reduction of Ti(IV) d⁰ to Ti(III) d¹ centers. Using this model system, we perform a systematic analysis of the potential energy surface based on semiclassical Marcus theory parametrized from the first-principles potential energy landscape. We show that F-doped TiO₂ only binds polaron weakly with effective dielectric screening after the second nearest neighbor. To tailor the polaron transport, we compare TiO₂ to two metal-organic frameworks (MOFs): MIL-125 and ACM-1. The choice of MOF ligands and connectivity of the TiO₆ octahedra largely vary the shape of the diabatic potential energy surface and the polaron mobility. Our models are applicable to other polaronic materials.

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.

DFT+U within the framework of linear combination of numerical atomic orbitals

We present a formulation and implementation of the density functional theory (DFT)+U method within the framework of linear combination of numerical atomic orbitals (NAO). Our implementation not only enables single-point total energy and electronic-structure calculations but also provides access to atomic forces and cell stresses, hence allowing for full structure relaxations of periodic systems. Furthermore, our implementation allows one to deal with non-collinear spin texture, with the spin-orbit coupling (SOC) effect treated self-consistently. The key aspect behind our implementation is a suitable definition of the correlated subspace when multiple atomic orbitals with the same angular momentum are used, and this is addressed via the "Mulliken charge projector" constructed in terms of the first (most localized) atomic orbital within the d/f angular momentum channel. The important Hubbard U and Hund J parameters can be estimated from a screened Coulomb potential of the Yukawa type, with the screening parameter either chosen semi-empirically or determined from the Thomas-Fermi screening model. Benchmark calculations are performed for four late transition metal monoxide bulk systems, i.e., MnO, FeO, CoO, and NiO, and for the 5d-electron compounds IrO₂. For the former type of systems, we check the performance of our DFT+U implementation for calculating bandgaps, magnetic moments, electronic band structures, as well as forces and stresses; for the latter, the efficacy of our DFT+U+SOC implementation is assessed. Systematic comparisons with available experimental results, especially with the results from other implementation schemes, are carried out, which demonstrate the validity of our NAO-based DFT+U formalism and implementation.

Epitaxial Core-Shell Oxide Nanoparticles: First-Principles Evidence for Increased Activity and Stability of Rutile Catalysts for Acidic Oxygen Evolution

Due to their high activity and favorable stability in acidic electrolytes, Ir and Ru oxides are primary catalysts for the oxygen evolution reaction (OER) in proton-exchange membrane (PEM) electrolyzers. For a future large-scale application, core-shell nanoparticles are an appealing route to minimize the demand for these precious oxides. Here, we employ first-principles density-functional theory (DFT) and ab initio thermodynamics to assess the feasibility of encapsulating a cheap rutile-structured TiO₂ core with coherent, monolayer-thin IrO₂ or RuO₂ films. Resulting from a strong directional dependence of adhesion and strain, a wetting tendency is only obtained for some low-index facets under typical gas-phase synthesis conditions. Thermodynamic stability in particular of lattice-matched RuO₂ films is instead indicated for more oxidizing conditions. Intriguingly, the calculations also predict an enhanced activity and stability of such epitaxial RuO₂ /TiO₂ core-shell particles under OER operation.

Best practices for first-principles simulations of epitaxial inorganic interfaces

At an interface between two materials physical properties and functionalities may be achieved, which would not exist in either material alone. Epitaxial inorganic interfaces are at the heart of semiconductor, spintronic, and quantum devices. First principles simulations based on density functional theory (DFT) can help elucidate the electronic and magnetic properties of interfaces and relate them to the structure and composition at the atomistic scale. Furthermore, DFT simulations can predict the structure and properties of candidate interfaces and guide experimental efforts in promising directions. However, DFT simulations of interfaces can be technically elaborate and computationally expensive. To help researchers embarking on such simulations, this review covers best practices for first principles simulations of epitaxial inorganic interfaces, including DFT methods, interface model construction, interface structure prediction, and analysis and visualization tools.

Excited state dynamics in monolayer black phosphorus revisited: Accounting for many-body effects

The dynamics of electron-hole recombination in pristine and defect-containing monolayer black phosphorus (ML-BP) has been studied computationally by several groups relying on the one-particle description of electronic excited states. Our recent developments enabled a more sophisticated and accurate treatment of excited states dynamics in systems with pronounced excitonic effects, including 2D materials such as ML-BP. In this work, I present a comprehensive characterization of optoelectronic properties and nonadiabatic dynamics of the ground state recovery in pristine and divacancy-containing ML-BP, relying on the linear-response time-dependent density functional theory description of excited states combined with several trajectory surface hopping methodologies and decoherence correction schemes. This work presents a revision and new implementation of the decoherence-induced surface hopping methodology. Several popular algorithms for nonadiabatic dynamics algorithms are assessed. The kinetics of nonradiative relaxation of lower-lying excited states in ML-BP systems is revised considering the new methodological developments. A general mechanism that explains the sensitivity of the nonradiative dynamics to the presence of divacancy defect in ML-BP is proposed. According to this mechanism, the excited states' relaxation may be inhibited by the presence of energetically close higher-energy states if electronic decoherence is present in the system.

Replacing hybrid density functional theory: motivation and recent advances

Density functional theory (DFT) is the most widely-used electronic structure approximation across chemistry, physics, and materials science. Every year, thousands of papers report hybrid DFT simulations of chemical structures, mechanisms, and spectra. Unfortunately, hybrid DFT's accuracy is ultimately limited by tradeoffs between over-delocalization and under-binding. This review summarizes these tradeoffs, and introduces six modern attempts to go beyond them while maintaining hybrid DFT's relatively low computational cost: DFT+U, self-interaction corrections, localized orbital scaling corrections, local hybrid functionals, real-space nondynamical correlation, and our rung-3.5 approach. The review concludes with practical suggestions for DFT users to identify and mitigate these tradeoffs' impact on their simulations.

Tilting and Distortion in Rutile-Related Mixed Metal Ternary Uranium Oxides: A Structural, Spectroscopic, and Theoretical Investigation

A systematic investigation examining the origins of structural distortions in rutile-related ternary uranium AUO₄ oxides using a combination of high-resolution structural and spectroscopic measurements supported by ab initio calculations is presented. The structures of β-CdUO₄, MnUO₄, CoUO₄, and MgUO₄ are determined at high precision by using a combination of neutron powder diffraction (NPD) and synchrotron X-ray powder diffraction (S-XRD) or single crystal X-ray diffraction. The structure of β-CdUO₄ is best described by space group Cmmm whereas MnUO₄, CoUO₄, and MgUO₄ are described by the lower symmetry Ibmm space group and are isostructural with the previously reported β-NiUO₄ [Murphy et al. Inorg. Chem. 2018, 57, 13847]. X-ray absorption spectroscopy (XAS) analysis shows all five oxides contain hexavalent uranium. The difference in space group can be understood on the basis of size mismatch between the A²⁺ and U⁶⁺ cations whereby unsatisfactory matching results in structural distortions manifested through tilting of the AO₆ polyhedra, leading to a change in symmetry from Cmmm to Ibmm. Such tilts are absent in the Cmmm structure. Heating the Ibmm AUO₄ oxides results in reduction of the tilt angle. This is demonstrated for MnUO₄ where in situ S-XRD measurements reveal a second-order phase transition to Cmmm near T = 200 °C. Based on the extrapolation of variable temperature in situ S-XRD data, CoUO₄ is predicted to undergo a continuous phase transition to Cmmm at ∼1475 °C. Comparison of the measured and computed data highlights inadequacies in the DFT+U approach, and the conducted analysis should guide future improvements in computational methods. The results of this investigation are discussed in the context of the wider AUO₄ family of oxides.

Ag5-induced stabilization of multiple surface polarons on perfect and reduced TiO2 rutile (110)

The recent advent of cutting-edge experimental techniques allows for a precise synthesis of subnanometer metal clusters composed of just a few atoms, opening new possibilities for subnanometer science. In this work, via first-principles modeling, we show how the decoration of perfect and reduced TiO₂ surfaces with Ag₅ atomic clusters enables the stabilization of multiple surface polarons. Moreover, we predict that Ag₅ clusters are capable of promoting defect-induced polarons transfer from the subsurface to the surface sites of reduced TiO₂ samples. For both planar and pyramidal Ag₅ clusters, and considering four different positions of bridging oxygen vacancies, we model up to 14 polaronic structures, leading to 134 polaronic states. About 71% of these configurations encompass coexisting surface polarons. The most stable states are associated with large inter-polaron distances (>7.5 Å on average), not only due to the repulsive interaction between trapped Ti³⁺ 3d¹ electrons, but also due to the interference between their corresponding electronic polarization clouds [P. López-Caballero et al., J. Mater. Chem. A 8, 6842-6853 (2020)]. As a result, the most stable ferromagnetic and anti-ferromagnetic arrangements are energetically quasi-degenerate. However, as the average inter-polarons distance decreases, most (≥70%) of the polaronic configurations become ferromagnetic. The optical excitation of the midgap polaronic states with photon energy at the end of the visible region causes the enlargement of the polaronic wave function over the surface layer. The ability of Ag₅ atomic clusters to stabilize multiple surface polarons and extend the optical response of TiO₂ surfaces toward the visible region bears importance in improving their (photo-)catalytic properties and illustrates the potential of this new generation of subnanometer-sized materials.

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.

On the use of DFT+U to describe the electronic structure of TiO2 nanoparticles: (TiO2)35 as a case study

One of the main drawbacks in the density functional theory (DFT) formalism is the underestimation of the energy gaps in semiconducting materials. The combination of DFT with an explicit treatment of the electronic correlation with a Hubbard-like model, known as the DFT+U method, has been extensively applied to open up the energy gap in materials. Here, we introduce a systematic study where the selection of the U parameter is analyzed considering two different basis sets: plane-waves and numerical atomic orbitals (NAOs), together with different implementations for including U, to investigate the structural and electronic properties of a well-defined bipyramidal (TiO₂)₃₅ nanoparticle. This study reveals, as expected, that a certain U value can reproduce the experimental value for the energy gap. However, there is a high dependence on the choice of basis set and on the U parameter employed. The present study shows that the linear combination of the NAO basis functions, as implemented in Fritz Haber Institute ab initio molecular simulation (FHI-aims), requires, requires a lower U value than the simplified rotationally invariant approach, as implemented in the Vienna ab initio simulation package (VASP). Therefore, the transfer of U values between codes is unfeasible and not recommended, demanding initial benchmark studies for the property of interest as a reference to determine the appropriate value of U.

Mobile Small Polarons Qualitatively Explain Conductivity in Lithium Titanium Oxide Battery Electrodes

Lithium titanium oxide Li₄Ti₅O₁₂ is an intriguing anode material promising particularly long-life batteries, due to its remarkable phase stability during (dis)charging of the cell. However, its usage is limited by its low intrinsic electronic conductivity. Introducing oxygen vacancies can be one method for overcoming this drawback, possibly by altering the charge carrier transport mechanism. We use Hubbard corrected density functional theory to show that polaronic states in combination with a possible hopping mechanism can play a crucial role in the experimentally observed increase in electronic conductivity. To gauge polaronic charge mobility, we compute the relative stabilities of different localization patterns and estimate polaron hopping barrier heights.

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

Anatase and brookite are robust materials with enhanced photocatalytic properties. In this study, we used density functional theory (DFT) with a hybrid functional and the Hubbard on-site potential methods to determine electron- and hole-polaron geometries for anatase and brookite and their energetics. Localized electron and hole polarons were predicted not to form in anatase using DFT with hybrid functionals. In contrast, brookite formed both electron and hole polarons. The brookite electron-polaronic solution exhibits coexisting localized and delocalized states, with hole polarons mainly dispersed on two-coordinated oxygen ions. Hubbard on-site potential testing over the wide 4.0-10 eV range revealed that brookite polarons are formed at U = 6 eV, while anatase polarons are formed at U = 8 eV. The brookite electron polaron was always localized on a single titanium ion under the Hubbard model, whereas the hole polaron was dispersed over four oxygen atoms, consistent with the hybrid DFT studies. The anatase electron polarons were dispersed at lower on-site potentials but were more localized at higher potentials. Both methods predict that brookite has a higher driving force for the formation of polarons than anatase.