Density functional theory in transition-metal chemistry: a self-consistent Hubbard U approach

Defective TiOx overlayers catalyze propane dehydrogenation promoted by base metals

The industrial catalysts utilized for propane dehydrogenation (PDH) to propylene, an important alternative to petroleum-based cracking processes, either use expensive metals or metal oxides that are environmentally unbenign. We report that a typically less-active oxide, titanium oxide (TiO2), can be combined with earth-abundant metallic nickel (Ni) to form an unconventional Ni@TiOx catalyst for efficient PDH. The catalyst demonstrates a 94% propylene selectivity at 40% propane conversion and superior stability under industrially relevant conditions. Complete encapsulation of Ni nanoparticles was allowed at elevated temperatures (>550°C). A mechanistic study suggested that the defective TiOx overlayer consisting of tetracoordinated Ti sites with oxygen vacancies is catalytically active. Subsurface metallic Ni acts as an electronic promoter to accelerate carbon-hydrogen bond activation and hydrogen (H2) desorption on the TiOx overlayer.

The energy landscape of magnetic materials

Magnetic materials can display many solutions to the electronic-structure problem, corresponding to different local or global minima of the energy functional. In Hartree-Fock or density-functional theory different single-determinant solutions lead to different magnetizations, ionic oxidation states, hybridizations, and inter-site magnetic couplings. The vast majority of these states can be fingerprinted through their projection on the atomic orbitals of the magnetic ions. We have devised an approach that provides an effective control over these occupation matrices, allowing us to systematically explore the landscape of the potential energy surface. We showcase the emergence of a complex zoology of self-consistent states; even more so when semi-local density-functional theory is augmented - and typically made more accurate - by Hubbard corrections. Such extensive explorations allow to robustly identify the ground state of magnetic systems, and to assess the accuracy (or not) of current functionals and approximations.

Combining Local Range Separation and Local Hybrids: A Step in the Quest for Obtaining Good Energies and Eigenvalues from One Functional

Some of the most successful exchange-correlation approximations in density functional theory are "hybrids", i.e., they rely on combining semilocal density functionals with exact nonlocal Fock exchange. In recent years, two classes of hybrid functionals have emerged as particularly promising: range-separated hybrids on the one hand, and local hybrids on the other hand. These functionals offer the hope to overcome a long-standing "observable dilemma", i.e., the fact that density functionals typically yield either a good description of binding energies, as obtained, e.g., in global and local hybrids, or physically interpretable eigenvalues, as obtained, e.g., in optimally tuned range-separated hybrids. Obtaining both of these characteristics from one and the same functional with the same set of parameters has been a long-standing challenge. We here discuss combining the concepts of local range separation and local hybrids as part of a constraint-guided quest for functionals that overcome the observable dilemma.

Phase transition and electrochemical properties of S-functionalized MXene anodes for Li-ion batteries: a first-principles investigation

The advancement of anode materials for achieving high energy storage is a crucial topic for high-performance Li-ion batteries (LIBs). Here, first-principles calculations were used to conduct a thorough and systematic investigation into lithium storage properties of MXenes with new S functional groups as LIB anode materials. Density of states, diffusion energy barriers, open circuit voltages and storage capacities were calculated to comprehensively evaluate the lithium storage properties of S-functionalized MXenes. Based on the computational results, Ti2CS2 and V2CS2 were selected as excellent candidates from ten M2CS2 MXenes. The diffusion energy barriers of M2CS2 within the range of 0.26-0.32 eV are lower than those of M2CO2 and M2CF2, indicating that M2CS2 anodes exhibit faster charge/discharge rates. By examining the stable crystal structures and comparing atomic positions before and after Li adsorptions, structural phase transitions during Li-ion adsorptions could happen for nearly all M2CS2 MXenes. The phase transitions predicted were directly observed using ab initio molecular dynamic simulations. The cycle stability, storage capacity and other lithium storage properties were enhanced by the reversible structural phase transition.

Differences in Kondo Splitting of Surface Quantum Systems Induced by Two Distinct Magnetic Tips: A Joint Method of DFT and HEOM

The interactions between a magnetic tip and local spin impurities initiate unconventional Kondo phenomena, such as asymmetric suppression or even splitting of the Kondo peak. However, a lack of realistic theoretical models and comprehensive explanations for this phenomenon persists due to the complexity of the interactions. This research employs a joint method of density functional theory (DFT) and hierarchical equation of motion (HEOM) to simulate and contrast the modulation of the spin state and Kondo behavior in the Fe/Cu(100) system with two distinct magnetic tips. A cobalt tip, possessing a larger magnetic moment, incites greater atomic displacement of the iron atom, more notable alterations in electronic structure, and enhanced charge transfer with the environment compared with the control process utilizing a nickel tip. Furthermore, the Kondo resonance undergoes asymmetric splitting as a result of the ferromagnetic correlation between the iron atom and the magnetic tip. The Co tip's higher spin polarization results in a wider spacing between the splitting peaks. This investigation underscores the precision of the DFT + HEOM approach in predicting complex quantum phenomena and explaining the underlying physical principles. This provides valuable theoretical support for developing more sophisticated quantum regulation experiments.

Impact of quantum size effects to the band gap of catalytic materials: a computational perspective

The evolution of nanotechnology has facilitated the development of catalytic materials with controllable composition and size, reaching the sub-nanometer limit. Nowadays, a viable strategy for tailoring and optimizing the catalytic activity involves controlling the size of the catalyst. This strategy is underpinned by the fact that the properties and reactivity of objects with dimensions on the order of nanometers can differ from those of the corresponding bulk material, due to the emergence of quantum size effects. Quantum size effects have a deep influence on the band gap of semiconducting catalytic materials. Computational studies are valuable for predicting and estimating the impact of quantum size effects. This perspective emphasizes the crucial role of modeling quantum size effects when simulating nanostructured catalytic materials. It provides a comprehensive overview of the fundamental principles governing the physics of quantum confinement in various experimentally observable nanostructures. Furthermore, this work may serve as a tutorial for modeling the electronic gap of simple nanostructures, highlighting that when working at the nanoscale, the finite dimensions of the material lead to an increase of the band gap because of the emergence of quantum confinement. This aspect is sometimes overlooked in computational chemistry studies focused on surfaces and nanostructures.

Orbital-Resolved DFT+U for Molecules and Solids

We present an orbital-resolved extension of the Hubbard U correction to density-functional theory (DFT). Compared to the conventional shell-averaged approach, the prediction of energetic, electronic and structural properties is strongly improved, particularly for compounds characterized by both localized and hybridized states in the Hubbard manifold. The numerical values of all Hubbard parameters are readily obtained from linear-response calculations. The relevance of this more refined approach is showcased by its application to bulk solids pyrite (FeS2) and pyrolusite (β-MnO2), as well as to six Fe(II) molecular complexes. Our findings indicate that a careful definition of Hubbard manifolds is indispensable for extending the applicability of DFT+U beyond its current boundaries. The present orbital-resolved scheme aims to provide a computationally undemanding yet accurate tool for electronic structure calculations of charge-transfer insulators, transition-metal (TM) complexes and other compounds displaying significant orbital hybridization.

The enhanced bandgap and birefringence of rare-earth phosphates XPO4 (X = Sc, Y, La, and Lu): a first-principles investigation

Rare-earth phosphates were thought to be good candidates as ultraviolet/deep ultraviolet optical materials due to their relatively large bandgap and optical properties. In this paper, the authors screened out a family of XPO4 (X = Sc, Y, La, and Lu) compounds with an enhanced bandgap (HSE06 bandgap ≥ 7.61 eV) and birefringence (0.0934-0.2003@1064 nm) using first-principles calculations. The origin of enhanced optical properties was investigated using projected density of states, distortion indices, and Born effective charges. The results show that the PO4 anionic groups and X-O polyhedra give the main contribution in determining the optical properties, and the PO4 anionic groups give more contribution than other functional basic units. The spin-orbit interaction was also investigated. Similar band structures were found after spin-orbit coupling (SOC) was considered, and slightly enhanced birefringence was found when SOC was applied to these rare-earth phosphates.

Unraveling the Hydration Shell Structure and Dynamics of Group 10 Aqua Ions

We present ab initio simulations based on subsystem DFT of group 10 aqua ions accurately compared against experimental data on hydration structure. Our simulations provide insights into the molecular structures and dynamics of hydration shells, offering recalibrated interpretations of experimental results. We observe a soft, but distinct second hydration shell in Palladium (Pd) due to a balance between thermal fluctuations, metal-water interactions, and hydrogen bonding. Nickel (Ni) and platinum (Pt) exhibit more rigid hydration shells. Notably, our simulations align with experimental findings for Pd, showing axial hydration marked by a broad peak at about 3 Å in the Pd-O radial distribution function, revising the previously sharp "mesoshell" prediction. We introduce the "hydrogen bond dome" concept to describe a resilient network of hydrogen-bonded water molecules around the metal, which plays a critical role in the axial hydration dynamics.

Highly sensitive sensing of CO and HF gases by monolayer CuCl

Using a first-principles approach, the adsorption characteristics of CO and HF on a CuCl monolayer (ML) are studied with Grimme-scheme DFT-D2 for accurate description of the long-range (van der Waals) interactions. According to our study, CO gas molecules undergo chemisorption and HF gas molecules show a physisorption phenomenon on the CuCl monolayer. The adsorption energy for CO is -1.80 eV, which is quite a large negative value compared to that on other previously studied substrates, like InN (-0.223 eV), phosphorene (0.325 eV), Janus Te2Se (-0.171 eV), graphene (P-graphene, -0.12 eV, B-graphene, -0.14 eV, N-graphene, -0.1 eV) and monolayer ZnS (-0.96 eV), as well as pristine hBN (0.21 eV) and Ti-doped hBN (1.66 eV). Meanwhile, for HF, the adsorption energy value is -0.31 eV (greater than that of Ti-doped hBN, 0.27 eV). For CO, the large value of the diffusion energy barrier (DEB = 1.26 eV) during its movement between two optimal sites indicates that clustering can be prevented if many molecules of CO are adsorbed on the CuCl ML. For HF, the value of the DEB (0.082 eV) implies that the adsorption phenomenon may happen quite easily upon the CuCl ML. The transfer of charge according to Bader charge analysis and the variation in the work function depend only on the properties of the elements involved, i.e., their nature, rather than the local binding environment. The work function and band-gap energy variation of the CuCl ML (before and after adsorption) show high sensitivity and selectivity of CO and HF binding with the CuCl monolayer. HF molecules give a more rapid recovery time of 1.09 × 10-7 s compared to that of CO molecules at a room temperature (RT) of 300 K, which indicates that the necessary adsorption and reusability of the CuCl ML for HF can be accomplished effectively at RT. Significant changes in the conductivity are observed due to the CO adsorption at various temperatures, as compared to adsorption of HF, which suggests the possibility of a modification in the conductivity of the CuCl ML.

Unconventional Surface Doping Effect on the Spin State of an Adsorbed Magnetic Molecule

Magnetic molecules adsorbed on two-dimensional (2D) substrates have attracted broad attention because of their potential applications in quantum device applications. Experimental observations have demonstrated substantial alteration in the spin excitation energy of iron phthalocyanine (FePc) molecules when adsorbed on nitrogen-doped graphene substrates. However, the underlying mechanism responsible for this notable change remains unclear. To shed light on this, we employ an embedding method and ab initio quantum chemistry calculations to investigate the effects of surface doping on molecular properties. Our study unveils an unconventional chemical bonding at the interface between the FePc molecule and the N-doped graphene. This bonding interaction, stronger than non-covalent interactions, significantly modifies the magnetic anisotropy energy of the adsorbed molecule, consistent with experimental observations. These findings provide valuable insights into the electronic and magnetic properties of molecules on 2D substrates, offering a promising pathway for precise manipulation of molecular spin states.

Continuous Flow Electrochemical Synthesis of Olivine-Structured NaFePO4 Cathode Material for Sodium-Ion Batteries from Recycle LiFePO4

To mitigate the environmental impact of the improper disposal of spent LiFePO4 batteries and reduce resource waste, the development of LiFePO4 recycling technologies is of paramount importance. Meanwhile, olivine-structured NaFePO4 in sodium-ion batteries has received great attention, due to its high theoretical specific capacity of 154 mAh g-1 and excellent stability. However, olivine NaFePO4 only can be synthesized from olivine LiFePO4. Accordingly, in this proposal, developing the continuous flow electrochemical solid-liquid reactor-based metal ion insertion technology is to utilize the olivine FePO4, recycled from LiFePO4, and to synthesize NaFePO4. Additionally, by employing I- as the reducing agent, NaFePO4 is successfully synthesized with a discharge-specific capacity of 134 mAh g-1 at 0.1C and a remarkable capacity retention rate of 86.5% after 100 cycles at 0.2C. And the reasons for sodium deficiency in the synthesized NFP are elucidated through first-principles calculations. Furthermore, the kinetics of the solid-solution reaction 2 (Na2/3+βPO4→ Na1-αFePO4) mechanism improve with cycling and are sensitive to temperature. Utilizing a minimal amount of reducing agent in the electrochemical reactor, NaFePO4 synthesis is successfully achieved. This innovative approach offers a new, cost-effective, and environmentally friendly strategy for preparing NaFePO4 from recycling LiFePO4.

Enhanced Cathode Performance in Pr0.5Sr0.5FeO3-δ of Perovskite Catalytic Materials via Doping with VB Subgroup Elements (V, Nb, and Ta)

Perovskite-style materials are cathode systems known for their stability in solid oxide fuel cells (SOFCs). Pr0.5Sr0.5FeO3-δ (PSF) exhibits excellent electrode performance in perovskite cathode systems at high temperatures. Via VB subgroup metals (V, Nb, and Ta) modifying the B-site, the oxidation and spin states of iron elements can be adjusted, thereby ultimately adjusting the cathode's physicochemical properties. Theoretical predictions indicate that PSF has poor stability, but the relative arrangement of the three elements on the B-site can significantly improve this material's properties. The modification of Nb has a large effect on the stability of PSF cathode materials, reaching a level of -2.746 eV. The surface structure of PSF becomes slightly more stable with an increase in the percentage of oxygen vacancy structures, but the structural instability persists. Furthermore, the differential charge density distribution and adsorption state density of the three modified cathode materials validate our adsorption energy prediction results. The initial and final states of the VB subgroup metal-doped PSF indicate that PSFN is more likely to complete the cathode surface adsorption reaction. Interestingly, XRD and EDX characterization are performed on the synthesized pure and Nb-doped PSF material, which show the orthorhombic crystal system of the composite theoretical model structure and subsequent experimental components. Although PSF exhibits strong catalytic activity, it is highly prone to decomposition and instability at high temperatures. Furthermore, PSFN, with the introduction of Nb, shows greater stability and can maintain its activity for the ORR. EIS testing clearly indicates that Nb most significantly improves the cathode. The consistency between the theoretical predictions and experimental validations indicates that Nb-doped PSF is a stable and highly active cathode electrode material with excellent catalytic activity.

Full-waveform tomography reveals iron spin crossover in Earth's lower mantle

Three-dimensional models of Earth's seismic structure can be used to identify temperature-dependent phenomena, including mineralogical phase and spin transformations, that are obscured in 1-D spherical averages. Full-waveform tomography maps seismic wave-speeds inside the Earth in three dimensions, at a higher resolution than classical methods. By providing absolute wave speeds (rather than perturbations) and simultaneously constraining bulk and shear wave speeds over the same frequency range, it becomes feasible to distinguish variations in temperature from changes in composition or spin state. We present a quantitative joint interpretation of bulk and shear wave speeds in the lower mantle, using a recently published full-waveform tomography model. At all depths the diversity of wave speeds cannot be explained by an isochemical mantle. Between 1000 and 2500 km depth, hypothetical mantle models containing an electronic spin crossover in ferropericlase provide a significantly better fit to the wave-speed distributions, as well as more realistic temperatures and silica contents, than models without a spin crossover. Below 2500 km, wave speed distributions are explained by an enrichment in silica towards the core-mantle boundary. This silica enrichment may represent the fractionated remains of an ancient basal magma ocean.

Universal Generalization of Density Functional Theory for Static Correlation

A major challenge for density functional theory (DFT) is its failure to treat static correlation, yielding errors in predicted charges, band gaps, van der Waals forces, and reaction barriers. Here we combine one- and two-electron reduced density matrix (1- and 2-RDM) theories with DFT to obtain a universal O(N^{3}) generalization of DFT for static correlation. Using the lowest unitary invariant of the cumulant 2-RDM, we generate a 1-RDM functional theory that corrects the convexity of any DFT functional to capture static correlation in its fractional orbital occupations. Importantly, the unitary invariant yields a predictive theory by revealing the dependence of the correction's strength upon the trace of the two-electron repulsion matrix. We apply the theory to the barrier to rotation in ethylene, the relative energies of the benzynes, as well as an 11-molecule, dissociation benchmark. By inheriting the computational efficiency of DFT without sacrificing the treatment of static correlation, the theory opens new possibilities for the prediction and interpretation of significant quantum molecular effects and phenomena.

Tuning ferroelectric photovoltaic performance in R3c-CuNbO3 through compressive strain engineering: a first-principles study

Most ferroelectric oxides exhibit relatively wide bandgaps, which pose limitations on their suitability for photovoltaics application. CuNbO3 possesses potential ferroelectric properties with an R3c polar structure that facilitate the separation of charge carriers under illumination, promoting the generation of photovoltaic effects. The optical and ferroelectric properties of R3c-CuNbO3, as well as the effect of strain on the properties are investigated by first-principles calculation in this paper. The calculated results indicate that R3c-CuNbO3 possesses a moderate band gap to absorb visible light. The interaction of Cu-O and Nb-O bonds is considered to have a crucial role in the photovoltaic properties of CuNbO3, contributing to the efficient absorption of visible light. The bandgap of CuNbO3 becomes smaller and the density of states near the conduction and valence bands becomes relatively uniform in distribution under compressive conditions, which improves the photoelectric conversion efficiency to 29.9% under conditions of bulk absorption saturation. The ferroelectric properties of CuNbO3 are driven by the Nb-O bond interactions, which are not significantly weakened by the compressive strain. CuNbO3 is expected to be an excellent ferroelectric photovoltaic material by modulation of compressive strain due to the stronger visible light absorption and excellent ferroelectric behavior.

Artificial Neural Network-Based Density Functional Approach for Adiabatic Energy Differences in Transition Metal Complexes

During the past decades, approximate Kohn-Sham density functional theory schemes have garnered many successes in computational chemistry and physics, yet the performance in the prediction of spin state energetics is often unsatisfactory. By means of a machine learning approach, an enhanced exchange and correlation functional is developed to describe adiabatic energy differences in transition metal complexes. The functional is based on the computationally efficient revision of the regularized, strongly constrained, and appropriately normed functional and improved by an artificial neural network correction trained over a small data set of electronic densities, atomization energies, and/or spin state energetics. The training process, performed using a bioinspired nongradient-based approach adapted for this work from the particle swarm optimization, is analyzed and discussed extensively. The resulting machine learned meta-generalized gradient approximation functional is shown to outperform most known density functionals in the prediction of adiabatic energy differences for a diverse set of transition metal complexes with varying local coordinations and metal choices.

Modeling Single-Atom Catalysis

Electronic structure calculations represent an essential complement of experiments to characterize single-atom catalysts (SACs), consisting of isolated metal atoms stabilized on a support, but also to predict new catalysts. However, simulating SACs with quantum chemistry approaches is not as simple as often assumed. In this work, the essential factors that characterize a reliable simulation of SACs activity are examined. The Perspective focuses on the importance of precise atomistic characterization of the active site, since even small changes in the metal atom's surroundings can result in large changes in reactivity. The dynamical behavior and stability of SACs under working conditions, as well as the importance of adopting appropriate methods to solve the Schrödinger equation for a quantitative evaluation of reaction energies are addressed. The Perspective also focuses on the relevance of the model adopted. For electrocatalysis this must include the effects of the solvent, the presence of electrolytes, the pH, and the external potential. Finally, it is discussed how the similarities between SACs and coordination compounds may result in reaction intermediates that usually are not observed on metal electrodes. When these aspects are not adequately considered, the predictive power of electronic structure calculations is quite limited.

Perspective from a Hubbard U-density corrected scheme towards a spin crossover-mediated change in gas affinity

By employing a recently proposed Hubbard U density-corrected scheme within density functional theory, we provide design principles towards the design of materials exhibiting a spin crossover-assisted gas release. Small molecular fragments are used as case study to identify two main mechanisms behind the change in binding energy upon spin transitions. The feasibility of the proposed mechanism in porous crystals is assessed by correlating the change in binding energy of CO2, CO, N2, and H2, upon spin crossover, with the adiabatic energy difference associated with the spin state change of the square-planar metal in Hofmann-type clathrates (M = Fe, Mn, Ni). A few promising cases are identified for the adsorption of intermediate ligand field strength molecules such as N2 and H2. The latter stands out as the most original result as the strong interaction in low spin, as expected from a Kubas mechanism, results in a large change in binding energy. This work provides a general perspective towards the engineering of open-metal site frameworks exhibiting local environments designed to have a spin crossover upon adsorption of specific gas molecules.

Spin state and magnetic coupling in polynuclear Ni(II) complexes from density functional theory: is there an optimal amount of Fock exchange?

Reliable prediction of the ground-state spin and magnetic coupling constants in transition-metal complexes is a well-known challenge for density functional theory (DFT). One popular strategy for addressing this long-standing issue involves the modification of the fraction of Fock exchange in a hybrid functional. Here we explore the viability of this approach using three polynuclear metal-organic complexes based on a Ni4O4 cubane motif, having different ground state spin values (S = 0, 2, 4) owing to the use of different ligands. We systematically search for an optimum fraction of Fock exchange, across various global, range-separated, and double hybrid functionals. We find that for all functionals tested, at best there only exists a very narrow range of Fock exchange fractions which results in a correct prediction of the ground-state spin for all three complexes. The useful range is functional dependent, but general trends can be identified. Typically, at least two similar systems must be used in order to determine both an upper and lower limit of the optimal range. This is likely owing to conflicting demands of minimizing delocalization errors, which typically requires a higher percentage of Fock exchange, and addressing static correlation, which typically requires a lower one. Furthermore, we find that within the optimal range of Fock exchange, the sign and relative magnitude of Ni-Ni magnetic coupling constants are reasonably well reproduced, but there is still room for quantitative improvement in the prediction. Thus, the prediction of spin state and magnetic coupling in polynuclear complexes remains an ongoing challenge for DFT.

Enhanced anodic catalytic performance in PrFeO3-δ of perovskite materials via Co-doping with Sr and VB subgroup metals (V, Nb, Ta)

The anodic catalytic capability of PrFeO3-δ is restricted by the Fe-site element type in the perovskite material structure due to its low electrical conductivity of electrons. Here, we present a strategy for tuning the Fe-site element type via Sr and VB subgroup metals (V, Nb, Ta) co-doping to enhance the anodic catalytic performance of PrFeO3-δ anode materials. Our calculations show that Sr and Nb co-doping has suitable hydrogen adsorption energy for PrFeO3-δ anode materials, and its adsorption energy is adjusted to -0.717 eV, which is more suitable to absorb the hydrogen molecule than other high-profile perovskite anode materials. Meanwhile, after the doped surface is adsorbed by hydrogen molecules, the bond length lengthens until it breaks, and one of the broken hydrogen atoms moves directly above the surface oxygen atom, which is beneficial for accelerating the anodic catalytic reaction. Thus, the Pr0.5Sr0.5Fe0.875Nb0.125O3-δ material is a promising perovskite anode catalyst. Interestingly, the stability of PrFeO3-δ is significantly affected by the oxygen vacancy content; the structural stability of the undoped system can be maintained via Sr and Nb co-doping to avoid decomposition, which provides new thinking to maintain the high stability of perovskite ferrite materials. Furthermore, we find that relative to the PrFeO3-δ, the Pr0.5Sr0.5Fe0.875Nb0.125O3-δ surface of hydrogen adsorption has obvious charge transfer and upward shift of the d-band center. Our anodic catalytic theoretical work shows that Sr and Nb co-doping can effectively enhance the catalytic performance of the PrFeO3-δ ferrite materials.

Transition Temperature for Spin-Crossover Materials with the Mean Value Ensemble Hubbard-U Correction

Calculation of transition temperatures T1/2 for thermally driven spin-crossover in condensed phases is challenging, even with sophisticated state-of-the-art density functional approximations. The first issue is the accuracy of the adiabatic crossover energy difference ΔEHL between the low- and high-spin states of the bistable metal-organic complexes. The other is the proper inclusion of entropic contributions to the Gibbs free energy from the electronic and vibrational degrees of freedom. We discuss the effects of treatments of both contributions upon the calculation of thermochemical properties for a set of 20 spin-crossover materials using a Hubbard-U correction obtained from a reference ensemble spin-state. The U values obtained from a simplest bimolecular representation may overcorrect, somewhat, the ΔEHL values, hence giving somewhat excessive reduction of the T1/2 results with respect to their U = 0 values in the crystalline phase. We discuss the origins of the discrepancies by analyzing different sources of uncertainties. By use of a first-coordination-sphere approximation and the assumption that vibrational contributions from the outermost atoms in a metal-organic complex are similar in both low- and high-spin states, we achieve T1/2 results with the low-cost, widely used PBE generalized gradient density functional approximation comparable to those from the more costly, more sophisticated r2SCAN meta-generalized gradient approximation. The procedure is promising for use in high-throughput materials screening, because it combines rather low computational effort requirements with freedom from user manipulation of parameters.

Growth mechanism study and band structure modulation of a manganese doped two-dimensional BlueP-Au network

Two-dimensional (2D) materials are a very promising material family. The two-dimensional inorganic metal network called BlueP-Au network is rapidly attracting the attention of researchers due to its customizable architecture, adjustable chemical functions and electronic properties. Herein, manganese (Mn) was successfully doped on a BlueP-Au network for the first time, then the doping mechanism and electronic structure evolution was studied by in situ X-ray photoelectron spectroscopy (XPS) based on synchrotron radiation, X-ray absorption spectroscopy (XAS), Scanning Tunneling Microscopy (STM), Density functional theory (DFT), Low-energy electron diffraction (LEED), Angle resolved photoemission spectroscopy (ARPES), etc. Mn atoms tend to be stably adsorbed on two sites of the BlueP-Au network. It was the first observation that atoms can absorb on the two sites stably simultaneously. It is different from the previous adsorption models of BlueP-Au networks. The band structure was also successfully modulated, and overall down about 0.25 eV relative to the Fermi edge. It provided a new strategy for customizing the functional structure of the BlueP-Au network, which has provided new insights into monatomic catalysis, energy storage and nano electronic devices.

Broad Electronic Modulation of Two-Dimensional Metal-Organic Frameworks over Four Distinct Redox States

Two-dimensional (2D) inorganic materials have emerged as exciting platforms for (opto)electronic, thermoelectric, magnetic, and energy storage applications. However, electronic redox tuning of these materials can be difficult. Instead, 2D metal-organic frameworks (MOFs) offer the possibility of electronic tuning through stoichiometric redox changes, with several examples featuring one to two redox events per formula unit. Here, we demonstrate that this principle can be extended over a far greater span with the isolation of four discrete redox states in the 2D MOFs Li_xFe₃(THT)₂ (x = 0-3, THT = triphenylenehexathiol). This redox modulation results in 10,000-fold greater conductivity, p- to n-type carrier switching, and modulation of antiferromagnetic coupling. Physical characterization suggests that changes in carrier density drive these trends with relatively constant charge transport activation energies and mobilities. This series illustrates that 2D MOFs are uniquely redox flexible, making them an ideal materials platform for tunable and switchable applications.

Unraveling the effects of inter-site Hubbard interactions in spinel Li-ion cathode materials

Accurate first-principles predictions of the structural, electronic, magnetic, and electrochemical properties of cathode materials can be key in the design of novel efficient Li-ion batteries. Spinel-type cathode materials Li_xMn₂O₄ and Li_xMn_1.5Ni_0.5O₄ are promising candidates for Li-ion battery technologies, but they present serious challenges when it comes to their first-principles modeling. Here, we use density-functional theory with extended Hubbard functionals-DFT+U+V with on-site U and inter-site V Hubbard interactions-to study the properties of these transition-metal oxides. The Hubbard parameters are computed from first-principles using density-functional perturbation theory. We show that while U is crucial to obtain the right trends in properties of these materials, V is essential for a quantitative description of the structural and electronic properties, as well as the Li-intercalation voltages. This work paves the way for reliable first-principles studies of other families of cathode materials without relying on empirical fitting or calibration procedures.

Ultralow diffusion barrier induced by intercalation in layered N-based cathode materials for sodium-ion batteries

Sodium-ion batteries (SIBs) have attracted huge attention due to not only the similar electrochemical properties to Lithium-ion batteries (LIBs) but also the abundant natural reserves of sodium. However, the high diffusion barrier has hindered its application. In this work, we have theoretically studied the relationship between the strain and the diffusion barrier/path of sodium ions in layered CrN₂ by first-principles calculation. Our results show that the strain can not only effectively decrease the diffusion barrier but also change the sodium diffusion path, which can be realized by alkali metal intercalation. Moreover, the diffusion barrier is as low as 0.04 eV with the Cs atoms embedding in layered CrN₂ (Cs_1/16CrN₂), suggesting an excellent candidate cathode for SIBs. In addition, the decrease of the barrier mainly originated from the fact that interlayer electronic coupling weakened with the increase of interlayer spacing. Our findings provide an effective way to enhance sodium diffusion performance, which is beneficial for the design of SIB electrode materials.

Comparative study of first-principles approaches for effective Coulomb interaction strength Ueff between localized f-electrons: Lanthanide metals as an example

As correlation strength has a key influence on the simulation of strongly correlated materials, many approaches have been proposed to obtain the parameter using first-principles calculations. However, a comparison of the different Coulomb strengths obtained using these approaches and an investigation of the mechanisms behind them are still needed. Taking lanthanide metals as an example, we research the factors that affect the effective Coulomb interaction strength, U_eff, by local screened Coulomb correction (LSCC), linear response (LR), and constrained random-phase approximation (cRPA) in the Vienna Ab initio Simulation Package. The U_eff ^LSCC value increases from 4.75 to 7.78 eV, U_eff ^LR is almost stable at about 6.0 eV (except for Eu, Er, and Yb), and U_eff ^cRPA shows a two-stage decreasing trend in both light and heavy lanthanides. To investigate these differences, we establish a scheme to analyze the coexistence and competition between the orbital localization and the screening effect. We find that LSCC and cRPA are dominated by the orbital localization and the screening effect, respectively, whereas LR shows the balance of the competition between the two factors. Additionally, the performance of these approaches is influenced by different starting points from the Perdew-Burke-Ernzerhof (PBE) and PBE + U, especially for cRPA. Our results provide useful knowledge for understanding the U_eff of lanthanide materials, and similar analyses can also be used in the research of other correlation strength simulation approaches.

Tweezer-like magnetic tip control of the local spin state in the FeOEP/Pb(111) adsorption system: a preliminary exploration based on first-principles calculations

The magnetic interactions between the spin-polarized scanning tunnelling microscopy (SP-STM) tip and the localized spin impurities lead to various forms of the Kondo effect. Although these intriguing phenomena enrich Kondo physics, detailed theoretical simulations and explanations are still lacking due to the rather complex formation mechanisms. Here, by combining density functional theory (DFT), complete active space self-consistent field (CASSCF) theory, and hierarchical equations of motion (HEOM) methods, we perform first-principles-based simulation to elaborate the regulation process of the magnetic Co-tip on the spin state and transport behaviour of FeOEP/Pb(111) system. Compared with the non-magnetic tip, the stronger interaction between the magnetic tip and FeOEP molecule results in a more drastic deformation of the molecular structure with more electron transfer from the local environment to Fe-3d orbitals. The magnetic anisotropy of FeOEP changes very drastically from positive values in the tunnelling region to negative values in the contact region. The ferromagnetic electron correlation between the magnetic tip and the molecule induces an asymmetric Kondo line-shape near the Fermi level. This work highlights that the DFT + CASSCF + HEOM approach can not only predict complex quantum phenomena and explain underlying physical mechanisms, but also facilitate the design of more fascinating quantum control experiments.

Mean Value Ensemble Hubbard-U Correction for Spin-Crossover Molecules

High-throughput searches for spin-crossover molecules require Hubbard-U corrections to common density functional exchange-correlation (XC) approximations. However, the U_eff values obtained from linear response or based on previous studies overcorrect the spin-crossover energies. We demonstrate that employing a linearly mixed ensemble average spin state as the reference configuration for the linear response calculation of U_eff resolves this issue. Validation on a commonly used set of spin-crossover complexes shows that these ensemble U_eff values consistently are smaller than those calculated directly on a pure spin state, irrespective of whether that be low- or high-spin. Adiabatic crossover energies using this methodology for a generalized gradient approximation XC functional are closer to the expected target energy range than with conventional U_eff values. Based on the observation that the U_eff correction is similar for different complexes that share transition metals with the same oxidation state, we devise a set of recommended averaged U_eff values for high-throughput calculations.

Unveiling the Decisive Factor for the Sharp Transition in the Scanning Tunneling Spectroscopy of a Single Nickelocene Molecule

Scanning tunneling microscopy (STM) has been utilized to realize the precise measurement and control of local spin states. Experiments have demonstrated that when a nickelocene (Nc) molecule is attached to the apex of an STM tip, the dI/dV spectra exhibit a sharp or a smooth transition when the tip is displaced toward the substrate. However, what leads to the two distinct types of transitions remains unclear, and more intriguingly, the physical origin of the abrupt change in the line shape of dI/dV spectra remains unclear. To clarify these intriguing issues, we perform first-principles-based simulations on the STM tip control process for the Cu tip/Nc/Cu(100) junction. In particular, we find that the suddenly enhanced hybridization between the d orbitals on the Ni ion and the metallic bands in the substrate leads to Kondo correlation overwhelming spin excitation, which is the main cause of the sharp transition in the dI/dV spectra observed experimentally.

Theoretical Study of ZnS Monolayer Adsorption Behavior for CO and HF Gas Molecules

Adsorption of carbon monoxide (CO) and hydrogen fluoride (HF) gas molecules on a ZnS monolayer with weak van der Waals interactions is studied using the DFT + U method. From our calculation, the ZnS monolayer shows chemisorption with CO (E _ads = -0.96 eV) and HF (E _ads = -0.86 eV) gas molecules. Bader charge analysis shows that charge transfer is independent of the binding environment. A higher energy barrier for CO when migrating from one optimal site to another suggests that clustering may be avoided by the introduction of multiple CO molecules upon ZnS, while the diffusion energy barrier (DEB) for HF suggests that binding may occur more easily for HF gas upon the ZnS ML. Adsorption of the considered diatomic molecule also results in a significant variation in effective mass and therefore can be used to enhance the carrier mobility of the ZnS ML. Additionally, the calculation of recovery time shows that desirable sensing and desorption performance for CO and HF gas molecules can be achieved at room temperature (300 K).

Linker Redox Mediated Control of Morphology and Properties in Semiconducting Iron-Semiquinoid Coordination Polymers

The emergence of conductive 2D and less commonly 3D coordination polymers (CPs) and metal-organic frameworks (MOFs) promises novel applications in many fields. However, the synthetic parameters for these electronically complex materials are not thoroughly understood. Here we report a new 3D semiconducting CP Fe₅ (C₆ O₆ )₃ , which is a fusion of 2D Fe-semiquinoid materials and 3D cubic Fe_x (C₆ O₆ )_y materials, by using a different initial redox-state of the C₆ O₆ linker. The material displays high electrical conductivity (0.02 S cm^-1 ), broad electronic transitions, promising thermoelectric behavior (S² σ=7.0×10^-9  W m^-1  K^-2 ), and strong antiferromagnetic interactions at room temperature. This material illustrates how controlling the oxidation states of redox-active components in conducting CPs/MOFs can be a "pre-synthetic" strategy to carefully tune material topologies and properties in contrast to more commonly encountered post-synthetic modifications.

Investigations on structural, electronic and optical properties of ZnO in two-dimensional configurations by first-principles calculations

The electronic structures and optical properties of two-dimensional (2D) ZnO monolayers in a series of configurations were systematically investigated by first-principles calculations with HubbardUevaluated by the linear response approach. Three types of 2D ZnO monolayers, as planer hexagonal-honeycomb (Plan), double-layer honeycomb (Dlhc), and corrugated tetragonal (Tile) structures, show a mechanical and dynamical stability, while the Dlhc-ZnO is the most energetically stable configuration and Plan-ZnO is the second one. Each 2D ZnO monolayer behaves as a semiconductor with that Plan-, Dlhc-ZnO have a direct band gap of 1.81 eV and 1.85 eV at theΓpoint, respectively, while Tile-ZnO has an indirect band gap of 2.03 eV. Interestingly, the 2D ZnO monolayers all show a typical near-free-electron character for the bottom conduction band with a small effective mass, leading to a tremendous optical absorption in the whole visible and ultraviolet window, and this origination was further confirmed by the transition dipole moment. Our investigations suggest a potential candidate in the photoelectric field and provide a theoretical guidance for the exploration of wide-band-gap 2D semiconductors.

Koopmans Spectral Functionals in Periodic Boundary Conditions

Koopmans spectral functionals aim to describe simultaneously ground-state properties and charged excitations of atoms, molecules, nanostructures, and periodic crystals. This is achieved by augmenting standard density functionals with simple but physically motivated orbital-density-dependent corrections. These corrections act on a set of localized orbitals that, in periodic systems, resemble maximally localized Wannier functions. At variance with the original, direct supercell implementation (Phys. Rev. X 2018, 8, 021051), we discuss here (i) the complex but efficient formalism required for a periodic boundary code using explicit Brillouin zone sampling and (ii) the calculation of the screened Koopmans corrections with density functional perturbation theory. In addition to delivering improved scaling with system size, the present development makes the calculation of band structures with Koopmans functionals straightforward. The implementation in the open-source Quantum ESPRESSO distribution and the application to prototypical insulating and semiconducting systems are presented and discussed.

Structural transition and re-emergence of iron's total electron spin in (Mg,Fe)O at ultrahigh pressure

Fe-bearing MgO [(Mg_1−xFe_x)O] is considered a major constituent of terrestrial exoplanets. Crystallizing in the B1 structure in the Earth’s lower mantle, (Mg_1−xFe_x)O undergoes a high-spin (S = 2) to low-spin (S = 0) transition at ∼45 GPa, accompanied by anomalous changes of this mineral’s physical properties, while the intermediate-spin (S = 1) state has not been observed. In this work, we investigate (Mg_1−xFe_x)O (x ≤ 0.25) up to 1.8 TPa via first-principles calculations. Our calculations indicate that (Mg_1−xFe_x)O undergoes a simultaneous structural and spin transition at ∼0.6 TPa, from the B1 phase low-spin state to the B2 phase intermediate-spin state, with Fe’s total electron spin S re-emerging from 0 to 1 at ultrahigh pressure. Upon further compression, an intermediate-to-low spin transition occurs in the B2 phase. Depending on the Fe concentration (x), metal–insulator transition and rhombohedral distortions can also occur in the B2 phase. These results suggest that Fe and spin transition may affect planetary interiors over a vast pressure range.

Iron spin transition occurs at ultrahigh pressure. The total electron spin increases from 0 to 1 as the structural transition of (Mg,Fe)O occurs (~0.6 TPa) and drops back to 0 at higher pressure. Its effects on exoplanet interiors are anticipated.

Lattice dynamical properties of antiferromagnetic oxides calculated using self-consistent extended Hubbard functional method

We study the lattice dynamics of antiferromagnetic transition-metal oxides by using self-consistent Hubbard functionals. We calculate the ground states of the oxides with the on-site and intersite Hubbard interactions determined self-consistently within the framework of density functional theory. The on-site and intersite Hubbard terms fix the errors associated with the electron self-interaction in the local and semilocal functionals. Inclusion of the intersite Hubbard terms in addition to the on-site Hubbard terms produces accurate phonon dispersion of the transition-metal oxides. Calculated Born effective charges and high-frequency dielectric constants are in good agreement with experiment. Our study provides a computationally inexpensive and accurate set of first-principles calculations for strongly-correlated materials and related phenomena.

Molecular orbital projectors in non-empirical jmDFT recover exact conditions in transition-metal chemistry

Low-cost, non-empirical corrections to semi-local density functional theory are essential for accurately modeling transition-metal chemistry. Here, we demonstrate the judiciously modified density functional theory (jmDFT) approach with non-empirical U and J parameters obtained directly from frontier orbital energetics on a series of transition-metal complexes. We curate a set of nine representative Ti(III) and V(IV) d1 transition-metal complexes and evaluate their flat-plane errors along the fractional spin and charge lines. We demonstrate that while jmDFT improves upon both DFT+U and semi-local DFT with the standard atomic orbital projectors (AOPs), it does so inefficiently. We rationalize these inefficiencies by quantifying hybridization in the relevant frontier orbitals. To overcome these limitations, we introduce a procedure for computing a molecular orbital projector (MOP) basis for use with jmDFT. We demonstrate this single set of d1 MOPs to be suitable for nearly eliminating all energetic delocalization error and static correlation error. In all cases, MOP jmDFT outperforms AOP jmDFT, and it eliminates most flat-plane errors at non-empirical values. Unlike DFT+U or hybrid functionals, jmDFT nearly eliminates energetic delocalization error and static correlation error within a non-empirical framework.

Eliminating Delocalization Error to Improve Heterogeneous Catalysis Predictions with Molecular DFT + U

Approximate semilocal density functional theory (DFT) is known to underestimate surface formation energies yet paradoxically overbind adsorbates on catalytic transition-metal oxide surfaces due to delocalization error. The low-cost DFT + U approach only improves surface formation energies for early transition-metal oxides or adsorption energies for late transition-metal oxides. In this work, we demonstrate that this inefficacy arises due to the conventional usage of metal-centered atomic orbitals as projectors within DFT + U. We analyze electron density rearrangement during surface formation and O atom adsorption on rutile transition-metal oxides to highlight that a standard DFT + U correction fails to tune properties when the corresponding density rearrangement is highly delocalized across both metal and oxygen sites. To improve both surface properties simultaneously while retaining the simplicity of a single-site DFT + U correction, we systematically construct multi-atom-centered molecular-orbital-like projectors for DFT + U. We demonstrate this molecular DFT + U approach for tuning adsorption energies and surface formation energies of minimal two-dimensional models of representative early (i.e., TiO₂) and late (i.e., PtO₂) transition-metal oxides. Molecular DFT + U simultaneously corrects adsorption energies and surface formation energies of multilayer models of rutile TiO₂(110) and PtO₂(110) to resolve the paradoxical description of surface stability and surface reactivity of semilocal DFT.

Machine learning to tame divergent density functional approximations: a new path to consensus materials design principles

Virtual high-throughput screening (VHTS) with density functional theory (DFT) and machine-learning (ML)-acceleration is essential in rapid materials discovery. By necessity, efficient DFT-based workflows are carried out with a single density functional approximation (DFA). Nevertheless, properties evaluated with different DFAs can be expected to disagree for cases with challenging electronic structure (e.g., open-shell transition-metal complexes, TMCs) for which rapid screening is most needed and accurate benchmarks are often unavailable. To quantify the effect of DFA bias, we introduce an approach to rapidly obtain property predictions from 23 representative DFAs spanning multiple families, “rungs” (e.g., semi-local to double hybrid) and basis sets on over 2000 TMCs. Although computed property values (e.g., spin state splitting and frontier orbital gap) differ by DFA, high linear correlations persist across all DFAs. We train independent ML models for each DFA and observe convergent trends in feature importance, providing DFA-invariant, universal design rules. We devise a strategy to train artificial neural network (ANN) models informed by all 23 DFAs and use them to predict properties (e.g., spin-splitting energy) of over 187k TMCs. By requiring consensus of the ANN-predicted DFA properties, we improve correspondence of computational lead compounds with literature-mined, experimental compounds over the typically employed single-DFA approach.

Machine learning (ML)-based feature analysis reveals universal design rules regardless of density functional choices. Using the consensus among multiple functionals, we identify robust lead complexes in ML-accelerated chemical discovery.

Seismological expression of the iron spin crossover in ferropericlase in the Earth's lower mantle

The two most abundant minerals in the Earth’s lower mantle are bridgmanite and ferropericlase. The bulk modulus of ferropericlase (Fp) softens as iron d-electrons transition from a high-spin to low-spin state, affecting the seismic compressional velocity but not the shear velocity. Here, we identify a seismological expression of the iron spin crossover in fast regions associated with cold Fp-rich subducted oceanic lithosphere: the relative abundance of fast velocities in P- and S-wave tomography models diverges in the ~1,400-2,000 km depth range. This is consistent with a reduced temperature sensitivity of P-waves throughout the iron spin crossover. A similar signal is also found in seismically slow regions below ~1,800 km, consistent with broadening and deepening of the crossover at higher temperatures. The corresponding inflection in P-wave velocity is not yet observed in 1-D seismic profiles, suggesting that the lower mantle is composed of non-uniformly distributed thermochemical heterogeneities which dampen the global signature of the Fp spin crossover.

This study identifies the predicted seismic expression of the high-to-low iron spin crossover in the deep Earth mineral ferropericlase. A depth-dependent signal is detected in the fastest and slowest regions, related to lateral temperature variations, of several global seismic tomography models.

Ab Initio Electron-Phonon Interactions in Correlated Electron Systems

Electron-phonon (e-ph) interactions are pervasive in condensed matter, governing phenomena such as transport, superconductivity, charge-density waves, polarons, and metal-insulator transitions. First-principles approaches enable accurate calculations of e-ph interactions in a wide range of solids. However, they remain an open challenge in correlated electron systems (CES), where density functional theory often fails to describe the ground state. Therefore reliable e-ph calculations remain out of reach for many transition metal oxides, high-temperature superconductors, Mott insulators, planetary materials, and multiferroics. Here we show first-principles calculations of e-ph interactions in CES, using the framework of Hubbard-corrected density functional theory (DFT+U) and its linear response extension (DFPT+U), which can describe the electronic structure and lattice dynamics of many CES. We showcase the accuracy of this approach for a prototypical Mott system, CoO, carrying out a detailed investigation of its e-ph interactions and electron spectral functions. While standard DFPT gives unphysically divergent and short-ranged e-ph interactions, DFPT+U is shown to remove the divergences and properly account for the long-range Fröhlich interaction, allowing us to model polaron effects in a Mott insulator. Our work establishes a broadly applicable and affordable approach for quantitative studies of e-ph interactions in CES, a novel theoretical tool to interpret experiments in this broad class of materials.

Computational Discovery of Transition-metal Complexes: From High-throughput Screening to Machine Learning

Transition-metal complexes are attractive targets for the design of catalysts and functional materials. The behavior of the metal-organic bond, while very tunable for achieving target properties, is challenging to predict and necessitates searching a wide and complex space to identify needles in haystacks for target applications. This review will focus on the techniques that make high-throughput search of transition-metal chemical space feasible for the discovery of complexes with desirable properties. The review will cover the development, promise, and limitations of "traditional" computational chemistry (i.e., force field, semiempirical, and density functional theory methods) as it pertains to data generation for inorganic molecular discovery. The review will also discuss the opportunities and limitations in leveraging experimental data sources. We will focus on how advances in statistical modeling, artificial intelligence, multiobjective optimization, and automation accelerate discovery of lead compounds and design rules. The overall objective of this review is to showcase how bringing together advances from diverse areas of computational chemistry and computer science have enabled the rapid uncovering of structure-property relationships in transition-metal chemistry. We aim to highlight how unique considerations in motifs of metal-organic bonding (e.g., variable spin and oxidation state, and bonding strength/nature) set them and their discovery apart from more commonly considered organic molecules. We will also highlight how uncertainty and relative data scarcity in transition-metal chemistry motivate specific developments in machine learning representations, model training, and in computational chemistry. Finally, we will conclude with an outlook of areas of opportunity for the accelerated discovery of transition-metal complexes.

A local-orbital density functional formalism for a many-body atomic Hamiltonian: Hubbard-Hund's coupling and DFT + U functional

In the conventional DFT + U approach, the mean field solution of the Hubbard Hamiltonian associated with thedorf(iσ) electrons of a transition metal atom is used to define the DFT + U potential acting on theiσ-electrons. In this work, we go beyond that mean field solution by analyzing the correlation energy and potential for a multi-level atom described by a Kanamori Hamiltonian connected to different channels representing the environment. As a first step, we analyze the many-body solution of our model, using a local-orbital density functional formalism that takes as independent variables the orbital occupancies,n_iσ, of the atomic orbitals; accordingly, we present the corresponding density functional solution describing the correlation energy and potential as a function ofn_iσ. Then, we use this analysis to introduce a DFT + U potential extending previous proposals to materials with arbitrarily high correlation. In particular, we find that this potential mainly screens the conventional mean field potential contribution, and also yields new terms associated with the number of atomic electrons. Our results show that the atomic correlation effects enhance the role played by the intra-atomic exchange interaction and favor the formation of magnetic solutions.