Where Does the Density Localize in the Solid State? Divergent Behavior for Hybrids and DFT+U

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.

A systematic DFT study of structure and electronic properties of titanium dioxide

DFT functionals are of paramount importance for an accurate electronic and structural description of transition metal systems. In this work, a systematic analysis using some well-known and commonly used DFT functionals is performed. A comparison of the structural and energetic parameters calculated with the available experimental data is made in order to find the adequate functional for an accurate description of the TiO2 bulk and surface of both anatase and rutile structures. In the absence of experimental data on the surface energy, the theoretical predictions obtained using the high-accuracy HSE06 functional were used as a reference to compare against the surface energy values calculated with the other DFT functionals. A clear improvement in the electronic description of both anatase and rutile was observed by introducing the Hubbard U correction term to PBE, PW91, and OptPBE functionals. The OptPBE-U4 functional was found to offer a good compromise between accurately describing the structural and electronic properties of titania.

Benchmarking a Molecular Flake Model on the Road to Programmable Graphene-Based Single-Atom Catalysts

Single-atom catalysts (SACs) of embedding an active metal in nitrogen-doped graphene are emergent catalytic materials in various applications. The rational design of efficient SACs necessitates an electronic and mechanistic understanding of those materials with reliable quantum mechanical simulations. Conventional computational methods of modeling SACs involve using an infinite slab model with periodic boundary condition, limiting to the selection of generalized gradient approximations as the exchange correlation (XC) functional within density functional theory (DFT). However, these DFT approximations suffer from electron self-interaction error and delocalization error, leading to errors in predicted charge-transfer energetics. An alternative strategy is using a molecular flake model, which carved out the important catalytic center by cleaving C-C bonds and employing a hydrogen capping scheme to saturate the innocent dangling bonds at the molecular boundary. By doing so, we can afford more accurate hybrid XC functionals, or even high-level correlated wavefunction theory, to study those materials. In this work, we compared the structural, electronic, and catalytic properties of SACs simulated using molecular flake models and periodic slab models with first-row transition metals as the active sites. Molecular flake models successfully reproduced structural properties, including both global distortion and local metal-coordination environment, as well as electronic properties, including spin magnetic moments and metal partial charges, for all transition metals studied. In addition, we calculated CO binding strength as a descriptor for electrochemical CO2 reduction reactivity and noted qualitatively similar trends between two models. Using the computationally efficient molecular flake models, we investigated the effect of tuning Hartree-Fock exchange in a global hybrid functional on the CO binding strength and observed system-dependent sensitivities. Overall, our calculations provide valuable insights into the development of accurate and efficient computational tools to simulate SACs.

Fabrication and characterization of NiCu/GO and NiCu/rGO nanocomposites for fuel cell application

This study investigated the electrochemical behavior of NiCu, NiCu/GO, and NiCu/rGO nanocomposites designed by combining a modified Hummers' method and hydrothermal technique. The prepared nanocomposites are tested as electrocatalysts in direct alcohol oxidation fuel cells (DAFCs) to identify the role of GO and rGO as catalyst supports for the enhancement of the NiCu composite performance. The production of the NiCu/GO and NiCu/rGO composites was demonstrated by FTIR spectroscopy, EDX, and SEM analyses. In DAFCs experiments, NiCu/rGO has better catalytic activity than pure NiCu and NiCu/GO composites, whereas the use of rGO and GO as supports enhances the performance of NiCu by 468.2% and 377.7% in methanol and 255.6% and 105.9% in ethanol, respectively. The higher performance was caused by the increased density of active dots and the combined electronic effects in the designed catalysts. The stabilities of the catalysts and charge carriers' dynamics are studied using chronoamperometry and electrochemical impedance spectroscopy.

Hierarchical Ohmic Contact Interface Engineering for Efficient Hydrazine-Assisted Hydrogen Evolution Reaction

Hydrazine oxidation reaction coupled with hydrogen evolution reaction (HER) is an effective strategy to achieve low energy water splitting for hydrogen production. In order to realize the application of hydrazine-assisted HER system, researchers have been focusing on the development of electrocatalysts with integrated dual active sites, while the performance under high current density is still unsatisfying. In this work, hierarchical Ohmic contact interface engineering is designed and used as a bridge between the NiMo and Ni2 P heterojunction toward industrial current density applications, with the charge transfer impedance greatly eliminated via such a pathway with low energy barrier. As a proof-of-concept, the importance of charge redistribution and energy barrier at the Ohmic contact interface is investigated by significantly reducing the voltage of overall hydrazine splitting (OHzS) at high current density. Intriguingly, the NiMo/Ni2 P hierarchical Ohmic contact heterojunction can drive current densities of 100 and 500 mA cm-2 with only 181 and 343 mV cell voltage in the OHzS electrolyzer with high electrocatalytic stability. The proposed hierarchical Ohmic contact interface engineering paves new avenue for hydrogen production with low energy consumption.

First-Principles Calculations of Magnetite (Fe3O4) above the Verwey Temperature by Using Self-Consistent DFT + U + V

In this report, we have used the DFT + U + V approach, an extension of the DFT + U approach that takes into account both on-site and intersite interactions, to simulate structural, magnetic, and electronic properties together with the Fe and O K-edge XAS spectra of Fe3O4 above the Verwey temperature (Tv). Moreover, we compared the simulated XAS spectra with experimental XAS data. We examined both orthogonalized and nonorthogonalized atomic orbital projectors and compared DFT + U + V to DFT, DFT + U, and HSE as a hybrid functional. It is noteworthy that, despite the widespread use of the same Hubbard U value for Feoct and Fetet at the DFT + U level in the literature, the HP code identified two distinct values for them using the Hubbard approaches (DFT + U and DFT + U + V). The resulting Hubbard U and V parameters are strongly dependent on the chosen orbital projectors. This study demonstrates how DFT + U + V can improve the structural, magnetic, and electronic properties of Fe3O4 compared to approximate DFT and DFT + U. In this context, DFT + U + V supports the half-metallic character of the bulk crystal Fe3O4 above Tv, since the Fermi level is found in the t2g band with a Feoct down-spin. Thus, the observations in the current study emphasize the significance of intersite interactions in the theoretical analysis of Fe3O4 above the Tv.

The Structure, Preparation, Characterization, and Intercalation Mechanism of Layered Hydroxides Intercalated with Guest Anions

Since the intercalation of anions into layered hydroxides (LHs) has a great impact not only on their nucleation and growth but also on their structure, composition, and size, the intercalation chemistry of LHs has aroused the strong interest of researchers. However, the progress in the fundamental understanding of LHs intercalated with guest anions have not been paralleled by a concomitant development of the preparation and performance improvement of such materials. Considering the guidance of a timely in-depth review for scientists in this area, a systematic introduction about the development that is made on the above-mentioned issues is highly needed but yet missing so far. Herein, recent advances in understanding the chemical composition and structure of LHs intercalated with guest anions are systematically summarized. Meanwhile, typical and emerging bottom-up synthesis methods of LHs intercalated with anions are reviewed, and the potential impact of external reaction parameters on the intercalation of anions into LHs are discussed . Besides, different analytical characterization techniques employed in the examination of guest anion-intercalated LHs are deliberated upon. Finally, although progress is slow in exploring the intercalation mechanism, as many examples as possible are included in this review and inferred the possible intercalation mechanism.

Electrochemistry from the atomic scale, in the electronically grand-canonical ensemble

The ability to simulate electrochemical reactions from first-principles has advanced significantly in recent years. Here, we discuss the atomistic interpretation of electrochemistry at three scales: from the electronic structure to elementary processes to constant-potential reactions. At each scale, we highlight the importance of the grand-canonical nature of the process and show that the grand-canonical energy is the natural thermodynamic state variable, which has the additional benefit of simplifying calculations. We show that atomic forces are the derivative of the grand-potential energy when the potential is fixed. We further examine the meaning of potential at the atomic scale and its link to the chemical potential and discuss the link between charge transfer and potential in several situations.

Electrochemical Hydrogenation of CO on Cu(100): Insights from Accurate Multiconfigurational Wavefunction Methods

Copper (Cu) remains the most efficacious electrocatalyst for electrochemical CO₂ reduction (CO₂R). Its activity and selectivity are highly facet-dependent. We recently examined the commonly proposed rate-limiting CO hydrogenation step on Cu(111) via embedded correlated wavefunction (ECW) theory and demonstrated that only this higher-level theory yields predictions consistent with potential-dependent experimental kinetics. Here, to understand the differing activities of Cu(111) and Cu(100) in catalyzing CO₂R, we explore CO hydrogenation on Cu(100) using ECW theory. We predict that the preferred pathway involves the reduction of adsorbed CO (*CO) to *COH via proton-coupled electron transfer (PCET) at working potentials, although *CHO also may form with a kinetically accessible but higher barrier. In contrast, our earlier work on Cu(111) concluded that *COH and *CHO formation via PCET are equally feasible. This work illustrates one possible origin of the facet dependence of CO₂R mechanisms and products on Cu electrodes and sheds light on how the selectivity of CO₂R electrocatalysts can be controlled by the surface morphology.

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

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

Structural Properties and Magnetic Ground States of 100 Binary d-Metal Oxides Studied by Hybrid Density Functional Methods

d-metal oxides play a crucial role in numerous technological applications and show a great variety of magnetic properties. We have systematically investigated the structural properties, magnetic ground states, and fundamental electronic properties of 100 binary d-metal oxides using hybrid density functional methods and localized basis sets composed of Gaussian-type functions. The calculated properties are compared with experimental information in all cases where experimental data are available. The used PBE0 hybrid density functional method describes the structural properties of the studied d-metal oxides well, except in the case of molecular oxides with weak intermolecular forces between the molecular units. Empirical D3 dispersion correction does not improve the structural description of the molecular oxides. We provide a database of optimized geometries and magnetic ground states to facilitate future studies on the more complex properties of the binary d-metal oxides.

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.

Electronic Structures of Hydroxyled Low Index Surfaces of Rutile and Anatase-Type Titanium Dioxide

Different surface planes of various types of TiO2 crystals have diverse catalysis effects on the splitting of H2O and H2 and the electronic structures of the formed hydroxylated titanium dioxide...

Revisiting Understanding of Electrochemical CO2 Reduction on Cu(111): Competing Proton-Coupled Electron Transfer Reaction Mechanisms Revealed by Embedded Correlated Wavefunction Theory

Copper (Cu) electrodes, as the most efficacious of CO₂ reduction reaction (CO₂RR) electrocatalysts, serve as prototypes for determining and validating reaction mechanisms associated with electrochemical CO₂ reduction to hydrocarbons. As in situ electrochemical mechanism determination by experiments is still out of reach, such mechanistic analysis typically is conducted using density functional theory (DFT). The semilocal exchange-correlation (XC) approximations most often used to model such catalysis unfortunately engender a basic error: predicting the wrong adsorption site for CO (a key CO₂RR intermediate) on the most ubiquitous facet of Cu, namely, Cu(111). This longstanding inconsistency casts lingering doubt on previous DFT predictions of the attendant CO₂RR kinetics. Here, we apply embedded correlated wavefunction (ECW) theory, which corrects XC functional error, to study the CO₂RR on Cu(111) via both surface hydride (*H) transfer and proton-coupled electron transfer (PCET). We predict that adsorbed CO (*CO) reduces almost equally to two intermediates, namely, hydroxymethylidyne (*COH) and formyl (*CHO) at -0.9 V vs the RHE. In contrast, semilocal DFT approximations predict a strong preference for *COH. With increasing applied potential, the dominance of *COH (formed via potential-independent surface *H transfer) diminishes, switching to the competitive formation of both *CHO and *COH (both formed via potential-dependent PCET). Our results also demonstrate the importance of including explicitly modeled solvent molecules in predicting electron-transfer barriers and reveal the pitfalls of overreliance on simple surface *H transfer models of reduction reactions.

The Role of Metal Ions in the Electron Transport through Azurin-Based Junctions

We studied the coherent electron transport through metal–protein–metal junctions based on a blue copper azurin, in which the copper ion was replaced by three different metal ions (Co, Ni and Zn). Our results show that neither the protein structure nor the transmission at the Fermi level change significantly upon metal replacement. The discrepancy with previous experimental observations suggests that the transport mechanism taking place in these types of junctions is probably not fully coherent.

Reaction pathways in the solid state and the Hubbard U correction

We investigate how the Hubbard U correction influences vacancy defect migration barriers in transition metal oxide semiconductors. We show that, depending on the occupation of the transition metal d orbitals, the Hubbard U correction can cause severe instabilities in the migration barrier energies predicted using generalized gradient approximation density functional theory (GGA DFT). For the d⁰ oxide SrTiO₃, applying a Hubbard correction to the Ti⁴⁺ 3d orbitals below 4-5 eV yields a migration barrier of ∼0.4 eV. However, above this threshold, the barrier increases suddenly to ∼2 eV. This sudden increase in the transition state barrier arises from the Hubbard U correction changing the Ti⁴⁺ t_2g/e_g orbital occupation, and hence electron density localization, along the migration pathway. Similar results are observed in the d¹⁰ oxide ZnO; however, significantly larger Hubbard U corrections must be applied to the Zn²⁺ 3d orbitals for the same instability to be observed. These results highlight important limitations to the application of the Hubbard U correction when modeling reactive pathways in solid state materials using GGA DFT.

Defects as catalytic sites for the oxygen evolution reaction in Earth-abundant MOF-74 revealed by DFT

The oxygen evolution reaction (OER) is the bottleneck of hydrogen production via water splitting and understanding electrocatalysts at atomic level becomes paramount to enhance the efficiency of this process.

The Hubbard-U correction and optical properties of d0 metal oxide photocatalysts

We report a systematic investigation of individual and multisite Hubbard-U corrections for the electronic, structural, and optical properties of the metal titanate oxide d⁰ photocatalysts SrTiO₃ and rutile/anatase TiO₂. Accurate bandgaps for these materials can be reproduced with local density approximation and generalized gradient approximation exchange-correlation density functionals via a continuous series of empirically derived U^d and U^p combinations, which are relatively insensitive to the choice of functional. On the other hand, lattice parameters are much more sensitive to the choice of U^d and U^p, but in a systematic way that enables the U^d and U^p corrections to be used to qualitatively gauge the extent of self-interaction error in the electron density. Modest U^d corrections (e.g., 4 eV-5 eV) yield the most reliable dielectric response functions for SrTiO₃ and are comparable to the range of U^d values derived via linear response approaches. For r-TiO₂ and a-TiO₂, however, the U^d,p corrections that yield accurate bandgaps fail to accurately describe both the parallel and perpendicular components of the dielectric response function. Analysis of individual U^d and U^p corrections on the optical properties of SrTiO₃ suggests that the most consequential of the two individual corrections is U^d, as it predominately determines the accuracy of the dominant excitation from O-2p to the Ti-3d t_2g/e_g orbitals. U^p, on the other hand, can be used to shift the entire optical response uniformly to higher frequencies. These results will assist high-throughput and machine learning approaches to screening photoactive materials based on d⁰ photocatalysts.

Calculating and Characterizing the Charge Distributions in Solids

Accurate estimation of the partial atomic charges on metal centers is useful for understanding electronic and catalytic properties of materials. However, different methods of calculating these charges may give quite different results; this issue has been more widely studied for molecules than for solids. Here we study the charges on the metal centers of a test set of 18 solids containing transition metals by using density functional theory with several density functionals (PBE, PBE+U, TPSS, revTPSS, HLE17, revM06-L, B3LYP, B3LYP*, and other exchange-modified B3LYP functionals) and four charge models (Bader, Hirshfeld, CM5, and DDEC6). The test set contains 12 systems with nonmagnetic metal centers (eight metal oxides (MO₂), two metal sulfides (MS₂), and two metal selenides (MSe₂)) and six ferromagnetic transition metal complexes. Our study shows that, among the four types of charges, Bader charges are the highest and Hirshfeld charges are the lowest for all the systems, regardless of the functional being used. The CM5 charges are bigger than DDEC6 charges for MX₂ with M = Ti or Mo and X = S or Se, but for the other 14 cases they are lower. We found that the most of the systems are sensitive to the Hubbard U parameters in PBE+U and to the percentage X of Hartree-Fock exchange in exchange-modified B3LYP; as we increase U or X, the charges on the metal atoms in MX₂ increase steadily. Testing different density functionals shows charges calculated with higher Hubbard U parameters in PBE+U are comparable to B3LYP (with 20% Hartree-Fock exchange). Among four meta-GGA functionals studied, the charges with HLE17 have the closest agreement with B3LYP. The variation of charges with choice of charge model is greater than the variation with choice of density functional.

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.

Localizing electron density errors in density functional theory

The accuracy of different density functional approximations is assessed through the use of quantum chemical topology on molecular electron densities. In particular, three simple yet ever-important systems are studied: N₂, CO and ethane. Our results exemplify how real-space descriptors can help understand the sources of errors in density functional theory, avoiding unwanted error compensation present in simplified statistical metrics. Errors in "well-built" functionals are shown to be concentrated in chemically meaningful regions of space, and hence they are predictable. Conversely, strongly parametrized functionals show isotropic errors that cannot be traced back to chemically transferable units. Moreover, we will show that energetic corrections are mapped back into improvements in the density in chemically meaningful regions. These results point at the relevance of real-space perspectives when parametrizing or relating energy and density errors.

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.

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.

Designing in the Face of Uncertainty: Exploiting Electronic Structure and Machine Learning Models for Discovery in Inorganic Chemistry

Recent transformative advances in computing power and algorithms have made computational chemistry central to the discovery and design of new molecules and materials. First-principles simulations are increasingly accurate and applicable to large systems with the speed needed for high-throughput computational screening. Despite these strides, the combinatorial challenges associated with the vastness of chemical space mean that more than just fast and accurate computational tools are needed for accelerated chemical discovery. In transition-metal chemistry and catalysis, unique challenges arise. The variable spin, oxidation state, and coordination environments favored by elements with well-localized d or f electrons provide great opportunity for tailoring properties in catalytic or functional (e.g., magnetic) materials but also add layers of uncertainty to any design strategy. We outline five key mandates for realizing computationally driven accelerated discovery in inorganic chemistry: (i) fully automated simulation of new compounds, (ii) knowledge of prediction sensitivity or accuracy, (iii) faster-than-fast property prediction methods, (iv) maps for rapid chemical space traversal, and (v) a means to reveal design rules on the kilocompound scale. Through case studies in open-shell transition-metal chemistry, we describe how advances in methodology and software in each of these areas bring about new chemical insights. We conclude with our outlook on the next steps in this process toward realizing fully autonomous discovery in inorganic chemistry using computational chemistry.

Crystal Structure Prediction of Magnetic Transition-Metal Oxides by Using Evolutionary Algorithm and Hybrid DFT Methods

Although numerous crystal structures have been successfully predicted by using currently available computational techniques, prediction of strongly correlated systems such as transition-metal oxides remains a challenge. To overcome this problem, we have interfaced evolutionary algorithm-based USPEX method with the CRYSTAL code, enabling the use of Gaussian-type localized atomic basis sets and hybrid density functional (DFT) methods for the prediction of crystal structures. We report successful crystal structure predictions of several transition-metal oxides (NiO, CoO, α-Fe2O3, V2O3, and CuO) with correct atomic magnetic moments, spin configurations, and structures by using the USPEX method in combination with the CRYSTAL code and Perdew-Burke-Ernzerhof (PBE0) hybrid functional. Our benchmarking results demonstrate that USPEX + hybrid DFT is a suitable combination to reliably predict the magnetic structures of strongly correlated materials.

Theoretical Modeling of Electronic Excitations of Gas-Phase and Solvated TiO2 Nanoclusters and Nanoparticles of Interest in Photocatalysis

The optical absorption spectra of (TiO₂) _n, nanoclusters ( n = 1-20) and nanoparticles ( n = 35, 84) have been calculated from the frequency-dependent dielectric function in the independent particle approximation under the framework of density functional theory. The PBE generalized gradient approach based functional, the so-called PBE+ U method and the PBE0 and PBEx hybrid functionals-containing 25% and 12.5% of nonlocal Fock exchange, respectively-have been used. The simulated spectra have been obtained in the gas phase and in water on previously PBE0 optimized atomic structures. The effect of the solvent has been accounted for by using an implicit water solvation model. For the smallest nanoclusters, the spectra show discrete peaks, whereas for the largest nanoclusters and for the nanoparticles they resemble a continuum absorption band. In the gas phase and for a given density functional, the onset of the absorption (optical gap, O_gap) remains relatively constant for all nanoparticle sizes although it increases with the percentage of nonlocal Fock exchange, as expected. For all tested functionals, the tendency of O_gap in water is very similar to that observed in the gas phase with an almost constant upshift. For comparison, the optical gap has also been calculated at the TD-DFT level with the PBEx functional in the gas phase and in water. Both approaches agree reasonably well although the TD-DFT gap values are lower than those derived from the dielectric-function. Overall, the position of the spectral maxima and the width of the spectra are relatively constant and independent of particle size which may have implications in the understanding of photocatalysis by TiO₂.

Ab initio electronic structure calculations of entire blue copper azurins

We present a theoretical study of the blue-copper azurin extracted from Pseudomonas aeruginosa and several of its single amino acid mutants.