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

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.

Electronic structure of mononuclear Cu-based molecule from density-functional theory with self-interaction correction

We investigate the electronic structure of a planar mononuclear Cu-based molecule [Cu(C₆H₄S₂)₂]^z in two oxidation states (z = -2, -1) using density-functional theory (DFT) with Fermi-Löwdin orbital (FLO) self-interaction correction (SIC). The dianionic Cu-based molecule was proposed to be a promising qubit candidate. Self-interaction error within approximate DFT functionals renders severe delocalization of electron and spin densities arising from 3d orbitals. The FLO-SIC method relies on optimization of Fermi-Löwdin orbital descriptors (FODs) with which localized occupied orbitals are constructed to create SIC potentials. Starting with many initial sets of FODs, we employ a frozen-density loop algorithm within the FLO-SIC method to study the Cu-based molecule. We find that the electronic structure of the molecule remains unchanged despite somewhat different final FOD configurations. In the dianionic state (spin S = 1/2), FLO-SIC spin density originates from the Cu d and S p orbitals with an approximate ratio of 2:1, in quantitative agreement with multireference calculations, while in the case of SIC-free DFT, the orbital ratio is reversed. Overall, FLO-SIC lowers the energies of the occupied orbitals and, in particular, the 3d orbitals unhybridized with the ligands significantly, which substantially increases the energy gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) compared to SIC-free DFT results. The FLO-SIC HOMO-LUMO gap of the dianionic state is larger than that of the monoanionic state, which is consistent with experiment. Our results suggest a positive outlook of the FLO-SIC method in the description of magnetic exchange coupling within 3d-element-based systems.

Improved Spin-State Energy Differences of Fe(II) Molecular and Crystalline Complexes via the Hubbard U-Corrected Density

We recently showed that the DFT+U approach with a linear-response U yields adiabatic energy differences biased toward high spin [Mariano et al. J. Chem. Theory Comput. 2020, 16, 6755-6762]. Such bias is removed here by employing a density-corrected DFT approach where the PBE functional is evaluated on the Hubbard U-corrected density. The adiabatic energy differences of six Fe(II) molecular complexes computed using this approach, named PBE[U] here, are in excellent agreement with coupled cluster-corrected CASPT2 values for both weak- and strong-field ligands resulting in a mean absolute error (MAE) of 0.44 eV, smaller than that of the recently proposed Hartree-Fock density-corrected DFT (1.22 eV) and any other tested functional, including the best performer TPSSh (0.49 eV). We take advantage of the computational efficiency of this approach and compute the adiabatic energy differences of five molecular crystals using PBE[U] with periodic boundary conditions. The results show, again, an excellent agreement (MAE = 0.07 eV) with experimentally extracted values and a superior performance compared with the best performers M06-L (MAE = 0.08 eV) and TPSSh (MAE = 0.31 eV) computed on molecular fragments.

Magnetic Energy Landscape of Dimolybdenum Tetraacetate on a Bulk Insulator Surface

The magnetic states and the magnetic anisotropy barrier of a transition metal molecular complex, dimolybdenum tetraacetate, are investigated via density functional theory (DFT). Calculations are performed in the gas phase and on a calcite (10.4) bulk insulating surface, using the Generalized-Gradient Approximation (GGA)-PBE and the Hubbard-corrected DFT + U and DFT + U + V functionals. The molecular complex (denoted MoMo) contains two central metallic molybdenum atoms, embedded in a square cage of acetate groups. Recently, MoMo was observed to form locally regular networks of immobile molecules on calcite (10.4), at room conditions. As this is the first example of a metal-coordinated molecule strongly anchored to an insulator surface at room temperature, we explore here its magnetic properties with the aim to understand whether the system could be assigned features of a single molecule magnet (SMM) and could represent the basis to realize stable magnetic networks on insulators. After an introductory review on SMMs, we show that, while the uncorrected GGA-PBE functional stabilizes MoMo in a nonmagnetic state, the DFT + U and DFT + U + V approaches stabilize an antiferromagnetic ground state and several meta-stable ferromagnetic and ferrimagnetic states. Importantly, the energy landscape of magnetic states remains almost unaltered on the insulating surface. Finally, via a noncollinear magnetic formalism and a newly introduced algorithm, we calculate the magnetic anisotropy barrier, whose value indicates the stability of the molecule’s magnetic moment.

Molecular DFT+U: A Transferable, Low-Cost Approach to Eliminate Delocalization Error

While density functional theory (DFT) is widely applied for its combination of cost and accuracy, corrections (e.g., DFT+U) that improve it are often needed to tackle correlated transition-metal chemistry. In principle, the functional form of DFT+U, consisting of a set of localized atomic orbitals (AOs) and a quadratic energy penalty for deviation from integer occupations of those AOs, enables the recovery of the exact conditions of piecewise linearity and the derivative discontinuity. Nevertheless, for practical transition-metal complexes, where both atomic states and ligand orbitals participate in bonding, standard DFT+U can fail to eliminate delocalization error (DE). Here, we show that by introducing an alternative valence-state (i.e., molecular orbital or MO) basis to the DFT+U approach, we recover exact conditions in cases for which standard DFT+U corrections have no error-reducing effect. This MO-based DFT+U also eliminates DE where standard AO-based DFT+U is already successful. We demonstrate the transferability of our approach on representative transition-metal complexes with a range of ligand field strengths, electron configurations (i.e., from Sc to Zn), and spin states.

Large magnetic anisotropy in an OsIr dimer anchored in defective graphene

Single-atom magnets represent the ultimate limit of magnetic data storage. The identification of substrates that anchor atom-sized magnets firmly and, thus, prevent their diffusion and large magnetic anisotropy has been at the centre of intense research efforts for a long time. Using density functional theory we show the binding of transition metal (TM) atoms in defect sites in the graphene lattice: single vacancy and double vacancy, both pristine and decorated by pyridinic nitrogen atoms, are energetically more favourable than away from the centre of defects, which could be used for engineering the position of TMs with atomic precision. Relativistic calculations revealed magnetic anisotropy energy (MAE) of ∼10 meV for Ir@NSV with an easy axis parallel to the graphene plane. MAE can be remarkably boosted to 50 meV for OsIr@NSV with the easy axis perpendicular to the graphene plane, which paves the way to the storage density of ∼490 Tb/inch²with the blocking temperature of 14 K assuming the relaxation time of 10 years. Magnetic anisotropy is discussed based on the relativistic electronic structures. The influence of an orbital-dependent on-site Coulomb repulsionUand a non-local correlation functional optB86b-vdW on MAE is also discussed.

Extensive Benchmarking of DFT+U Calculations for Predicting Band Gaps

Accurate computational predictions of band gaps are of practical importance to the modeling and development of semiconductor technologies, such as (opto)electronic devices and photoelectrochemical cells. Among available electronic-structure methods, density-functional theory (DFT) with the Hubbard U correction (DFT+U) applied to band edge states is a computationally tractable approach to improve the accuracy of band gap predictions beyond that of DFT calculations based on (semi)local functionals. At variance with DFT approximations, which are not intended to describe optical band gaps and other excited-state properties, DFT+U can be interpreted as an approximate spectral-potential method when U is determined by imposing the piecewise linearity of the total energy with respect to electronic occupations in the Hubbard manifold (thus removing self-interaction errors in this subspace), thereby providing a (heuristic) justification for using DFT+U to predict band gaps. However, it is still frequent in the literature to determine the Hubbard U parameters semiempirically by tuning their values to reproduce experimental band gaps, which ultimately alters the description of other total-energy characteristics. Here, we present an extensive assessment of DFT+U band gaps computed using self-consistent ab initio U parameters obtained from density-functional perturbation theory to impose the aforementioned piecewise linearity of the total energy. The study is carried out on 20 compounds containing transition-metal or p-block (group III-IV) elements, including oxides, nitrides, sulfides, oxynitrides, and oxysulfides. By comparing DFT+U results obtained using nonorthogonalized and orthogonalized atomic orbitals as Hubbard projectors, we find that the predicted band gaps are extremely sensitive to the type of projector functions and that the orthogonalized projectors give the most accurate band gaps, in satisfactory agreement with experimental data. This work demonstrates that DFT+U may serve as a useful method for high-throughput workflows that require reliable band gap predictions at moderate computational cost.

The Missing Link in the Magnetism of Hybrid Cobalt Layered Hydroxides: The Odd-Even Effect of the Organic Spacer

A dramatic change in the magnetic behaviour, which solely depends on the parity of the organic linker molecules, has been found in a family of layered Co^II hydroxides covalently functionalized with dicarboxylic molecules. These layered hybrid materials have been synthesized at room temperature using a one-pot procedure through the epoxide route. While hybrids connected by odd alkyl chains exhibit coercive fields (H_c ) below ca. 3500 Oe and show spontaneous magnetization at temperatures (T_M ) below 20 K, hybrids functionalized with even alkyl chains behave as hard magnets with H_c >5500 Oe and display a T_M higher than 55 K. This intriguing behaviour was studied by density functional theory with the incorporation of a Hubbard term (DFT+U) calculations, unveiling the structural subtleties underlying this observation. Indeed, the different molecular orientation exhibited by the even/odd alkyl chains, and the orientation of the covalently linked carboxylic groups modify the intensity of the magnetic coupling of both octahedral and tetrahedral in-plane sublattices, thus strongly affecting the magnetic properties of the hybrid. These findings offer an outstanding level of tuning in the molecular design of hybrid magnetic materials based on layered hydroxides.

Quantum Information and Algorithms for Correlated Quantum Matter

Discoveries in quantum materials, which are characterized by the strongly quantum-mechanical nature of electrons and atoms, have revealed exotic properties that arise from correlations. It is the promise of quantum materials for quantum information science superimposed with the potential of new computational quantum algorithms to discover new quantum materials that inspires this Review. We anticipate that quantum materials to be discovered and developed in the next years will transform the areas of quantum information processing including communication, storage, and computing. Simultaneously, efforts toward developing new quantum algorithmic approaches for quantum simulation and advanced calculation methods for many-body quantum systems enable major advances toward functional quantum materials and their deployment. The advent of quantum computing brings new possibilities for eliminating the exponential complexity that has stymied simulation of correlated quantum systems on high-performance classical computers. Here, we review new algorithms and computational approaches to predict and understand the behavior of correlated quantum matter. The strongly interdisciplinary nature of the topics covered necessitates a common language to integrate ideas from these fields. We aim to provide this common language while weaving together fields across electronic structure theory, quantum electrodynamics, algorithm design, and open quantum systems. Our Review is timely in presenting the state-of-the-art in the field toward algorithms with nonexponential complexity for correlated quantum matter with applications in grand-challenge problems. Looking to the future, at the intersection of quantum information science and algorithms for correlated quantum matter, we envision seminal advances in predicting many-body quantum states and describing excitonic quantum matter and large-scale entangled states, a better understanding of high-temperature superconductivity, and quantifying open quantum system dynamics.

Enhanced magnetic anisotropy and Curie temperature of the NiI2 monolayer by applying strain: a first-principles study

Two-dimensional (2D) intrinsic ferromagnetic semiconductors with high magnetic anisotropy (MA) and Curie temperature (TC) are desirable for low-dimensional spintronic applications. We present here the structural stability, MA and TC of the semiconducting NiI2 monolayer under strain from -4% to 4% using first-principles calculations. The unstrained NiI2 monolayer exhibits an in-plane magnetic anisotropy energy of -0.11 meV per unit cell and a TC of 79 K. Most noteworthily, the in-plane MA and TC of the NiI2 monolayer are simultaneously enhanced under compressive strain; meanwhile, the NiI2 monolayer is still stable. In particular, when the compressive strain reaches -4%, the in-plane MA is more than three times higher than that in the unstrained system. Based on the second-order perturbation theory of spin-orbit coupling, the density of states and the orbital magnetic anisotropy contributions are analyzed, indicating that the compressive strain effect originates from the increase of the negative contribution from the spin-orbit coupling interaction between the opposite spin py and px orbitals of the I atom. This study provides a promising route for exploring new 2D ferromagnetic semiconductors with higher MA and TC.

Electronic Structure Modeling of Metal-Organic Frameworks

Owing to their molecular building blocks, yet highly crystalline nature, metal-organic frameworks (MOFs) sit at the interface between molecule and material. Their diverse structures and compositions enable them to be useful materials as catalysts in heterogeneous reactions, electrical conductors in energy storage and transfer applications, chromophores in photoenabled chemical transformations, and beyond. In all cases, density functional theory (DFT) and higher-level methods for electronic structure determination provide valuable quantitative information about the electronic properties that underpin the functions of these frameworks. However, there are only two general modeling approaches in conventional electronic structure software packages: those that treat materials as extended, periodic solids, and those that treat materials as discrete molecules. Each approach has features and benefits; both have been widely employed to understand the emergent chemistry that arises from the formation of the metal-organic interface. This Review canvases these approaches to date, with emphasis placed on the application of electronic structure theory to explore reactivity and electron transfer using periodic, molecular, and embedded models. This includes (i) computational chemistry considerations such as how functional, k-grid, and other model variables are selected to enable insights into MOF properties, (ii) extended solid models that treat MOFs as materials rather than molecules, (iii) the mechanics of cluster extraction and subsequent chemistry enabled by these molecular models, (iv) catalytic studies using both solids and clusters thereof, and (v) embedded, mixed-method approaches, which simulate a fraction of the material using one level of theory and the remainder of the material using another dissimilar theoretical implementation.

The ONETEP linear-scaling density functional theory program

We present an overview of the onetep program for linear-scaling density functional theory (DFT) calculations with large basis set (plane-wave) accuracy on parallel computers. The DFT energy is computed from the density matrix, which is constructed from spatially localized orbitals we call Non-orthogonal Generalized Wannier Functions (NGWFs), expressed in terms of periodic sinc (psinc) functions. During the calculation, both the density matrix and the NGWFs are optimized with localization constraints. By taking advantage of localization, onetep is able to perform calculations including thousands of atoms with computational effort, which scales linearly with the number or atoms. The code has a large and diverse range of capabilities, explored in this paper, including different boundary conditions, various exchange-correlation functionals (with and without exact exchange), finite electronic temperature methods for metallic systems, methods for strongly correlated systems, molecular dynamics, vibrational calculations, time-dependent DFT, electronic transport, core loss spectroscopy, implicit solvation, quantum mechanical (QM)/molecular mechanical and QM-in-QM embedding, density of states calculations, distributed multipole analysis, and methods for partitioning charges and interactions between fragments. Calculations with onetep provide unique insights into large and complex systems that require an accurate atomic-level description, ranging from biomolecular to chemical, to materials, and to physical problems, as we show with a small selection of illustrative examples. onetep has always aimed to be at the cutting edge of method and software developments, and it serves as a platform for developing new methods of electronic structure simulation. We therefore conclude by describing some of the challenges and directions for its future developments and applications.

Seeing Is Believing: Experimental Spin States from Machine Learning Model Structure Predictions

Determination of ground-state spins of open-shell transition-metal complexes is critical to understanding catalytic and materials properties but also challenging with approximate electronic structure methods. As an alternative approach, we demonstrate how structure alone can be used to guide assignment of ground-state spin from experimentally determined crystal structures of transition-metal complexes. We first identify the limits of distance-based heuristics from distributions of metal–ligand bond lengths of over 2000 unique mononuclear Fe(II)/Fe(III) transition-metal complexes. To overcome these limits, we employ artificial neural networks (ANNs) to predict spin-state-dependent metal–ligand bond lengths and classify experimental ground-state spins based on agreement of experimental structures with the ANN predictions. Although the ANN is trained on hybrid density functional theory data, we exploit the method-insensitivity of geometric properties to enable assignment of ground states for the majority (ca. 80–90%) of structures. We demonstrate the utility of the ANN by data-mining the literature for spin-crossover (SCO) complexes, which have experimentally observed temperature-dependent geometric structure changes, by correctly assigning almost all (>95%) spin states in the 46 Fe(II) SCO complex set. This approach represents a promising complement to more conventional energy-based spin-state assignment from electronic structure theory at the low cost of a machine learning model.

Quasi-degenerate states and their dynamics in oxygen deficient reducible metal oxides

The physical and chemical properties of oxides are defined by the presence of oxygen vacancies. Experimentally, non-defective structures are almost impossible to achieve due to synthetic constraints. Therefore, it is crucial to account for vacancies when evaluating the characteristics of these materials. The electronic structure of oxygen-depleted oxides deeply differs from that of the native forms, in particular, of reducible metal oxides, where excess electrons can localize in various distinct positions. In this perspective, we present recent developments from our group describing the complexity of these defective materials that highlight the need for an accurate description of (i) intrinsic vacancies in polar terminations, (ii) multiple geometries and complex electronic structures with several states attainable at typical working conditions, and (iii) the associated dynamics for both vacancy diffusion and the coexistence of more than one electronic structure. All these aspects widen our current understanding of defects in oxides and need to be adequately introduced in emerging high-throughput screening methodologies.

Characterisation of the temperature-dependent M1 to R phase transition in W-doped VO2 nanorod aggregates by Rietveld refinement and theoretical modelling

Synchrotron XRD Rietveld refinement is combined with first-principles calculations to probe the effect of W doping on the IMT mechanism in VO₂ nanorods, providing insights into the connection between atomic-scale phenomena and macro-scale properties.

Interface-induced perpendicular magnetic anisotropy in Co2FeAl/NiFe2O4 superlattice: first-principles study

A large PMA of up to 1.07 mJ m⁻² can be obtained at the interface between Co-terminated Co₂FeAl and NiO-terminated NiFe₂O₄.

Piecewise linearity, freedom from self-interaction, and a Coulomb asymptotic potential: three related yet inequivalent properties of the exact density functional

Three properties of the exact energy functional of DFT are important in general and for spectroscopy in particular, but are not necessarily obeyed by approximate functionals. We explain what they are, why they are important, and how they are related yet inequivalent.

Large-scale comparison of 3d and 4d transition metal complexes illuminates the reduced effect of exchange on second-row spin-state energetics

The origin of distinct 3d vs. 4d transition metal complex sensitivity to exchange is explored over a large data set.

Lithium Clustering during the Lithiation/Delithiation Process in LiFePO4 Olivine-Structured Materials

Olivine-structured LiFePO4 is one of the most popular cathode materials in lithium-ion batteries (LIBs) for sustainable applications. Significant attention has been paid to investigating the dynamics of the lithiation/delithiation process in Li x FePO4 (0 ≤ x ≤ 1), which is crucial for the development of high-performance LiFePO4 material. Various macroscopic models based on experimental evidence have been proposed to explain the mechanism of phase transition from LiFePO4 to FePO4, such as the shrinking core (i.e., core-shell) model, Laffont's (i.e., new core-shell) model, domino-cascade model, phase transformation wave, solid solution model, many-particle models, etc. However, these models, unfortunately, contradict each other and their validity is still under debate. An atomistic model is urgently required to depict the lithiation/delithiation process in Li x FePO4. In this article, we reveal the lithiation/delithiation process in LiFePO4 simulated by a computational model using the generalized gradient approximation (GGA + U) method. We find that the clustered configuration is the most energetically favorable, leading to co-operative Jahn-Teller distortion among the inter-polyhedrons that can be observed clearly from the bond patterns. This atomistic model not only offers answers to experimental results obtained at moderate or high rates but also gives the direction to further improve the rate capability of LiFePO4 cathode material for high-power LIBs.

In Situ Observation of the Effect of Accelerating Voltage on Electron Beam Damage of Layered Cathode Materials for Lithium-Ion Batteries

Electron beam damage from transmission electron microscopy of layered lithium transition-metal oxides is a threshold phenomenon that depends on the electron beam energy, which we demonstrate in this study by varying the accelerating voltage of a scanning transmission electron microscope. The electron beam irradiation experiment shows that Ni in LiNiO₂ has much lower threshold energy for displacement than Co in LiCoO₂, which is supported by DFT calculations predicting that Ni has lower migration energy. The transition-metal ions are reduced from the oxidation state of +3 to +2 during migration from their original positions to the lithium sites, and Ni is more easily reduced than Co because of its electronic configuration. In addition, the high-energy electron beam induces oxygen release, which is another symptom of degradation of materials that occurs more strongly in Ni-containing materials with ion displacement.

Tunable electronic properties of monolayer MnPSe3/MoTe2 heterostructure: a first principles study

The construction of van der Waals heterostructures is deemed to be a novel scheme to circumvent the shortcomings of their components and bear potentials for applications in electronic devices. Here we systematically investigate the structural and electronic properties of a monolayer MnPSe₃/MoTe₂ heterostructure with the first principles calculations. The heterostructure stablizes in the antiferromagnetic state and possesses a typical type-II band alignment, with which the photoexcited electrons and holes can be effectively separated and their fast recombination can hence be suppressed. Meanwhile, an inherent electric field is observed at the interface between MnPSe₃ and MoTe₂. Interestingly, the band gap of the heterostructure shows a quasi-linear dependence on the external electric field applied, and is tunable within the semiconductor to semimetal range. The tunability with applied strain is also investigated and discussed.

Calculating spin crossover temperatures by a first-principles LDA+U scheme with parameter U evaluated from GW

The prediction of spin crossover (SCO) temperatures (T_1/2) depends sensitively on the description of local Coulomb correlation. Due to its balance between accuracy and computational cost, local density approximation combined with Hubbard U model (LDA+U) is an appealing tool for this purpose. Despite its accurate performance on energetic properties, such as spin adiabatic energy difference, it is well-known that the LDA+U approach would lose its predictive power if U is tuned to achieve close agreement with experiment for a certain property. On the other hand, a static U value cannot account for changes in the electronic structure. Here, we propose a framework to derive dynamical U (U_dyn) values for iron(ii) complexes from the many-body GW calculations. By performing model calculations on a series of compounds with varying ligand fields, we show that the U values determined in this way are local environment dependent, and the resulting LDA+U_dyn method could reproduce their experimental ground spin states. We present applications to selected SCO complexes illustrating that U_dyn considerably overcomes some of the drawbacks of employing a constant U in the calculation of thermochemical quantities. Using the described calculation procedure, the T_1/2 values are predicted with a small mean absolute error of 176 K with respect to experiment.

Two-dimensional magnetic metal-organic frameworks with the Shastry-Sutherland lattice

Mn-PBP is discovered to be the first ferromagnetic 2D MOF with the Shastry-Sutherland lattice and the predicted Curie temperature is 105 K.

Inspired by the successful synthesis of Fe/Cu-5,5′-bis(4-pyridyl)(2,2′-bipirimidine) (PBP), a family of two-dimensional (2D) metal–organic frameworks (MOFs) with the Shastry-Sutherland lattice, i.e., transition metal (TM)-PBP (TM = Cr, Mn, Fe, Co, Ni, Cu, Zn) has been systematically investigated by means of first-principles density functional theory calculations and Monte Carlo simulations. Mn-PBP is discovered to be the first ferromagnetic 2D MOF with the Shastry-Sutherland lattice and the Curie temperature is predicted to be about 105 K, while Fe-PBP, TM-PBP (TM = Cr, Co, Ni) and TM-PBP (TM = Cu, Zn) are found to be stripe-order antiferromagnetic, magnetic-dimerized and nonmagnetic, respectively. The electronic structure calculations reveal that TM-PBP MOFs are semiconductors with band gaps ranging from 0.12 eV to 0.85 eV, which could be easily modulated by various methods. Particularly, Mn-PBP would exhibit half-metallic behavior under compressive strain or appropriate electron/hole doping and a Mn-PBP based spintronic device has been proposed. This study not only improves the understanding of the geometric, electronic and magnetic properties of the 2D TM-PBP MOF family, but also provides a novel spin lattice playground for the research of 2D magnetic systems, which has diverse modulating possibilities and rich potential applications.

Catalytic Enhancement of CO Oxidation on LaFeO3 Regulated by Ruddlesden-Popper Stacking Faults

The influence of planar defects, in the form of stacking faults, within perovskite oxides on catalytic activity has received little attention because controlling stacking-fault densities presents a major synthetic challenge. Furthermore, stacking faults in ceramics are not thought to appreciably impact surface chemistry, which partly explains why their direct effect on catalysis is generally ignored. Here, we show that Ruddlesden-Popper (RP) stacking faults in otherwise stoichiometric LaFeO₃ can be broadly controlled by modulating the ceramic synthesis route. Electronic structure calculations along with electron microscopy and spectroscopy show that energetically favorable RP faults occur both near the surface and in bunches and enhance CO oxidation kinetics. Density functional theory (DFT) + U shows that subsurface RP faults strengthen the adsorption and co-adsorption of CO, O, and O₂, which could lower the apparent activation energy of CO oxidation on faulted catalysts compared to that on their pristine counterparts. Our work suggests that planar defects should be considered a new and useful feature in hierarchal nanoscale design of future catalysts.

Stable Surfaces That Bind Too Tightly: Can Range-Separated Hybrids or DFT+U Improve Paradoxical Descriptions of Surface Chemistry?

Approximate, semilocal density functional theory (DFT) suffers from delocalization error that can lead to a paradoxical model of catalytic surfaces that both overbind adsorbates yet are also too stable. We investigate the effect of two widely applied approaches for delocalization error correction, (i) affordable DFT+U (i.e., semilocal DFT augmented with a Hubbard U) and (ii) hybrid functionals with an admixture of Hartree-Fock (HF) exchange, on surface and adsorbate energies across a range of rutile transition metal oxides widely studied for their promise as water-splitting catalysts. We observe strongly row- and period-dependent trends with DFT+U, which increases surface formation energies only in early transition metals (e.g., Ti and V) and decreases adsorbate energies only in later transition metals (e.g., Ir and Pt). Both global and local hybrids destabilize surfaces and reduce adsorbate binding across the periodic table, in agreement with higher-level reference calculations. Density analysis reveals why hybrid functionals correct both quantities, whereas DFT+U does not. We recommend local, range-separated hybrids for the accurate modeling of catalysis in transition metal oxides at only a modest increase in computational cost over semilocal DFT.

Stability of non-metal dopants to tune the photo-absorption of TiO2 at realistic temperatures and oxygen partial pressures: A hybrid DFT study

TiO2 anatase is considered to play a significant importance in energy and environmental research. However, for developing artificial photosynthesis with TiO2, the major drawback is its large bandgap of 3.2 eV. Several non-metals have been used experimentally for extending the TiO2 photo-absorption to the visible region of the spectrum. It's therefore of paramount importance to provide theoretical guidance to experiment about the kind of defects that are thermodynamically stable at a realistic condition (e.g. Temperature (T), oxygen partial pressure ([Formula: see text]), doping). However, disentangling the relative stability of different types of defects (viz. substitution, interstitial, etc.) as a function of charge state and realistic T, [Formula: see text] is quite challenging. We report here using state-of-the-art first-principles based methodologies, the stability and meta-stability of different non-metal dopants X (X = N, C, S, Se) at various charge states and realistic conditions. The ground state electronic structure is very accurately calculated via density functional theory with hybrid functionals, whereas the finite T and [Formula: see text] effects are captured by ab initio atomistic thermodynamics under harmonic approximations. On comparing the defect formation energies at a given T and [Formula: see text] (relevant to the experiment), we have found that Se interstitial defect (with two hole trapped) is energetically most favored in the p-type region, whereas N substitution (with one electron trapped) is the most abundant defect in the n-type region to provide visible region photo-absorption in TiO2. Our finding validates that the most stable defects in X doped TiO2 are not the neutral defects but the charged defects. The extra stability of [Formula: see text] is carefully analyzed by comparing the individual effect of bond-making/breaking and the charge carrier trapping energies.

Non-empirical, low-cost recovery of exact conditions with model-Hamiltonian inspired expressions in jmDFT

Density functional theory (DFT) is widely applied to both molecules and materials, but well known energetic delocalization and static correlation errors in practical exchange-correlation approximations limit quantitative accuracy. Common methods that correct energetic delocalization errors, such as the Hubbard U correction in DFT+U or Hartree-Fock exchange in global hybrids, do so at the cost of worsening static correlation errors. We recently introduced an alternate approach [Bajaj et al., J. Chem. Phys. 147, 191101 (2017)] known as judiciously modified DFT (jmDFT), wherein the deviation from exact behavior of semilocal functionals over both fractional spin and charge, i.e., the so-called flat plane, was used to motivate functional forms of second order analytic corrections. In this work, we introduce fully nonempirical expressions for all four coefficients in a DFT+U+J-inspired form of jmDFT, where all coefficients are obtained only from energies and eigenvalues of the integer-electron systems. We show good agreement for U and J coefficients obtained nonempirically as compared with the results of numerical fitting in a jmDFT U+J/J' correction. Incorporating the fully nonempirical jmDFT correction reduces and even eliminates the fractional spin error at the same time as eliminating the energetic delocalization error. We show that this approach extends beyond s-electron systems to higher angular momentum cases including p- and d-electrons. Finally, we diagnose some shortcomings of the current jmDFT approach that limit its ability to improve upon DFT results for cases such as weakly bound anions due to poor underlying semilocal functional behavior.

Bridging the Homogeneous-Heterogeneous Divide: Modeling Spin for Reactivity in Single Atom Catalysis

Single atom catalysts (SACs) are emergent catalytic materials that have the promise of merging the scalability of heterogeneous catalysts with the high activity and atom economy of homogeneous catalysts. Computational, first-principles modeling can provide essential insight into SAC mechanism and active site configuration, where the sub-nm-scale environment can challenge even the highest-resolution experimental spectroscopic techniques. Nevertheless, the very properties that make SACs attractive in catalysis, such as localized d electrons of the isolated transition metal center, make them challenging to study with conventional computational modeling using density functional theory (DFT). For example, Fe/N-doped graphitic SACs have exhibited spin-state dependent reactivity that remains poorly understood. However, spin-state ordering in DFT is very sensitive to the nature of the functional approximation chosen. In this work, we develop accurate benchmarks from correlated wavefunction theory (WFT) for relevant octahedral complexes. We use those benchmarks to evaluate optimal DFT functional choice for predicting spin state ordering in small octahedral complexes as well as models of pyridinic and pyrrolic nitrogen environments expected in larger SACs. Using these guidelines, we determine Fe/N-doped graphene SAC model properties and reactivity as well as their sensitivities to DFT functional choice. Finally, we conclude with broad recommendations for computational modeling of open-shell transition metal single-atom catalysts.

Koopmans-Compliant Functionals and Potentials and Their Application to the GW100 Test Set

Koopmans-compliant (KC) functionals have been shown to provide accurate spectral properties through a generalized condition of piecewise linearity of the total energy as a function of the fractional addition/removal of an electron to/from any orbital. We analyze the performance of different KC functionals on a large and standardized set of 100 molecules, the GW100 test set, comparing vertical ionization potentials (taken as opposite of the orbital energies) to those obtained from accurate quantum chemistry methods, and to experimental results. We find excellent agreement, with a mean absolute error of 0.20 eV for the KIPZ functional on the first ionization potential, which is state-of-the-art for both density functional theory (DFT)-based calculations and many-body perturbation theory. We highlight similarities and differences between KC functionals and other electronic-structure approaches, such as dielectric-dependent hybrid functionals and Green's function methods, both from a theoretical and from a practical point of view, arguing that KC potentials can be considered as local and orbital-dependent approximations to the electronic self-energy, already including approximate vertex corrections.

Computational analysis and identification of battery materials

Crystallography is a powerful descriptor of the atomic structure of solid-state matter and can be applied to analyse the phenomena present in functional materials. Especially for ion diffusion – one of the main processes found in electrochemical energy storage materials – crystallography can describe and evaluate the elementary steps for the hopping of mobile species from one crystallographic site to another. By translating this knowledge into parameters and search for similar numbers in other materials, promising compounds for future energy storage materials can be identified. Large crystal structure databases like the ICSD, CSD, and PCD have accumulated millions of measured crystal structures and thus represent valuable sources for future data mining and big-data approaches. In this work we want to present, on the one hand, crystallographic approaches based on geometric and crystal-chemical descriptors that can be easily applied to very large databases. On the other hand, we want to show methodologies based onab initioand electronic modelling which can simulate the structure features more realistically, incorporating also dynamic processes. Their theoretical background, applicability, and selected examples are presented.

Altered chemistry of oxygen and iron under deep Earth conditions

A drastically altered chemistry was recently discovered in the Fe-O-H system under deep Earth conditions, involving the formation of iron superoxide (FeO₂Hx with x = 0 to 1), but the puzzling crystal chemistry of this system at high pressures is largely unknown. Here we present evidence that despite the high O/Fe ratio in FeO₂Hx, iron remains in the ferrous, spin-paired and non-magnetic state at 60-133 GPa, while the presence of hydrogen has minimal effects on the valence of iron. The reduced iron is accompanied by oxidized oxygen due to oxygen-oxygen interactions. The valence of oxygen is not -2 as in all other major mantle minerals, instead it varies around -1. This result indicates that like iron, oxygen may have multiple valence states in our planet's interior. Our study suggests a possible change in the chemical paradigm of how oxygen, iron, and hydrogen behave under deep Earth conditions.

Large tunneling magnetoresistance in magnetic tunneling junctions based on two-dimensional CrX3 (X = Br, I) monolayers

Magnetic tunneling junctions (MTJs) have atomic thickness due to the use of two-dimensional (2D) materials. Combining density functional theory with non-equilibrium Green's function formalism, we systematically investigate the structural and magnetic properties of CrX₃/h-BN/CrX₃ (X = Br, I) MTJs, as well as their spin-dependent transport characteristics. Through calculation of the transmission spectrum, the large tunneling magnetoresistance (TMR) effect was observed in these MTJs. Moreover, their conductance based on two-dimensional materials was greatly improved over that of traditional MTJs. The transmission mechanism was analyzed using the symmetry of the orbit and the eigenstates of the transmitted electrons. We also discuss the problem of Schottky contact between different metal electrodes and devices. Our results suggest that MTJs based on two-dimensional ferromagnets are feasible.

Unraveling the Oxidation and Spin State of Mn-Corrole through X-ray Spectroscopy and Quantum Chemical Analysis

The interplay between Mn ions and corrole ligands gives rise to complex scenarios regarding the metal centers' electronic properties expressing a range of high oxidation states and spin configurations. The resulting potential of Mn-corroles for applications such as catalysts or fuel cells has recently been demonstrated. However, despite being crucial for their functionality, the electronic structure of Mn-corroles is often hardly accessible with traditional techniques and thus is still under debate, especially under interfacial conditions. Here, we unravel the electronic ground state of the prototypical Mn-5,10,15-tris(pentafluorophenyl)corrole complex through X-ray spectroscopic investigations of ultrapure thin films and quantum chemical analysis. The theory-based interpretation of Mn photoemission and absorption fine structure spectra (3s and 2p and L_2,3-edge, respectively) evidence a Mn(III) oxidation state with an S = 2 high-spin configuration. By referencing density functional theory calculations with the experiments, we lay the basis for extending our approach to the characterization of complex interfaces.

Influence of Oxygen Vacancy Density on the Polaronic Configuration in Rutile

Polaronic configurations that were introduced by oxygen vacancy in rutile TiO₂ crystal have been studied by the DFT + U method. It is found that the building block of TiO₆ will expand when extra electron is trapped in the central Ti atom as polaron. With manually adjusting the initial geometry of oxygen vacancy structure, a variety of polaronic configurations are obtained after variable-cell relaxation. By calculating different sizes of supercell model, it is found that the most stable configuration can be influenced by the density of oxygen vacancy. With increasing interaction between vacancies, the most stable polaronic configuration change from small polaronic configuration to mixed configuration.

Probing magnetic interactions in metal-organic frameworks and coordination polymers microscopically

Materials with magnetic interactions between their metal centres play a tremendous role in modern technologies and can exhibit unique physical phenomena. In recent years, magnetic metal-organic frameworks and coordination polymers have attracted significant attention because their unique structural flexibility enables them to exhibit multifunctional magnetic properties or unique magnetic states not found in the conventional magnetic materials, such as metal oxides. Techniques that enable the magnetic interactions in these materials to be probed at the atomic scale, long established to be key for developing other magnetic materials, are not well established for studying metal-organic frameworks and coordination polymers. This review focuses on studies where metal-organic frameworks and coordination polymers have been examined using such microscopic probes, with a particular focus on neutron scattering and density-functional theory, the most-well established experimental and computational techniques for understanding magnetic materials in detail. This paper builds on a brief introduction to these techniques to describe how such probes have been applied to a variety of magnetic materials starting with select historical examples before discussing multifunctional, low dimensional and frustrated magnets. This review highlights the information that can be obtained from such microscopic studies, including the strengths and limitations of these techniques. The article then concludes with a brief perspective on the future of this area.

Describing strong correlation with fractional-spin correction in density functional theory

An effective fractional-spin correction is developed to describe static/strong correlation in density functional theory. Combined with the fractional-charge correction from recently developed localized orbital scaling correction (LOSC), a functional, the fractional-spin LOSC (FSLOSC), is proposed. FSLOSC, a correction to commonly used functional approximations, introduces the explicit derivative discontinuity and largely restores the flat-plane behavior of electronic energy at fractional charges and fractional spins. In addition to improving results from conventional functionals for the prediction of ionization potentials, electron affinities, quasiparticle spectra, and reaction barrier heights, FSLOSC properly describes the dissociation of ionic species, single bonds, and multiple bonds without breaking space or spin symmetry and corrects the spurious fractional-charge dissociation of heteroatom molecules of conventional functionals. Thus, FSLOSC demonstrates success in reducing delocalization error and including strong correlation, within low-cost density functional approximation.

Spontaneous valley splitting and valley pseudospin field effect transistors of monolayer VAgP2Se6

Valleytronics has attracted much attention due to its potential applications in the information processing industry. Creation of permanent valley polarization (PVP), i.e. unbalanced occupation at different valleys, is a vital requirement for practical devices in valleytronics. However, the development of an appropriate material with PVP remains a main challenge. Here we used first-principles calculations to predict that the spin-orbit coupling and magnetic ordering allow spontaneous valley Zeeman-type splitting in the pristine monolayer of VAgP₂Se₆. After suitable doping of VAgP₂Se₆, the Zeeman-type valley splitting results in a PVP, similar to the effect of spin polarization in spintronics. The VAgP₂Se₆ monolayer has nonequivalent valleys which can emit or absorb circularly polarized photons with opposite chirality. It thus shows great potential to be used as a photonic chirality filter and a circularly polarized light source. We then designed a valley pseudospin field effect transistor (VPFET) based on the monolayer VAgP₂Se₆, akin to the spin field effect transistors. In contrast to the current common transistors, VPFETs carry information of not only the electrons but also the valley pseudospins, far beyond common transistors.