Interpretable Data-Driven Descriptors for Establishing the Structure-Activity Relationship of Metal-Organic Frameworks Toward Oxygen Evolution Reaction.

The development of readily accessible and interpretable descriptors is pivotal yet challenging in the rational design of metal-organic framework (MOF) catalysts. This study presents a straightforward and physically interpretable activity descriptor for the oxygen evolution reaction (OER), derived from a dataset of bimetallic Ni-based MOFs. Through an artificial-intelligence (AI) data-mining subgroup discovery (SGD) approach, a combination of the d-band center and number of missing electrons in eg states of Ni, as well as the first ionization energy and number of electrons in eg states of the substituents, is revealed as a gene of a superior OER catalyst. The found descriptor, obtained from the AI analysis of a dataset of MOFs containing 3-5d transition metals and 13 organic linkers, has been demonstrated to facilitate in-depth understanding of structure-activity relationship at the molecular orbital level. The descriptor is validated experimentally for 11 Ni-based MOFs. Combining SGD with physical insights and experimental verification, our work offers a highly efficient approach for screening MOF-based OER catalysts, simultaneously providing comprehensive understanding of the catalytic mechanism.

Electronic Properties of Zn2V(1-x)NbxN3 Alloys to Model Novel Materials for Light-Emitting Diodes.

We propose the Zn2V(1-x)NbxN3 alloy as a new promising material for optoelectronic applications, in particular for light-emitting diodes (LEDs). We perform accurate electronic-structure calculations of the alloy for several concentrations x using density-functional theory with meta-GGA exchange-correlation functional TB09. The band gap is found to vary between 2.2 and 2.9 eV with varying V/Nb concentration. This range is suitable for developing bright LEDs with tunable band gap as potential replacements for the more expensive Ga(1-x)In(x)N systems. Effects of configurational disorder are taken into account by explicitly considering all possible distributions of the metal ions within the metal sublattice for the chosen supercells. We have evaluated the band gap's nonlinear behavior (bowing) with variation of V/Nb concentration for two possible scenarios: (i) only the structure with the lowest total energy is present at each concentration and (ii) the structure with minimum band gap is present at each concentration, which corresponds to experimental conditions when also metastable structures are presents. We found that the bowing is about twice larger in the latter case. However, in both cases, the bowing parameter is found to be lower than 1 eV, which is about twice smaller than that in the widely used Ga(1-x)In(x)N alloy. Furthermore, we found that both crystal volume changes due to alloying and local effects (atomic relaxation and the V-N/Nb-N bonding difference) have important contributions to the band gap bowing in Zn2V(1-x)NbxN3.

Statistical analysis of the performance of a variety of first-principles schemes for accurate prediction of binary semiconductor band gaps.

Standard density functional theory (DFT) approximations tend to strongly underestimate band gaps, while the more accurate GW and hybrid functionals are much more computationally demanding and unsuitable for high-throughput screening. In this work, we have performed an extensive benchmark of several approximations with different computational complexity [G0W0@PBEsol, HSE06, PBEsol, modified Becke-Johnson potential (mBJ), DFT-1/2, and ACBN0] to evaluate and compare their performance in predicting the bandgap of semiconductors. The benchmark is based on 114 binary semiconductors of different compositions and crystal structures, for about half of which experimental band gaps are known. Surprisingly, we find that, compared with G0W0@PBEsol, which exhibits a noticeable underestimation of the band gaps by about 14%, the much computationally cheaper pseudohybrid ACBN0 functional shows a competitive performance in reproducing the experimental data. The mBJ functional also performs well relative to the experiment, even slightly better than G0W0@PBEsol in terms of mean absolute (percentage) error. The HSE06 and DFT-1/2 schemes perform overall worse than ACBN0 and mBJ schemes but much better than PBEsol. Comparing the calculated band gaps on the whole dataset (including the samples with no experimental bandgap), we find that HSE06 and mBJ have excellent agreement with respect to the reference G0W0@PBEsol band gaps. The linear and monotonic correlations between the selected theoretical schemes and experiment are analyzed in terms of the Pearson and Kendall rank coefficients. Our findings strongly suggest the ACBN0 and mBJ methods as very efficient replacements for the costly G0W0 scheme in high-throughput screening of the semiconductor band gaps.

Hierarchical Symbolic Regression for Identifying Key Physical Parameters Correlated with Bulk Properties of Perovskites.

Symbolic regression identifies nonlinear, analytical expressions relating materials properties and key physical parameters. However, the pool of expressions grows rapidly with complexity, compromising its efficiency. We tackle this challenge hierarchically: identified expressions are used as inputs for further obtaining more complex expressions. Crucially, this framework can transfer knowledge among properties, as demonstrated using the sure-independence-screening-and-sparsifying-operator approach to identify expressions for lattice constant and cohesive energy, which are then used to model the bulk modulus of ABO_{3} perovskites.

Adatom Bonding Sites in a Nickel-Fe3 O4 (001) Single-Atom Model Catalyst and O2 Reactivity Unveiled by Surface Action Spectroscopy with Infrared Free-Electron Laser Light.

Single-atom (SA) catalysis presently receives much attention with its promise to decrease the cost of the active material while increasing the catalyst's performance. However, key details such as the exact location of SA species and their stability are often unclear due to a lack of atomic level information. Here, we show how vibrational spectra measured with surface action spectroscopy (SAS) and density functional theory (DFT) simulations can differentiate between different adatom binding sites and determine the location of Ni and Au single atoms on Fe3 O4 (001). We reveal that Ni and Au adatoms selectively bind to surface oxygen ions which are octahedrally coordinated to Fe ions. In addition, we find that the Ni adatoms can activate O2 to superoxide in contrast to the bare surface and Ni in subsurface positions. Overall, we unveil the advantages of combining SAS and DFT for improving the understanding of single-atom catalysts.

Artificial-intelligence-driven discovery of catalyst genes with application to CO2 activation on semiconductor oxides.

Catalytic-materials design requires predictive modeling of the interaction between catalyst and reactants. This is challenging due to the complexity and diversity of structure-property relationships across the chemical space. Here, we report a strategy for a rational design of catalytic materials using the artificial intelligence approach (AI) subgroup discovery. We identify catalyst genes (features) that correlate with mechanisms that trigger, facilitate, or hinder the activation of carbon dioxide (CO2) towards a chemical conversion. The AI model is trained on first-principles data for a broad family of oxides. We demonstrate that surfaces of experimentally identified good catalysts consistently exhibit combinations of genes resulting in a strong elongation of a C-O bond. The same combinations of genes also minimize the OCO-angle, the previously proposed indicator of activation, albeit under the constraint that the Sabatier principle is satisfied. Based on these findings, we propose a set of new promising catalyst materials for CO2 conversion.

Coherent vibrational dynamics reveals lattice anharmonicity in organic-inorganic halide perovskite nanocrystals.

The halide ions of organic-inorganic hybrid perovskites can strongly influence the interaction between the central organic moiety and the inorganic metal halide octahedral units and thus their lattice vibrations. Here, we report the halide-ion-dependent vibrational coherences in formamidinium lead halide (FAPbX3, X = Br, I) perovskite nanocrystals (PNCs) via the combination of femtosecond pump-probe spectroscopy and density functional theory calculations. We find that the FAPbX3 PNCs generate halide-dependent coherent vibronic wave packets upon above-bandgap non-resonant excitation. More importantly, we observe several higher harmonics of the fundamental modes for FAPbI3 PNCs as compared to FAPbBr3 PNCs. This is likely due to the weaker interaction between the central FA moiety and the inorganic cage for FAPbI3 PNCs, and thus the PbI64- unit can vibrate more freely. This weakening reveals the intrinsic anharmonicity in the Pb-I framework, and thus facilitating the energy transfer into overtone and combination bands. These findings not only unveil the superior stability of Br-based PNCs over I-based PNCs but are also important for a better understanding of their electronic and polaronic properties.

Single-atom alloy catalysts designed by first-principles calculations and artificial intelligence.

Single-atom-alloy catalysts (SAACs) have recently become a frontier in catalysis research. Simultaneous optimization of reactants' facile dissociation and a balanced strength of intermediates' binding make them highly efficient catalysts for several industrially important reactions. However, discovery of new SAACs is hindered by lack of fast yet reliable prediction of catalytic properties of the large number of candidates. We address this problem by applying a compressed-sensing data-analytics approach parameterized with density-functional inputs. Besides consistently predicting efficiency of the experimentally studied SAACs, we identify more than 200 yet unreported promising candidates. Some of these candidates are more stable and efficient than the reported ones. We have also introduced a novel approach to a qualitative analysis of complex symbolic regression models based on the data-mining method subgroup discovery. Our study demonstrates the importance of data analytics for avoiding bias in catalysis design, and provides a recipe for finding best SAACs for various applications.

Crystallographic Orientation Dependence of Surface Segregation and Alloying on PdCu Catalysts for CO2 Hydrogenation.

The influence of the crystallographic orientation on surface segregation and alloy formation in model PdCu methanol synthesis catalysts was investigated in situ using near-ambient pressure X-ray photoelectron spectroscopy under CO2 hydrogenation conditions. Combined with scanning tunneling microscopy and density functional theory calculations, the study showed that submonolayers of Pd undergo spontaneous alloy formation on Cu(110) and Cu(100) surfaces in vacuum, whereas they do not form an alloy on Cu(111). Upon heating in H2, inward diffusion of Pd into the Cu lattice is favored, facilitating alloying on all Cu surfaces. Under CO2 hydrogenation reaction conditions, the alloying trend becomes stronger, promoted by the reaction intermediate HCOO*, especially on Pd/Cu(110). This work demonstrates that surface alloying may be a key factor in the enhancement of the catalytic activity of PdCu catalysts as compared to their monometallic counterparts. Furthermore, it sheds light on the hydrogen activation mechanism during catalytic hydrogenation on copper-based catalysts.

First-Principles Atomistic Thermodynamics and Configurational Entropy.

In most applications, functional materials operate at finite temperatures and are in contact with a reservoir of atoms or molecules (gas, liquid, or solid). In order to understand the properties of materials at realistic conditions, statistical effects associated with configurational sampling and particle exchange at finite temperatures must consequently be taken into account. In this contribution, we discuss the main concepts behind equilibrium statistical mechanics. We demonstrate how these concepts can be used to predict the behavior of materials at realistic temperatures and pressures within the framework of atomistic thermodynamics. We also introduce and discuss methods for calculating phase diagrams of bulk materials and surfaces as well as point defect concentrations. In particular, we describe approaches for calculating the configurational density of states, which requires the evaluation of the energies of a large number of configurations. The cluster expansion method is therefore also discussed as a numerically efficient approach for evaluating these energies.

Surface core level BE shifts for CaO(100): insights into physical origins.

The relationship between the electronic structure of CaO and the binding energy, BE, shifts between surface and bulk atoms is examined and the physical origins of these shifts are established. Furthermore, the contribution of covalent mixing to the interaction, including the energetic importance, is investigated and found to be small. In particular, the small shift between surface and bulk O(1s) BEs is shown to originate from changes in the polarizable charge distribution of surface O anions. This relationship, which is relevant for the catalytic properties of CaO, follows because the BE shifts are dominated by initial state contributions and the relaxation in response to the core-ionization is similar for bulk and surface. In order to explain the dominance of initial state effects for the BE shifts, the relaxation is decomposed into atomic and extra-atomic contributions. The bonding and the core-level BE shifts have been studied using cluster models of CaO with Hartree-Fock wavefunctions. The theoretical shifts are compared with X-ray photoelectron spectroscopy measurements where both angular resolution and incident photon energy have been used to distinguish surface and bulk ionization.

Ni Single Atom Catalysts for CO2 Activation.

We report on the activation of CO2 on Ni single-atom catalysts. These catalysts were synthesized using a solid solution approach by controlled substitution of 1-10 atom % of Mg2+ by Ni2+ inside the MgO structure. The Ni atoms are preferentially located on the surface of the MgO and, as predicted by hybrid-functional calculations, favor low-coordinated sites. The isolated Ni atoms are active for CO2 conversion through the reverse water-gas shift (rWGS) but are unable to conduct its further hydrogenation to CH4 (or MeOH), for which Ni clusters are needed. The CO formation rates correlate linearly with the concentration of Ni on the surface evidenced by XPS and microcalorimetry. The calculations show that the substitution of Mg atoms by Ni atoms on the surface of the oxide structure reduces the strength of the CO2 binding at low-coordinated sites and also promotes H2 dissociation. Astonishingly, the single-atom catalysts stayed stable over 100 h on stream, after which no clusters or particle formation could be detected. Upon catalysis, a surface carbonate adsorbate-layer was formed, of which the decompositions appear to be directly linked to the aggregation of Ni. This study on atomically dispersed Ni species brings new fundamental understanding of Ni active sites for reactions involving CO2 and clearly evidence the limits of single-atom catalysis for complex reactions.

CO Adsorption on GaPd-Unravelling the Chemical Bonding in Real Space.

The electron localizability indicator-an efficient quantum chemical tool for analysis of chemical bonding-is applied to unveil the chemical bonding behind the CO adsorption on the (1‾ 1‾ 1‾ ) surface of the highly selective semi-hydrogenation catalyst GaPd. Refining the commonly applied Blyholder model, the obtained results are in excellent agreement with previous experimental and theoretical findings. The clean GaPd(1‾ 1‾ 1‾ ) surface presents unshielded negatively charged Pd centers and positively charged Ga species partially shielded by dangling bonds. The CO molecule adsorbs on-top of the Pd centers perperdicular to the surface, while no CO-Ga interaction is observed. The chemical bonding analysis results in deep understanding, thus enabling a cost efficient route to innovative materials by reverse engineering.

Formation of Water Chains on CaO(001): What Drives the 1D Growth?

Formation of partly dissociated water chains is observed on CaO(001) films upon water exposure at 300 K. While morphology and orientation of the 1D assemblies are revealed from scanning tunneling microscopy, their atomic structure is identified with infrared absorption spectroscopy combined with density functional theory calculations. The latter exploit an ab initio genetic algorithm linked to atomistic thermodynamics to determine low-energy H2O configurations on the oxide surface. The development of 1D structures on the C4v symmetric CaO(001) is triggered by symmetry-broken water tetramers and a favorable balance between adsorbate-adsorbate versus adsorbate-surface interactions at the constraint of the CaO lattice parameter.

Big data of materials science: critical role of the descriptor.

Statistical learning of materials properties or functions so far starts with a largely silent, nonchallenged step: the choice of the set of descriptive parameters (termed descriptor). However, when the scientific connection between the descriptor and the actuating mechanisms is unclear, the causality of the learned descriptor-property relation is uncertain. Thus, a trustful prediction of new promising materials, identification of anomalies, and scientific advancement are doubtful. We analyze this issue and define requirements for a suitable descriptor. For a classic example, the energy difference of zinc blende or wurtzite and rocksalt semiconductors, we demonstrate how a meaningful descriptor can be found systematically.

Stability and metastability of clusters in a reactive atmosphere: theoretical evidence for unexpected stoichiometries of MgMOx.

By applying a genetic algorithm and ab initio atomistic thermodynamics, we identify the stable and metastable compositions and structures of MgMOx clusters at realistic temperatures and oxygen pressures. We find that small clusters (M≲5) are in thermodynamic equilibrium when x>M. The nonstoichiometric clusters exhibit peculiar magnetic behavior, suggesting the possibility of tuning magnetic properties by changing environmental pressure and temperature conditions. Furthermore, we show that density-functional theory with a hybrid exchange-correlation functional is needed for predicting accurate phase diagrams of metal-oxide clusters. Neither a (sophisticated) force field nor density-functional theory with (semi)local exchange-correlation functionals is sufficient for even a qualitative prediction.

Concentration of vacancies at metal-oxide surfaces: case study of MgO(100).

We investigate the effects of doping on the formation energy and concentration of oxygen vacancies at a metal-oxide surface, using MgO(100) as an example. Our approach employs density-functional theory, where the performance of the exchange-correlation functional is carefully analyzed, and the functional is chosen according to a condition on density-functional theory ionization energies. The approach is further validated by coupled-cluster calculations, including single, double, and perturbative triple substitutions, for embedded clusters. We demonstrate that the concentration of oxygen vacancies at a doped oxide surface is largely determined by the formation of a macroscopically extended space-charge region.

Rigorous definition of oxidation states of ions in solids.

We present justification and a rigorous procedure for electron partitioning among atoms in extended systems. The method is based on wave-function topology and the modern theory of polarization, rather than charge density partitioning or wave-function projection, and, as such, reformulates the concept of oxidation state without assuming real-space charge transfer between atoms. This formulation provides rigorous electrostatics of finite-extent solids, including films and nanowires.

Influence of ferroelectric polarization on the equilibrium stoichiometry of lithium niobate (0001) surfaces.

We present a first-principles density functional theory study predicting the relative thermodynamic stability of ferroelectric lithium niobate (LiNbO3) (0001) surfaces of different stoichiometry. We predict that the equilibrium stoichiometries are different for the positively and negatively polarized LiNbO3 surfaces under the same conditions. Based on the modern theory of polarization, we demonstrate how a simple ionic model can be used to calculate surface charges for ferroelectric surfaces with intrinsic polar stacking. It is found that surface charge passivation by ions is thermodynamically favored over passivation by mobile carriers in a wide range of chemical potentials.