Acetylene and Ethylene Adsorption during Floating Fe Catalyst Formation at the Onset of Carbon Nanotube Growth and the Effect of Sulfur Poisoning: a DFT Study

Here, we investigated the adsorption of acetylene and ethylene on iron clusters and nanoparticles, which is a crucial aspect in the nascent phase of carbon nanotube growth by floating catalyst chemical vapor deposition (FCCVD). The effect of sulfur on adsorption was also studied due to its indispensable role in the process and its commonly known impact on metal catalyst poisoning. We performed systematic density functional theory (DFT) computations, considering numerous adsorption configurations and iron particles of various sizes (Fen, n = 3-10, 13, 55). We found that acetylene binds significantly more strongly than ethylene and prefers different adsorption sites. The presence of sulfur decreased the adsorption strength only in the immediate proximity of the adsorbate, suggesting that the effect of sulfur is mainly of steric origin while electronic effects play only a minor role. Higher sulfur coverage of the catalyst surface significantly weakened the binding of acetylene or ethylene. To further investigate this interaction, Bader's atoms in molecules (AIM) analysis and charge density difference (CDD) were used, which showed electron transfer from iron clusters or nanoparticles to the adsorbate molecules. The charge transfer exhibited a decreasing trend as sulfur coverage increased. These results can also contribute to the understanding of other iron-based catalytic processes involving hydrocarbons and sulfur, such as the Fischer-Tropsch synthesis.

Data-driven stabilization of NimPdn-m nanoalloys: a study using density functional theory and data mining approaches

Green hydrogen, generated through the electrolysis of water, is a viable alternative to fossil fuels, although its adoption is hindered by the high costs associated with the catalysts. Among a wide variety of potential materials, binary nickel-palladium (NiPd) systems have garnered significant attention, particularly at the nanoscale, for their efficacious roles in catalyzing hydrogen and oxygen evolution reactions. However, our atom-level understanding of the descriptors that drive their energetic stability at the nanoscale remains largely incomplete. Here, we investigate by density functional theory calculations the descriptors that drives the stability of the NimPdn-m clusters for different sizes (n = 13, 27, 41) and compositions. To achieve our goals, a large number of trial configurations were generated and selected using data mining algorithms (k-means, t-SNE) and genetic algorithms, while the most important physical-chemical descriptors were identified using Spearman correlation analysis. We have found that core-shell formation, with the smaller Ni atoms lying in the center of the particle, plays a major role in the stabilization of the nanoalloys, and this effect causes the alloys to assume a icosahedral-fragment configuration (as the unary nickel cluster) instead of a fcc fragment (as the unary palladium cluster). However, the core-shell formation in this alloy is unique in that Pd poor compositions exhibit scattered Pd atoms on the surface. As the palladium content increases, this gives rise to the complete Pd shell. This stabilization mechanism is quantitatively supported by the different correlations observed in the number of Ni-Ni and Pd-Pd bonds with energy, in which the latter tends to decrease alloy stability. Furthermore, a notable trend is the correlation between the coordination number of Ni atoms with alloy stabilization, while the coordination of Pd atoms shows an inverse correlation.

Cage doping of Ti, Zr, and Hf-based 13-atom nanoclusters: two sides of the same coin

Transition metal nanoclusters can exhibit unique and tunable properties which result not only from their chemical composition but also from their atomic packing and quantized electronic structures. Here, we introduce a promising family of bimetallic TM@Ti12, TM@Zr12, and TM@Hf12 nanoclusters with icosahedral geometry, where TM represents an atom from groups 3 to 12. Density functional theory calculations show that their stability can be explained with familiar concepts of metal cluster electronic and atomic shell structures. The magnetic properties of these quasispherical clusters are entirely consistent with superatom electronic shells and Hund's rules, and can be tuned by the choice of the TM dopant. The computed cluster atomization energies were analyzed in terms of the elements' cohesive energy, Ecoh, and contributions from geometric distortion, Edis, surface energy, Es, and ionic bonding, Ei. Some clusters have anomalous stability relative to Ecoh + Edis + Es + Ei. We attribute this to superatomic character associated with a favorable atomic and electronic shell structure. This raises the possibility of designing stable superatoms and materials with tailored electronic and magnetic properties.

Investigating structural and electronic properties of neutral zinc clusters: a G0W0 and G0W0Г0(1) benchmark

The structural and electronic properties of zinc clusters (Znn) for a size range of n = 2-15 are studied using density functional theory. The particle swarm optimization algorithm is employed to search the structure and to determine the ground-state structure of the neutral Zn clusters. The structural motifs are optimized using the density functional theory approach to ensure that the structures are fully relaxed. Results are compared with the literature to validate the accuracy of the prediction method. The binding energy per cluster is obtained and compared with the reported literature to study the stability of these structures. We further assess the electronic properties, including the ionization potential, using the all-electron FHI-aims code employing G0W0 calculations, and the G0W0Г0(1) correction for a few smaller clusters, which provides a better estimation of the ionization potential compared to other methods.

Assignment of individual structures from intermetalloid nickel gallium cluster ensembles

Poorly selective mixed-metal cluster synthesis and separation yield reaction solutions of inseparable intermetalloid cluster mixtures, which are often discarded. High-resolution mass spectrometry, however, can provide precise compositional data of such product mixtures. Structure assignments can be achieved by advanced computational screening and consideration of the complete structural space. Here, we experimentally verify structure and composition of a whole cluster ensemble by combining a set of spectroscopic techniques. Our study case are the very similar nickel/gallium clusters of M12, M13 and M14 core composition Ni6+xGa6+y (x + y ≤ 2). The rationalization of structure, bonding and reactivity is built upon the organometallic superatom cluster [Ni6Ga6](Cp*)6 = [Ga6](NiCp*)6 (1; Cp* = C5Me5). The structural conclusions are validated by reactivity tests using carbon monoxide, which selectively binds to Ni sites, whereas (triisopropylsilyl)acetylene selectively binds to Ga sites.

Activating two-dimensional semiconductors for photocatalysis: a cross-dimensional strategy

The emerging two-dimensional (2D) semiconductors substantially extend materials bases for versatile applications such as semiconductor photocatalysis demanding semiconductive matrices and large surface areas. The dimensionality, while endowing 2D semiconductors the unique properties to host photocatalytic functionality of pollutant removal and hydrogen evolution, hurdles the activation paths to form heterogenous photocatalysts where the photochemical processes are normally superior over these on the mono-compositional counterparts. In this perspective, we present a cross-dimensional strategy to employ thenD (n= 0-2) clusters or nanomaterials as activation partners to boost the photocatalytic activities of the 2D semiconductors. The formation principles of heterogenous photocatalysts are illustrated specifically for the 2D matrices, followed by selection criteria of them among the vast 2D database. The computer investigations are illustrated in the density functional theory route and machine learning benefitted from the vast samples in the 2D library. Synthetic realizations and characterizations of the 2D heterogenous systems are introduced with an emphasis on chemical methods and advanced techniques to understand materials and mechanistic studies. The perspective outlooks cross-dimensional activation strategies of the 2D materials for other applications such as CO2removal, and materials matrices in other dimensions which may inspire incoming research within these fields.

Probing adsorption of methane onto vanadium cluster cations via vibrational spectroscopy

Photofragment spectroscopy is used to measure the vibrational spectra of V2+(CH4)n (n = 1-4), V3+(CH4)n (n = 1-3), and Vx+(CH4) (x = 4-8) in the C-H stretching region (2550-3100 cm-1). Spectra are measured by monitoring loss of CH4. The experimental spectra are compared to simulations at the B3LYP+D3/6-311++G(3df,3pd) level of theory to identify the geometry of the ions. Multi-reference configuration interaction with Davidson correction (MRCI+Q) calculations are also carried out on V2+ and V3+. The methane binding orientation in V2+(CH4)n (n = 1-4) evolves from η3 to η2 as more methane molecules are added. The IR spectra of metal-methane clusters can give information on the structure of metal clusters that may otherwise be hard to obtain from isolated clusters. For example, the V3+(CH4)n (n = 1-3) experimental spectra show an additional peak as the second and third methane molecules are added to V3+, which indicates that the metal atoms are not equivalent. The Vx+(CH4) show a larger red shift in the symmetric C-H stretch for larger clusters with x = 5-8 than for the small clusters with x = 2, 3, indicating increased covalency in the interaction of larger vanadium clusters with methane.

A database of low-energy atomically precise nanoclusters

The chemical and structural properties of atomically precise nanoclusters are of great interest in numerous applications, but the structures of the clusters can be computationally expensive to predict. In this work, we present the largest database of cluster structures and properties determined using ab-initio methods to date. We report the methodologies used to discover low-energy clusters as well as the energies, relaxed structures, and physical properties (such as relative stability, HOMO-LUMO gap among others) for 63,015 clusters across 55 elements. We have identified clusters for 593 out of 1595 cluster systems (element-size pairs) explored by literature that have energies lower than those reported in literature by at least 1 meV/atom. We have also identified clusters for 1320 systems for which we were unable to find previous low-energy structures in the literature. Patterns in the data reveal insights into the chemical and structural relationships among the elements at the nanoscale. We describe how the database can be accessed for future studies and the development of nanocluster-based technologies.

Molecular adsorption on coinage metal subnanoclusters: A DFT+D3 investigation

Gold and silver subnanoclusters with few atoms are prominent candidates for catalysis-related applications, primarily because of the large fraction of lower-coordinated atoms exposed and ready to interact with external chemical species. However, an in-depth energetic analysis is necessary to characterize the relevant terms within the molecular adsorption process that can frame the interactions within the Sabatier principle. Herein, we investigate the interaction between Ag_n and Au_n subnanoclusters (clu, n = 2-7) and N₂ , NO, CO, and O₂ molecules, using scalar-relativistic density functional theory calculations within van der Waals D3 corrections. The onefold top site is preferred for all chemisorption cases, with a predominance of linear (≈180°) and bent (≈120°) molecular geometries. A larger magnitude of adsorption energy is correlated with smaller distances between molecules and clusters and with the weakening of the adsorbates bond strength represented by the increase of the equilibrium distances and decrease of molecular stretching frequencies. From the energetic decomposition, the interaction energy term was established as an excellent descriptor to classify subnanoclusters in the adsorption/desorption process concomitant with the Sabatier principle. The limiting cases: (i) weak molecular adsorption on the subnanoclusters, which may compromise the reaction activation, where an interaction energy magnitude close to 0 eV is observed (e.g., physisorption in N₂ /Ag₆ ); and (ii) strong molecular interactions with the subnanoclusters, given the interaction energy magnitude is larger than at least one of the individual fragment binding energies (e.g., strong chemisorption in CO/Au₄ and NO/Au₄ ), conferring a decrease in the desorption rate and an increase in the possible poisoning rate. However, the intermediate cases are promising by involving interaction energy magnitudes between zero and fragment binding energies. Following the molecular closed-shell (open-shell) electronic configuration, we find a predominant electrostatic (covalent) nature of the physical interactions for N₂ ⋯clu and CO ⋯clu (O₂ ⋯clu and NO⋯clu), except in the physisorption case (N₂ /Ag₆ ) where dispersive interaction is dominant. Our results clarify questions about the molecular adsorption on subnanoclusters as a relevant mechanistic step present in nanocatalytic reactions.

Properties of Naked Silver Clusters with Up to 100 Atoms as Found with Embedded-Atom and Density-Functional Calculations

The structural and energetic properties of small silver clusters Agn with n = 2-100 atoms are reported. For n = 2-100 the embedded atom model for the calculation of the total energy of a given structure in combination with the basin-hopping search strategy for an unbiased structure optimization has been used to identify the energies and structures of the three energetically lowest-lying isomers. These optimized structures for n = 2-11 were subsequently studied further through density-functional-theory calculations. These calculations provide additional information on the electronic properties of the clusters that is lacking in the embedded-atom calculations. Thereby, also quantities related to the catalytic performance of the clusters are studied. The calculated properties in comparison to other available theoretical and experimental data show a good agreement. Previously unidentified magic (i.e., particularly stable) clusters have been found for n>80. In order to obtain a more detailed understanding of the structural properties of the clusters, various descriptors are used. Thereby, the silver clusters are compared to other noble metals and show some similarities to both copper and nickel systems, and also growth patterns have been identified. All vibrational frequencies of all the clusters have been calculated for the first time, and here we focus on the highest and lowest frequencies. Structural effects on the calculated frequencies were considered.

Enhancing the Performance of Global Optimization of Platinum Cluster Structures by Transfer Learning in a Deep Neural Network

The global optimization of metal cluster structures is an important research field. The traditional deep neural network (T-DNN) global optimization method is a good way to find out the global minimum (GM) of metal cluster structures, but a large number of samples are required. We developed a new global optimization method which is the combination of the DNN and transfer learning (DNN-TL). The DNN-TL method transfers the DNN parameters of the small-sized cluster to the DNN of the large-sized cluster to greatly reduce the number of samples. For the global optimization of Pt₉ and Pt₁₃ clusters in this research, the T-DNN method requires about 3-10 times more samples than the DNN-TL method, and the DNN-TL method saves about 70-80% of time. We also found that the average amplitude of parameter changes in the T-DNN training is about 2 times larger than that in the DNN-TL training, which rationalizes the effectiveness of transfer learning. The average fitting errors of the DNN trained by the DNN-TL method can be even smaller than those by the T-DNN method because of the reliability of transfer learning. Finally, we successfully obtained the GM structures of Pt_n (n = 8-14) clusters by the DNN-TL method.

Structure and size-dependent vibrational and thermal properties of Ni clusters: A systematic ab initio approach

There is scarce information on the vibrational and thermal properties of small Ni clusters. Here, the outcomes of ab initio spin-polarized density functional theory calculations on the size and geometry effects upon the vibrational and thermal properties of Ni_n (n = 13 and 55) clusters, are discussed. For theses clusters a comparison is presented between the closed shell symmetric octahedral (O_h) and the icosahedral (I_h) geometries. The results indicate that the I_h isomers are lower in energy. Besides, ab initio molecular dynamics runs at T = 300K show that Ni₁₃ and Ni₅₅ clusters transform from their initial O_h geometries towards the corresponding I_h ones. For Ni₁₃, we also consider the lowest energy less symmetric layered 1-3-6-3 structure, and the cuboid, recently observed experimentally for Pt₁₃, which is competitive in energy but is unstable, as phonon analysis reveals. We calculate their vibrational density of states (νDOS) and heat capacity, and compare with the Ni FCC bulk counterpart. The characteristic features of the νDOS curves of these clusters are interpreted in terms of the clusters' sizes, the interatomic distance contractions, the bond order values as well as the internal pressure and strains of the clusters. We find that the softest possible frequency of the clusters is size and structure-dependent, being the smallest for the O_h ones. We identify mostly shear, tangential type displacements involving mainly surface atoms for the lowest frequency of the spectra of both I_h and O_h isomers. For the maximum frequencies of these clusters the central atom shows anti-phase movements against groups of nearest neighbor atoms. An excess of heat capacity at low temperatures with respect to the bulk is found, while at high temperatures a constant limiting value, close but lower to the Dulong and Petit value, is determined.

Phosphine-Stabilized Hidden Ground States in Gold Clusters Investigated via a Aun(PH3)m Database

Nanoclusters are promising materials for catalysis and sensing due to their large surface areas and unique electronic structures which can be tailored through composition, geometry, and chemistry. However, relationships correlating synthesis parameters directly to outcomes are limited. While previous computational studies have mapped the potential energy surface of specific systems of bare nanoclusters by generating and calculating the energies of reasonable structures, it is known that environmental ions and ligands crucially impact the final shape and size. In this work, phosphine-stabilized gold is considered as a test system and DFT calculations are performed for clusters with and without ligands, producing a database containing >10000 structures for Aun(PH3)m (n ≤ 12). We find that the ligation of phosphines affects the thermodynamic stability, bonding, and electronic structure of Au nanoclusters, specifically such that "hidden" ground state cluster geometries are stabilized that are dynamically unstable in the pure gold system. Further, the addition of phosphine introduces steric effects that induce a transition from planar to nonplanar structures at 4-5 Au atoms rather than up to 13-14 Au atoms, as previously predicted for bare clusters. This work highlights the importance of considering the ligand environment in the prediction of nanocluster morphology and functionality, which adds complexity as well as a rich opportunity for tunability.

Big Data in a Nano World: A Review on Computational, Data-Driven Design of Nanomaterials Structures, Properties, and Synthesis

The recent rise of computational, data-driven research has significant potential to accelerate materials discovery. Automated workflows and materials databases are being rapidly developed, contributing to high-throughput data of bulk materials that are growing in quantity and complexity, allowing for correlation between structural-chemical features and functional properties. In contrast, computational data-driven approaches are still relatively rare for nanomaterials discovery due to the rapid scaling of computational cost for finite systems. However, the distinct behaviors at the nanoscale as compared to the parent bulk materials and the vast tunability space with respect to dimensionality and morphology motivate the development of data sets for nanometric materials. In this review, we discuss the recent progress in data-driven research in two aspects: functional materials design and guided synthesis, including commonly used metrics and approaches for designing materials properties and predicting synthesis routes. More importantly, we discuss the distinct behaviors of materials as a result of nanosizing and the implications for data-driven research. Finally, we share our perspectives on future directions for extending the current data-driven research into the nano realm.

Cytotoxic sub-nanometer aqueous platinum clusters as potential antitumoral agents

Ligand-free sub-nanometer metal clusters (MCs) of Pt, Ir, Rh, Au and Cu, are prepared here in neat water and used as extremely active (nM) antitumoral agents for HeLa and A2870 cells. The preparation just consists of adding the biocompatible polymer ethylene-vinyl alcohol (EVOH) to an aqueous solution of the corresponding metal salt, to give liters of a MC solution after filtration of the polymer. Since the MC solution is composed of just neat metal atoms and water, the intrinsic antitumoral activity of the different sub-nanometer metal clusters can now fairly be evaluated. Pt clusters show an IC₅₀ of 0.48 μM for HeLa and A2870 cancer cells, 23 times higher than that of cisplatin and 1000 times higher than that of Pt NPs, and this extremely high cytotoxicity also occurs for cisplatin-resistant (A2870 cis) cells, with a resistance factor of 1.4 (IC₅₀ = 0.68 μM). Rh and Ir clusters showed an IC₅₀ ∼ 1 μM. Combined experimental and computational studies support an enhanced internalization and cytotoxic activation.

An Open-Shell Superatom Cluster Ta10- with Enhanced Stability by United d-d π Bonds and d-Orbital Superatomic States

We carried out a comprehensive study on the gas-phase reactions of Ta_n^- (n = 5-27) with nitrogen using a customized reflection time-of-flight mass spectrometer coupled with a velocity map imaging apparatus (Re-TOFMS-VMI). Among the studied tantalum clusters, Ta₁₀^- exhibits prominent mass abundance indicative of its unique inertness. DFT calculation results revealed a D_4d bipyramidal prolate structure of the most stable Ta₁₀^-, which was verified by photoelectron spectroscopy experiments. The calculations also unveiled that Ta₁₀^- has the largest HOMO-LUMO gap and second-order difference of binding energy among the studied clusters. This is associated with its well-organized superatomic orbitals, which consist of both 6s and 5d orbitals of tantalum atoms, allowing for splitting of superatomic 1D and 2P orbitals and an enlarged gap between the singly occupied molecular orbital (SOMO) and unoccupied β counterpart, which brings forth stabilization energy pertaining to Jahn-Teller distortion. Also, the SOMO exhibits a united d-d π orbital pattern that embraces the central Ta₈^- moiety.

First-Principles Study of Irn (n = 3-5) Clusters Adsorbed on Graphene and Hexagonal Boron Nitride: Structural and Magnetic Properties

Magnetic clusters have attracted great attention and interest due to their novel electronic properties, and they have potential applications in nanoscale information storage devices and spintronics. The interaction between magnetic clusters and substrates is still one of the challenging research focuses. Here, by using the density functional theory (DFT), we study the structural stability and magnetic properties of iridium clusters (Ir_n, n = 3–5) adsorbed on two-dimensional (2D) substrates, such as graphene and hexagonal boron nitride (hBN). We find that the most favorable configurations of free Ir_n clusters change when adsorbed on 2D substrates. In the meantime, the magnetic moments of the most stable Ir_n reduce to 53% (graphene) and 23.6% (hBN) compared with those of the free−standing ones. Interestingly, about 12-times enlargement on the magnetic anisotropy energy can be found on hBN substrates. These theoretical results indicate that the cluster–substrate interaction has vital effects on the properties of Ir_n clusters.

What Determines the Drastic Reactivity of Nbn+ Clusters with Nitric Oxide under Thermalized Conditions?

We report an in-depth study of the adsorption and reaction of NO with cationic Nb_n⁺ (n = 1-20) clusters under thermalized conditions in a laminar flow tube reactor in tandem with a customized triple quadrupole mass spectrometer (FT-TQMS). It is found that the small-sized Nb_n⁺ clusters (2 ≤ n ≤ 7) readily react with NO giving rise to dominant fragmentation products pertaining to the loss of a stable diatomic molecule NbO or NbN. In contrast, the reaction products of larger-sized clusters (n ≥ 10) proceed through diverse channels, including NO adsorption, N₂/N₂O release, and even NO₂ formation. These experimental observations provided the incentive for us to dig deep into the reaction mechanism with the help of DFT calculations. In contrast to the NO-donation coordination in transition metal complexes, here the cationic Nb_n⁺ clusters exhibit dominant electronic donation in initiating the reactions with NO molecules. We fully demonstrated the reaction rate constants, compared the reaction energy diagram of typical Nb_n⁺ clusters, and unveiled the distinct interaction mechanism of niobium clusters available for NO activation and conversion.

Structures of Small Platinum Cluster Anions Ptn-: Experiment and Theory

The structures of platinum cluster anions Pt6--Pt13- have been investigated by trapped ion electron diffraction. Structures were assigned by comparing experimental and simulated scattering functions using candidate structures obtained by density functional theory computations, including spin-orbit coupling. We find a structural evolution from planar structures (Pt6-, Pt7-) and amorphous-like structures (Pt7--Pt9-) to structures based on distorted tetrahedra (Pt9--Pt11-). Finally, Pt12- and Pt13- are based on hcp fragments. While the structural parameters are well described by density functional theory computations for all clusters studied, the predicted lowest energy structure is found in the experiment only for Pt6-. For larger clusters, higher energy isomers are necessary to obtain a fit to the scattering data.

Ab initio study of the adsorption properties of CO2 reduction intermediates: The effect of Ni5Ga3 alloy and the Ni5Ga3/ZrO2 interface

The Ni5Ga3 alloy supported on ZrO2 is a promising catalyst for the reduction of CO2 due to its higher selectivity to methanol at ambient pressure, e.g., activity comparable to industrial catalysts. However, our atomistic understanding of the role of the cooperative effects induced by the Ni5Ga3 alloy formation and its Ni5Ga3/ZrO2 interface in the CO2 reduction is still far from satisfactory. In this work, we tackle these questions by employing density functional theory calculations to investigate the adsorption properties of key CO2 reduction intermediates (CO2, H2, cis-COOH, trans-COOH, HCOO, CO, HCO, and COH) on Ni8, Ga8, Ni5Ga3, (ZrO2)16, and Ni5Ga3/(ZrO2)16. We found that Ni containing clusters tended to assume wetting configurations on the (ZrO2)16 cluster, while the presence of Ga atoms weakens the adsorption energies on the oxide surface. We also observed that CO2 was better activated on the metal–oxide interfaces and on the oxide surface, where it was able to form CO3-like structures. Meanwhile, H2 activation was only observed on Ni sites, which indicates the importance of distinct adsorption sites that can favor different CO2 reduction steps. Moreover, the formation of the metal–oxide interface showed to be beneficial for the adsorption of COOH isomers and unfavorable for the adsorption of HCOO.

Ab initio investigation of the role of the d-states on the adsorption and activation properties of CO2 on 3d, 4d, and 5d transition-metal clusters

We report a theoretical investigation of the adsorption and activation properties of CO2 on eight-atom 3 d, 4 d, and 5 d transition-metal (TM) clusters based on density functional theory calculations. From our results and analyses, in the lowest energy configurations, CO2 binds via a chemisorption mechanism on Fe, Co, Ni, Ru, Rh, Pd, Os, Ir, and Pt (adsorption energy from −0.49 eV on Pt up to −1.40 eV on Os), where CO2 breaks its linearity and adopts an angular configuration due to the charge transfer from the clusters toward the C atom in the adsorbed CO2. In contrast, it binds via physisorption on Cu, Ag, and Au and maintains its linearity due to a negligible charge transfer toward CO2 and has a small adsorption energy (from −0.17 eV on Cu up to −0.18 eV on Ag). There is an energetic preference for twofold bridge TM sites, which favors binding of C with two TM atoms, which enhances the charge transfer ten times than on the top TM sites (onefold). We identified that the strength of the CO2–TM8 interaction increases when the energy values of the highest occupied molecular orbital (HOMO) of the TM8 are closer to the energy values of the lowest unoccupied molecular orbital of CO2, which contributes to maximize the charge transfer toward the molecule. Beyond the energy position of the HOMO states, the delocalization of 5 d orbitals plays an important role in the adsorption strength in TM, especially for the iron group, e.g., the adsorption energies are −1.08 eV (Fe, 3 d), −1.19 eV (Ru, 4 d), and −1.40 eV (Os, 5 d).

Carbide coating on nickel to enhance the stability of supported metal nanoclusters

The influence on the growth of cobalt (Co)-based nanostructures of a surface carbide (Ni₂C) layer formed at the Ni(100) surface is revealed via complementary scanning tunneling microscopy (STM) measurements and first-principles calculations. On clean Ni(100) below 200 °C in the sub-monolayer regime, Co forms randomly distributed two-dimensional (2D) islands, while on Ni₂C it grows in the direction perpendicular to the surface as well, thus forming two-atomic-layers high islands. We present a simple yet powerful model that explains the different Co growth modes for the two surfaces. A jagged step decoration, not visible on stepped Ni(100), is present on Ni₂C. This contrasting behavior on Ni₂C is explained by the sharp differences in the mobility of Co atoms for the two cases. By increasing the temperature, Co dissolution is activated with almost no remaining Co at 250 °C on Ni(100) and Co islands still visible on the Ni₂C surface up to 300 °C. The higher thermal stability of Co above the Ni₂C surface is rationalized by ab initio calculations, which also suggest the existence of a vacancy-assisted mechanism for Co dissolution in Ni(100). The methodology presented in this paper, combining systematically STM measurements with first-principles calculations and computational modelling, opens the way to controlled engineering of bimetallic surfaces with tailored properties.

Assessment of Various Density Functional Theory Methods for Finding Accurate Structures of Actinide Complexes

Density functional theory (DFT) is a widely used computational method for predicting the physical and chemical properties of metals and organometals. As the number of electrons and orbitals in an atom increases, DFT calculations for actinide complexes become more demanding due to increased complexity. Moreover, reasonable levels of theory for calculating the structures of actinide complexes are not extensively studied. In this study, 38 calculations, based on various combinations, were performed on molecules containing two representative actinides to determine the optimal combination for predicting the geometries of actinide complexes. Among the 38 calculations, four optimal combinations were identified and compared with experimental data. The optimal combinations were applied to a more complicated and practical actinide compound, the uranyl complex (UO₂(2,2′-(1E,1′E)-(2,2-dimethylpropane-1,3-dyl)bis(azanylylidene)(CH₃OH)), for further confirmation. The corresponding optimal calculation combination provides a reasonable level of theory for accurately optimizing the structure of actinide complexes using DFT.

Exploring AuRh nanoalloys: a computational perspective on the formation and physical properties

We studied the formation of AuRh nanoalloys (between 20–150 atoms) in the gas phase by means of Molecular Dynamics (MD) calculations, exploring three possible formation processes: one‐by‐one growth, coalescence, and nanodroplets annealing. As a general trend, we recover a predominance of Rh@Au core‐shell ordering over other chemical configurations. We identify new structural motifs with enhanced thermal stabilities. The physical features of those selected systems were studied at the Density Functional Theory (DFT) level, revealing profound correlations between the nanoalloys morphology and properties. Surprisingly, the arrangement of the inner Rh core seems to play a dominant role on nanoclusters’ physical features like the HOMO‐LUMO gap and magnetic moment. Strong charge separations are recovered within the nanoalloys suggesting the existence of charge‐transfer transitions.

Role of quantum-size effects in the dehydrogenation of CH4 on 3d TMn clusters: DFT calculations combined with data mining

Adsorption modes identified by clustering algorithms for CH4 adsorption on TMn clusters.

Assessment of the van der Waals, Hubbard U parameter and spin-orbit coupling corrections on the 2D/3D structures from metal gold congeners clusters

The coinage-metal clusters possess a natural complexity in their theoretical treatment that may be accompanied by inherent shortcomings in the methodological approach. Herein, we performed a scalar-relativistic density functional theory study, considering Perdew, Burke, and Ernzerhof (PBE) with (empirical and semi empirical) van der Waals (vdW), spin-orbit coupling (SOC), +U (Hubbard term), and their combinations, to treat the Cu 13 , Ag 13 , and Au 13 clusters in different structural motifs. The energetic scenario is given by the confirmation of the 3D lowest energy configurations for Cu 13 and Ag 13 within all approaches, while for Au 13 there is a 2D/3D competition, depending on the applied correction. The 2D geometry is 0.43 eV more stable with plain PBE than the 3D one, the SOC, +U, and/or vdW inclusion decreases the overestimated stability of the planar configurations, where the most surprising result is found by the D3 and D3BJ vdW corrections, for which the 3D configuration is 0.29 and 0.11 eV, respectively, more stable than the 2D geometry (with even higher values when SOC and/or +U are added). The D3 dispersion correction represents 7.9% (4.4%) of the total binding energy for the 3D (2D) configuration, (not) being enough to change the sd hybridization and the position of the occupied d -states. Our predictions are in agreement with experimental results and in line with the best results obtained for bulk systems, as well as with hybrid functionals within D3 corrections. The properties description undergoes small corrections with the different approaches, where general trends are maintained, that is, the average bond length is smaller (larger) for lower (higher)-coordinated structures, since a same number of electrons are shared by a smaller (larger) number of bonds, consequently, the bonds are stronger (weaker) and shorter (longer) and the sd hybridization index is larger (smaller). Thus, Au has a distinct behavior in relation to its lighter congeners, with a complex potential energy surface, where in addition to the relevant relativistic effects, correlation and dispersion effects must also be considered.

Effects of Temperature on Enantiomerization Energy and Distribution of Isomers in the Chiral Cu13 Cluster

In this study, we report the lowest energy structure of bare Cu₁₃ nanoclusters as a pair of enantiomers at room temperature. Moreover, we compute the enantiomerization energy for the interconversion from minus to plus structures in the chiral putative global minimum for temperatures ranging from 20 to 1300 K. Additionally, employing nanothermodynamics, we compute the probabilities of occurrence for each particular isomer as a function of temperature. To achieve that, we explore the free energy surface of the Cu₁₃ cluster, employing a genetic algorithm coupled with density functional theory. Moreover, we discuss the energetic ordering of isomers computed with various density functionals. Based on the computed thermal population, our results show that the chiral putative global minimum strongly dominates at room temperature.

Evolution of Ferromagnetic and Antiferromagnetic States in Iron Nitride Clusters FenN and FenN2 (n = 1-10)

First-principles density functional theory calculations on neutral and singly negatively and positively charged iron clusters Fe_n and iron nitride clusters Fe_nN and Fe_nN₂ (n = 1-10) in the range of 1 ≤ n ≤ 10 revealed that there is a strong competition between ferromagnetic and antiferromagnetic states especially in the Fe_nN₂^0,±1 cluster series. This phenomenon was related to superexchange via a bridging N atom between two iron atoms in the Fe_nN₂^0,±1 cluster series and to a double superexchange effect via a Fe atom shared by two N atoms in the Fe_nN₂^0,±1 series. A thorough examination of the structure-energy-spin state relationships in these clusters is conducted, leading to new insights and confirmation of available experimental results on structural parameters and dissociation energetics. The bond energies of both nitrogen atoms in the Fe_nN₂ series are approximately the same. They weakly depend on the charge of the host cluster and fluctuate around 5.5 eV when moving along the series. The energy of N₂ desorption is relatively small; it varies by about 1.0 eV and depends on the charge of the cluster. The experimental finding that N₂ dissociates on the Fe_n⁺ clusters beginning with n = 4 was supported by the results of our computations. Our computed values of the Fe_n⁺-N bonding energies agree with the experimental data within the experimental uncertainty bars. It was found that the attachment of one or two N atoms does not seriously affect the polarizability, electron affinity, or ionization energy of the host iron clusters independent of the charge.

Role of the OH-group in the adsorption properties of methanol, ethanol, and ethylene glycol on 15-atom 3d, 4d, and 5d transition-metal clusters

The adsorption of alcohols on transition-metal (TM) substrates has received the attention of many researchers due to the applications of alcohols in several technological fields. However, our atomic-level understanding is still far from satisfactory, in particular for the interaction of alcohols with finite-size TM clusters, where new effects can arise due to the presence of quantum-size effects. In this work, we report a theoretical investigation of the adsorption properties of methanol, ethanol, and ethylene glycol on 12 different 3d, 4d, and 5d TM₁₅ clusters based on density functional theory calculations within the semi-empirical D3 van der Waals corrections. From the correlation analysis of all the lowest- and high-energy configurations, we identified the adsorption modes of methanol, ethanol, and ethylene glycol on the TM₁₅ clusters, in which the OH group binds to the cationic TM sites via the O-TM and H-TM interactions. Due to the relatively weak alcohol-TM₁₅ interaction, the changes induced on the TM₁₅ clusters are small, except for Au₁₅ and Ru₁₅, where the bare cluster changes its structure to a nearby minimum in the potential energy surface. The adsorption energy for the alcohol/TM₁₅ systems is correlated to the combination of several parameters, in which the main contribution is connected with the O-TM interaction and the HOTM angles. Furthermore, the TM electronegativity is an important descriptor for the methanol and ethanol adsorption energies, while charge transfer is important for ethylene glycol.

Investigation of the Stability Mechanisms of Eight-Atom Binary Metal Clusters Using DFT Calculations and k-means Clustering Algorithm

Here, we report density functional theory calculations combined with the k-means clustering algorithm and the Spearman rank correlation analysis to investigate the stability mechanisms of eight-atom binary metal AB clusters, where A and B are Fe, Co, Ni, Cu, Ga, Al, and Zn (7 unary and 21 binary clusters). Based on the excess energy analysis, the six most stable binary clusters are NiAl, NiGa, CoAl, FeNi, NiZn, and FeAl, and except for FeNi, their highest energetic stabilities can be explained by the hybridization of the d- and sp-states, which is maximized at the 50% composition, i.e., A₄B₄. Based on the Spearman correlation analysis, the energetic stability of the binary clusters increases with an increase in the highest occupied molecule orbital-lowest unoccupied molecular orbital (HOMO-LUMO) energy separation, which can be considered as a global descriptor. Furthermore, reducing the total magnetic moment values increases the stability for binary clusters without the Fe, Co, and Ni species, while the binary FeB, CoB, and NiB clusters increase their energetic stability with a decrease in the cluster radius, respectively, i.e., an energetic preference for compact structures.

Stability Changes in Iridium Nanoclusters via Monoxide Adsorption: A DFT Study within the van der Waals Corrections

Small iridium nanoclusters are prominent subnanometric systems for catalysis-related applications, mainly because of a large surface-to-volume ratio, noncoalescence feature, and tunable properties, which are completely influenced by the number of atoms, geometry, and molecular interaction with the chemical environment. Herein, we investigate the interaction between Ir_n nanoclusters (n = 2-7) and polluting molecules, CO, NO, and SO, using van der Waals D3 corrected density functional theory calculations. Starting from a representative structural set, we determine the growth pattern of the lowest energy unprotected Ir_n nanoclusters, which is based on open structural motifs, and from the adsorption of a XO (X = C, N, and S) molecule, the preferred high-symmetric adsorption sites were determined, dominated by the onefold top site. For protected systems, 4XO/Ir₄ and 6XO/Ir₆, we found a reduction in the total magnetic moment, while the equilibrium bonds of the nanoclusters expanded (contracted) due to mCO and mNO (mSO) adsorption, with exceptions for systems with large structural distortions (4SO/Ir₄ and 6NO/Ir₆). Meanwhile, the C-O and N-O (S-O) bond strength decreases (increases) following an increase (decrease) in the C-O and N-O (S-O) distances upon adsorption. We show, through energetic analysis, that for the different chemical environments, relative stability changes occur from the most stable unprotected nanoclusters, planar square (Ir₄), and prism (Ir₆) to higher energy isomers. The change in the stability order between the two competing protected systems is feasible if the balance between the interaction energy (additive term) and distortion energies (nonadditive terms) compensates for the relative total energies of the unprotected configurations. For all systems, the interaction energy is the main reason responsible for stability alterations, except for 4SO/Ir₄, where the main contribution is from a small penalty due to Ir₄ distortions upon adsorption, and for 4NO/Ir₄, where the energetic effects from the adsorption do not overcome the difference between the binding energies of the unprotected nanoclusters. Finally, from energy decomposition and Hirshfeld charge analysis, we find a predominant covalent nature of the physical contributions in mOX···Ir_n interactions with a cationic core (Ir_n) and an anionic shell (XO coverage).

Structure, Energetics, and Thermal Behavior of Bimetallic Re-Pt Clusters

Bimetallic Re-Pt is a widely used catalyst in petroleum reforming to obtain high-octane gasoline, but experimental and theoretical information of such systems at the subnanometer scale-namely, as cluster aggregates-is currently lacking. Thus, in this work, we performed a density functional theory-based global optimization study to determine the physicochemical properties of the most stable Re-Pt gas-phase clusters up to six atoms for all compositions. Our results indicate that in these putative global minima (GM) geometries, Re atoms tend to aggregate, while most Pt atoms remain separated from each other. This is even observed in Pt-rich clusters-an indication of the strength of the Re-Re and Re-Pt bonds over pure Pt-Pt ones-due to a strong, directional hybridization of the Re half-filled 5d and the nearly full Pt 5d states. We observe that doping monometallic Pt clusters even with a single Re atom increases their binding energy values and widens the bimetallic cluster highest occupied molecular orbital-lowest unoccupied molecular orbital gap. As catalysis occurs at elevated temperatures, we explore the concept of cluster fluxionality for Re-Pt minima in terms of the calculated isomer occupation probability, P(T). This allows us to quantify the abundance of GM and low-energy isomer configurations as a function of temperature. This is done at size 5 atoms due to the wide isomer observed variety. Our calculations indicate that for pure Re₅, the P(T) of the GM configuration substantially decreases after 750 K. Especially, for Re₄Pt₁, the GM is the dominant structure up to nearly 700 K when the second-energy isomer becomes the stable one. Although no ordering changes are seen for Re₃Pt₂, Re₂Pt₃, and Re₁Pt₄, we do observe a structural transition-between the GM and the second isomer-for pure Pt₅ above 1000 K. We expect this type of combined first-principles analysis to add to the overall, continuous understanding of the stability and energetics of ultrafine and highly-dispersed Re-Pt petroleum-reforming catalysts and the scarce available information on this particular bimetallic system.

Energy Decomposition to Access the Stability Changes Induced by CO Adsorption on Transition-Metal 13-Atom Clusters

Our atomistic understanding of the physical-chemical parameters that drives the changes in the relative stability of clusters induced by adsorbed molecules is far from satisfactory. In this work, we employed density functional theory calculations to address this problem using CO adsorption on 13-atom transition-metal clusters, TM₁₃, namely, nCO/TM₁₃, where TM = Ru, Rh, Pd, and Ag, and n = 1-6. Unexpectedly, changes in the relative stability take place for all systems at a lower coverage, namely, at n = 3 (Ru₁₃), 4 (Rh₁₃, Ag₁₃), and 2 (Pd₁₃). To address the effects that lead to changes in the stability, we proposed an energy decomposition scheme for the binding energy of the nCO/TM₁₃ systems, which yields that the change in relative stability is dominated by the interaction energy and cluster distortion energy upon adsorption, where the interaction energy is higher for high-energy unprotected clusters. Furthermore, we characterized all adsorption parameters, which helps us to complement our atomistic understanding.

Ab initio investigation of the role of the d-states occupation on the adsorption properties of H2, CO, CH4 and CH3OH on the Fe13, Co13, Ni13 and Cu13 clusters

Here, we report a theoretical investigation, based on density functional theory calculations, into the role of the occupation d-states on the adsorption properties of CH₄, CO, H₂ and CH₃OH on 3d 13-atom transition-metal (TM₁₃) clusters (TM = Fe, Co, Ni, Cu). Except for Cu₁₃, a gradual increase in the occupation of the d-states, i.e., from Fe₁₃ to Ni₁₃, increases the magnitude of the adsorption energy almost linearly for the H₂/TM₁₃ and CO/TM₁₃ systems, which can be explained by the enhancement of the sp-d hybridization due to the shift of the d-states towards the highest occupied molecular orbital (HOMO). For Cu₁₃, the d-states are located well below the HOMO, which reduces the sp-d hybridization, and hence, a smaller adsorption energy is obtained. However, this picture does not hold for CH₄/TM₁₃ and CH₃OH/TM₁₃, where the adsorption energy has nearly the same value for all TM₁₃ clusters, which can be explained by electrostatic effects such as local polarization of the molecules and nearby TM atoms, and hence, the basic features of physisorption systems. Based on the electron density difference, the polarization effects are slightly larger for systems with empty d-states.

Ab initio screening of Pt-based transition-metal nanoalloys using descriptors derived from the adsorption and activation of CO2

In this study, we report an ab initio screening, based on density functional theory calculations, of Pt-based transition-metal nanoalloys using physicochemical descriptors derived from the adsorption and activation of CO2 on 55-atom nanoclusters, namely, PtnTM55-n, with n = 0, 13, 42, 55, TM = Fe, Co, Ni, Cu, Ru, Rh, Pd, Ag, Os, Ir, Au. From the adsorption on the unary and binary nanoclusters, at the chemisorption regime (bent CO2), we identified a linear correlation between the interaction energy and charge transfer from the nanoclusters towards CO2 and the bent CO2 angle; moreover, the interaction energy is enhanced for larger values of the molecular charge and angle. The alloying of Cu55, Ag55, and Au55 with Pt provides a path to change the CO2 adsorption from physisorption (linear, non-activated) to chemisorption (enhanced interaction energies, bent, activated), while the strong interaction energy of CO2 with Os55, Ru55, and Fe55 can be decreased by alloying with Pt using different structural configurations, i.e., the trends are similar for core-shell and segregated structures. Thus, based on our results and analyses, we can select different combinations of PtnTM55-n nanoalloys to yield the desired interaction strength and magnitude of the charge transfer towards the activated anionic CO2, which can help in the design of nanocatalysts for CO2 activation or different chemical reactions in which charge transfer plays a crucial role.

Correlation-Based Framework for Extraction of Insights from Quantum Chemistry Databases: Applications for Nanoclusters

The amount of quantum chemistry (QC) data is increasing year by year due to the continuous increase of computational power and development of new algorithms. However, in most cases, our atom-level knowledge of molecular systems has been obtained by manual data analyses based on selected descriptors. In this work, we introduce a data mining framework to accelerate the extraction of insights from QC datasets, which starts with a featurization process that converts atomic features into molecular properties (AtoMF). Then, it employs correlation coefficients (Pearson, Spearman, and Kendall) to investigate the AtoMF features relationship with a target property. We applied our framework to investigate three nanocluster systems, namely, Pt_nTM_55-n, Ce_nZr_15-nO₃₀, and (CH_n + mH)/TM₁₃. We found several interesting and consistent insights using Spearman and Kendall correlation coefficients, indicating that they are suitable for our approach; however, our results indicate that the Pearson coefficient is very sensitive to outliers and should not be used. Moreover, we highlight problems that can occur during this analysis and discuss how to handle them. Finally, we make available a new Python package that implements the proposed QC data mining framework, which can be used as is or modified to include new features.

Systematic cluster growth: a structure search method for transition metal clusters

The systematic cluster growth (SCG) method is a biased structure search strategy based on a seeding process for investigating the structural evolution and growth pattern of transition metal clusters.

Computational Methods in Heterogeneous Catalysis

The unprecedented ability of computations to probe atomic-level details of catalytic systems holds immense promise for the fundamentals-based bottom-up design of novel heterogeneous catalysts, which are at the heart of the chemical and energy sectors of industry. Here, we critically analyze recent advances in computational heterogeneous catalysis. First, we will survey the progress in electronic structure methods and atomistic catalyst models employed, which have enabled the catalysis community to build increasingly intricate, realistic, and accurate models of the active sites of supported transition-metal catalysts. We then review developments in microkinetic modeling, specifically mean-field microkinetic models and kinetic Monte Carlo simulations, which bridge the gap between nanoscale computational insights and macroscale experimental kinetics data with increasing fidelity. We finally review the advancements in theoretical methods for accelerating catalyst design and discovery. Throughout the review, we provide ample examples of applications, discuss remaining challenges, and provide our outlook for the near future.

Structural, electronic, and magnetic properties of Ni nanoparticles supported on the TiC(001) surface

Metals supported on transition metal carbides are known to exhibit good catalytic activity and selectivity, which is interpreted in terms of electron polarization induced by the support. In the present work we go one step further and investigate the effect that a titanium carbide (TiC) support has on the structural, electronic, and magnetic properties of a series of Ni nanoparticles of increasing size exhibiting a two- or three-dimensional morphology. The obtained results show that three-dimensional nanoparticles are more stable and easier to form than their homologous two-dimensional counterparts. Also, comparison to previous results indicates that, when used as the support, transition metal carbides have a marked different chemical activity with respect to oxides. The analysis of the magnetic moments of the supported nanoparticles evidences a considerable quenching of the magnetic moment that affects mainly the Ni atoms in close contact with the TiC substrate indicating that these atoms are likely to be responsible for the catalytic activity reported for these systems. The analysis of the electronic structure reveals the existence of chemical interactions between the Ni nanoparticles and the TiC support, even if the net charge transfer between both systems is negligible.

Ab initio investigation of quantum size effects on the adsorption of CO2, CO, H2O, and H2 on transition-metal particles

Adsorption is a crucial preliminary step for the conversion of CO2 into higher-value chemicals, nonetheless, the atomistic understanding of how substrate particle size affects this step is still incomplete. In this study, we employed density functional theory to investigate the effects of particle size on the adsorption of model molecules involved in the CO2 transformations (CO2, CO, H2O and H2) on Con, Nin and Cun particles with different sizes (n = 13, 55, 147) and on the respective close-packed surfaces. We found significant size-dependence of the adsorption properties for physisorbed (linear) and chemisorbed (bent) CO2 on the substrates and distinct (symmetric or asymmetric) stretching of the C-O bonds, which can play a crucial role to understand the CO2 dissociation pathways. For CO and H2, some properties showed small oscillations, due to size effects that induced alternation of the adsorption site preference for different particle sizes; for H2O, the adsorption properties were almost independent of particle size. The presence of low-coordinated adsorption sites resulted in a trend for stronger adsorption and greater charge transfer for smaller clusters. Fixing the size-independent factors (e.g., type of metal), our results show that CO2 adsorption on transition-metal clusters is significantly affected by particle size, suggesting that substrate particle size could be a key factor to understand and control the catalytic transformations of CO2.