Quantitative Description of Metal Center Organization and Interactions in Single-Atom Catalysts.

Ultra-high-density single-atom catalysts (UHD-SACs) present unique opportunities for harnessing cooperative effects between neighboring metal centers. However, the lack of tools to establish correlations between the density, types, and arrangements of isolated metal atoms and the support surface properties hinders efforts to engineer advanced material architectures. Here, this work precisely describes the metal center organization in various mono- and multimetallic UHD-SACs based on nitrogen-doped carbon (NC) supports by coupling transmission electron microscopy with tailored machine-learning methods (released as a user-friendly web app) and density functional theory simulations. This approach quantifies the non-negligible presence of multimers with increasing atom density, characterizes the size and shape of these low-nuclearity clusters, and identifies surface atom density criteria to ensure isolation. Further, it provides previously inaccessible experimental insights into coordination site arrangements in the NC host, uncovering a repulsive interaction that influences the disordered distribution of metal centers in UHD-SACs. This observation holds in multimetallic systems, where chemically-specific analysis quantifies the degree of intermixing. These fundamental insights into the materials chemistry of single-atom catalysts are crucial for designing catalytic systems with superior reactivity.

Alloying as a Strategy to Boost the Stability of Copper Nanocatalysts during the Electrochemical CO2 Reduction Reaction.

Copper nanocatalysts are among the most promising candidates to drive the electrochemical CO2 reduction reaction (CO2RR). However, the stability of such catalysts during operation is sub-optimal, and improving this aspect of catalyst behavior remains a challenge. Here, we synthesize well-defined and tunable CuGa nanoparticles (NPs) and demonstrate that alloying Cu with Ga considerably improves the stability of the nanocatalysts. In particular, we discover that CuGa NPs containing 17 at. % Ga preserve most of their CO2RR activity for at least 20 h while Cu NPs of the same size reconstruct and lose their CO2RR activity within 2 h. Various characterization techniques, including X-ray photoelectron spectroscopy and operando X-ray absorption spectroscopy, suggest that the addition of Ga suppresses Cu oxidation at open-circuit potential (ocp) and induces significant electronic interactions between Ga and Cu. Thus, we explain the observed stabilization of the Cu by Ga as a result of the higher oxophilicity and lower electronegativity of Ga, which reduce the propensity of Cu to oxidize at ocp and enhance the bond strength in the alloyed nanocatalysts. In addition to addressing one of the major challenges in CO2RR, this study proposes a strategy to generate NPs that are stable under a reducing reaction environment.

What do we talk about, when we talk about single-crystal termination-dependent selectivity of Cu electrocatalysts for CO2 reduction? A data-driven retrospective.

We mine from the literature experimental data on the CO2 electrochemical reduction selectivity of Cu single crystal surfaces. We then probe the accuracy of a machine learning model trained to predict faradaic efficiencies for 11 CO2 reduction reaction products, as a function of the applied voltage at which the reaction takes place, and the relative amounts of non equivalent surface sites, distinguished according to their nominal coordination. A satisfactory model accuracy is found only when discriminating data according to their provenance. On one hand, this result points at a qualitative agreement across reported experimental CO2 reduction reactions trends for single-crystal surfaces with well-defined terminations. On the other, this finding hints at the presence of differences in nominally identical catalysts and/or CO2 reduction reaction measurements, which result in quantitative disagreement between experiments.

Structural characterisation of nanoalloys for (photo)catalytic applications with the Sapphire library.

A non-trivial interplay rules the relationship between the structure and the chemophysical properties of a nanoparticle. In this context, characterization experiments, molecular dynamics simulations and electronic structure calculations may allow the variables that determine a given property to be pinpointed. Conversely, a rigorous computational characterization of the geometry and chemical ordering of metallic nanoparticles and nanoalloys enables discrimination of which descriptors could be linked with their stability and performance. To this end, we introduce a modular and open-source library, Sapphire, which may classify the structural characteristics of a given nanoparticle through several structural analysis techniques and order parameters. A special focus is geared towards using geometrical descriptors to make predictions on a given nanoparticle's catalytic activity.

Accelerating the theoretical study of Li-polysulfide adsorption on single-atom catalysts via machine learning approaches.

Li-S batteries are a promising alternative to Li-ion batteries, offering large energy storage capacity and wide operating temperature range. However, their performance is heavily affected by the Li-polysulfide (LiPS) shuttling. Computational screening of LiPS adsorption on single-atom catalyst (SAC) substrates is of great aid to the design of Li-S batteries which are robust against the LiPS shuttling from the cathode to the anode and the electrolyte. To facilitate this process, we develop a machine learning (ML) protocol to accelerate the systematic mapping of dominant local energy minima found with calculations based on the density functional theory (DFT), and, in turn, fast screening of LiPS adsorption properties on SACs. We first validate the approach by probing the potential energy surface for LiPS adsorbed on graphene decorated with a Fe-N4-C SAC. We identify minima whose binding energies are better or on par with the one previously reported in the literature. We then move to analyze the adsorption trends on Zn-N4-C SAC and observe similar adsorption strength and behavior with the Fe-N4-C SAC, highlighting the good predictive power of our protocol. Our approach offers a comprehensive and computationally efficient alternative to conventional approaches studying LiPS adsorption.

Colloidal-ALD-Grown Hybrid Shells Nucleate via a Ligand-Precursor Complex.

Colloidal atomic layer deposition (c-ALD) enables the growth of hybrid organic-inorganic oxide shells with tunable thickness at the nanometer scale around ligand-functionalized inorganic nanoparticles (NPs). This recently developed method has demonstrated improved stability of NPs and of their dispersions, a key requirement for their application. Nevertheless, the mechanism by which the inorganic shells form is still unknown, as is the nature of multiple complex interfaces between the NPs, the organic ligands functionalizing the surface, and the shell. Here, we demonstrate that carboxylate ligands are the key element that enables the synthesis of these core-shell structures. Dynamic nuclear polarization surface-enhanced nuclear magnetic resonance spectroscopy (DNP SENS) in combination with density functional theory (DFT) structure calculations shows that the addition of the aluminum organometallic precursor forms a ligand-precursor complex that interacts with the NP surface. This ligand-precursor complex is the first step for the nucleation of the shell and enables its further growth.

Shaping Copper Nanocatalysts to Steer Selectivity in the Electrochemical CO2 Reduction Reaction.

The carbon-neutral production of fuels and chemical feedstocks is one of the grand challenges for our society to solve. The electrochemical conversion of CO2 is emerging as a promising technology contributing to this goal. Despite the huge amount of progress made over the past decade, selectivity still remains a challenge. This Account presents an overview of recent progress in the design of selective catalysts by exploiting the structural sensitivity of the electrochemical CO2 reduction reaction (CO2RR). In particular, it shows that the accurate and precise control of the shape and size of Cu nanocatalysts is instrumental in understanding and in discovering the structure-selectivity relationships governing the reduction of CO2 to valuable hydrocarbons, such as methane and ethylene. It further illustrates the use of faceted Cu nanocatalysts to interrogate catalytic pathways and to increase selectivity toward oxygenates, such as ethanol, in the framework of tandem schemes. The last part of the Account highlights the role of well-defined nanocatalysts in identifying reconstruction mechanisms which might occur during operation. An outlook for the emerging paradigms which will empower the design of novel catalysts for CO2RR concludes the Account.

Elucidating the structure-dependent selectivity of CuZn towards methane and ethanol in CO2 electroreduction using tailored Cu/ZnO precatalysts.

Understanding the catalyst compositional and structural features that control selectivity is of uttermost importance to target desired products in chemical reactions. In this joint experimental-computational work, we leverage tailored Cu/ZnO precatalysts as a material platform to identify the intrinsic features of methane-producing and ethanol-producing CuZn catalysts in the electrochemical CO2 reduction reaction (CO2RR). Specifically, we find that Cu@ZnO nanocrystals, where a central Cu domain is decorated with ZnO domains, and ZnO@Cu nanocrystals, where a central ZnO domain is decorated with Cu domains, evolve into Cu@CuZn core@shell catalysts that are selective for methane (∼52%) and ethanol (∼39%), respectively. Operando X-ray absorption spectroscopy and various microscopy methods evidence that a higher degree of surface alloying along with a higher concentration of metallic Zn improve the ethanol selectivity. Density functional theory explains that the combination of electronic and tandem effects accounts for such selectivity. These findings mark a step ahead towards understanding structure-property relationships in bimetallic catalysts for the CO2RR and their rational tuning to increase selectivity towards target products, especially alcohols.

Data-driven simulation and characterisation of gold nanoparticle melting.

The simulation and analysis of the thermal stability of nanoparticles, a stepping stone towards their application in technological devices, require fast and accurate force fields, in conjunction with effective characterisation methods. In this work, we develop efficient, transferable, and interpretable machine learning force fields for gold nanoparticles based on data gathered from Density Functional Theory calculations. We use them to investigate the thermodynamic stability of gold nanoparticles of different sizes (1 to 6 nm), containing up to 6266 atoms, concerning a solid-liquid phase change through molecular dynamics simulations. We predict nanoparticle melting temperatures in good agreement with available experimental data. Furthermore, we characterize the solid-liquid phase change mechanism employing an unsupervised learning scheme to categorize local atomic environments. We thus provide a data-driven definition of liquid atomic arrangements in the inner and surface regions of a nanoparticle and employ it to show that melting initiates at the outer layers.

Compact atomic descriptors enable accurate predictions via linear models.

We probe the accuracy of linear ridge regression employing a three-body local density representation derived from the atomic cluster expansion. We benchmark the accuracy of this framework in the prediction of formation energies and atomic forces in molecules and solids. We find that such a simple regression framework performs on par with state-of-the-art machine learning methods which are, in most cases, more complex and more computationally demanding. Subsequently, we look for ways to sparsify the descriptor and further improve the computational efficiency of the method. To this aim, we use both principal component analysis and least absolute shrinkage operator regression for energy fitting on six single-element datasets. Both methods highlight the possibility of constructing a descriptor that is four times smaller than the original with a similar or even improved accuracy. Furthermore, we find that the reduced descriptors share a sizable fraction of their features across the six independent datasets, hinting at the possibility of designing material-agnostic, optimally compressed, and accurate descriptors.

Born to be different: the formation process of Cu nanoparticles tunes the size trend of the activity for CO2 to CH4 conversion.

We investigate the impact of the formation process of Cu nanoparticles on the distribution of adsorption sites and hence on their activity. Using molecular dynamics, we model formation pathways characteristic of physical synthesis routes as the annealing of a liquid droplet, the growth proceeding via the addition of single atoms, and the coalescence of individual nanoparticles. Each formation process leads to different and characteristic size-dependent distributions of their adsorption sites, catalogued and monitored on-the-fly by means of a suitable geometrical descriptor. Annealed or coalesced nanoparticles present a rather homogeneous distribution in the kind and relative abundance of non-equivalent adsorption sites. Atom-by-atom grown nanoparticles, instead, exhibit a more marked occurrence of adsorption sites corresponding to adatoms and small islands on (111) and (100) facets. Regardless of the formation process, highly coordinated sites are more likely in larger nanoparticles, while the abundance of low-coordination sites depends on the formation process and on the nanoparticle size. Furthermore, we show how each characteristic distribution of adsorption sites reflects in different size trends for the Cu-nanoparticle activity, taking as an example the electro-reduction of CO2 into CH4. To this end, we employ a multi-scale method and observe that the faceted but highly defected structures obtained during the atom-by-atom growth become more and more active with increasing size, with a mild dependence on the original seed. In contrast, the activity of Cu-nanoparticles obtained by annealing decreases with their size, while coalesced nanoparticles' activity shows a non-monotonic behaviour.

Uncertainty estimation for molecular dynamics and sampling.

Machine-learning models have emerged as a very effective strategy to sidestep time-consuming electronic-structure calculations, enabling accurate simulations of greater size, time scale, and complexity. Given the interpolative nature of these models, the reliability of predictions depends on the position in phase space, and it is crucial to obtain an estimate of the error that derives from the finite number of reference structures included during model training. When using a machine-learning potential to sample a finite-temperature ensemble, the uncertainty on individual configurations translates into an error on thermodynamic averages and leads to a loss of accuracy when the simulation enters a previously unexplored region. Here, we discuss how uncertainty quantification can be used, together with a baseline energy model, or a more robust but less accurate interatomic potential, to obtain more resilient simulations and to support active-learning strategies. Furthermore, we introduce an on-the-fly reweighing scheme that makes it possible to estimate the uncertainty in thermodynamic averages extracted from long trajectories. We present examples covering different types of structural and thermodynamic properties and systems as diverse as water and liquid gallium.

A universal signature in the melting of metallic nanoparticles.

Predicting when phase changes occur in nanoparticles is fundamental for designing the next generation of devices suitable for catalysis, biomedicine, optics, chemical sensing and electronic circuits. The estimate of the temperature at which metallic nanoparticles become liquid is, however, a challenge and a standard definition is still missing. We discover a universal feature in the distribution of the atomic-pair distances that distinguishes the melting transition of monometallic nanoparticles. We analyse the solid-liquid change of several late-transition metals nanoparticles, i.e. Ni, Cu, Pd, Ag, Au and Pt, through classical molecular dynamics. We consider various initial shapes from 146 to 976 atoms, corresponding to the 1.5-4.1 nm size range, placing the nanoparticles in either a vacuum or embedded in a homogeneous environment, simulated by an implicit force-field. Regardless of the material, its initial shape, size and environment, the second peak in the pair-distance distribution function, expected at the bulk lattice distance, disappears when the nanoparticle melts. As the pair-distance distribution is a measurable quantity, the proposed criterion holds for both numerical and experimental investigations. For a more straightforward calculus of the melting temperature, we demonstrate that the cross-entropy between a reference solid pair-distance distribution function and the one of nanoparticles at increasing temperatures present a quasi-first order transition at the phase-change temperature.

Simulating Solvation and Acidity in Complex Mixtures with First-Principles Accuracy: The Case of CH3SO3H and H2O2 in Phenol.

We present a generally applicable computational framework for the efficient and accurate characterization of molecular structural patterns and acid properties in an explicit solvent using H2O2 and CH3SO3H in phenol as an example. To address the challenges posed by the complexity of the problem, we resort to a set of data-driven methods and enhanced sampling algorithms. The synergistic application of these techniques makes the first-principle estimation of the chemical properties feasible without renouncing to the use of explicit solvation, involving extensive statistical sampling. Ensembles of neural network (NN) potentials are trained on a set of configurations carefully selected out of preliminary simulations performed at a low-cost density functional tight-binding (DFTB) level. The energy and forces of these configurations are then recomputed at the hybrid density functional theory (DFT) level and used to train the neural networks. The stability of the NN model is enhanced by using DFTB energetics as a baseline, but the efficiency of the direct NN (i.e., baseline-free) is exploited via a multiple-time-step integrator. The neural network potentials are combined with enhanced sampling techniques, such as replica exchange and metadynamics, and used to characterize the relevant protonated species and dominant noncovalent interactions in the mixture, also considering nuclear quantum effects.

Correlating Oxygen Reduction Reaction Activity and Structural Rearrangements in MgO-Supported Platinum Nanoparticles.

We develop a multi-scale approach towards the design of metallic nanoparticles with applications as catalysts in electrochemical reactions. The here discussed method exploits the relationship between nanoparticle architecture and electrochemical activity and is applied to study the catalytic properties of MgO(100)-supported Pt nanosystems undergoing solid-solid and solid-liquid transitions. We observe that a major increment in the activity is associated to the reconstruction of the interface layers, supporting the need for a full geometrical characterisation of such structures also when in-operando.

A genomic characterisation of monometallic nanoparticles.

Because size and shape can affect the chemo-physical properties of nanoparticles, we extend the use of geometrical descriptors to sequence a genome of monometallic nanoparticles. Selecting the generalised coordination number as a descriptor, the derived geometrical genome distinguishes, catalogues, and counts the variety of adsorption sites available on each isomer with a diameter up to 10 nm, therefore it depends on the nanoparticle size and shape. This procedure allows us to elucidate the effects of morphological diversity within a sample and those of thermally activated structural rearrangements among isomers on nanocatalyst activity. By screening the geometrical genome of archetypal shapes, we forecast Pt stellated twinned nanoparticles, elongated along their five-fold axis and with their shortest diameter of ∼2 nm, as optimal candidates for the electro-reduction of molecular oxygen at room temperature, in agreement with available experimental data.

Building machine learning force fields for nanoclusters.

We assess Gaussian process (GP) regression as a technique to model interatomic forces in metal nanoclusters by analyzing the performance of 2-body, 3-body, and many-body kernel functions on a set of 19-atom Ni cluster structures. We find that 2-body GP kernels fail to provide faithful force estimates, despite succeeding in bulk Ni systems. However, both 3- and many-body kernels predict forces within an ∼0.1 eV/Šaverage error even for small training datasets and achieve high accuracy even on out-of-sample, high temperature structures. While training and testing on the same structure always provide satisfactory accuracy, cross-testing on dissimilar structures leads to higher prediction errors, posing an extrapolation problem. This can be cured using heterogeneous training on databases that contain more than one structure, which results in a good trade-off between versatility and overall accuracy. Starting from a 3-body kernel trained this way, we build an efficient non-parametric 3-body force field that allows accurate prediction of structural properties at finite temperatures, following a newly developed scheme [A. Glielmo et al., Phys. Rev. B 95, 214302 (2017)]. We use this to assess the thermal stability of Ni19 nanoclusters at a fractional cost of full ab initio calculations.

Mapping the conformational free energy of aspartic acid in the gas phase and in aqueous solution.

The conformational free energy landscape of aspartic acid, a proteogenic amino acid involved in a wide variety of biological functions, was investigated as an example of the complexity that multiple rotatable bonds produce even in relatively simple molecules. To efficiently explore such a landscape, this molecule was studied in the neutral and zwitterionic forms, in the gas phase and in water solution, by means of molecular dynamics and the enhanced sampling method metadynamics with classical force-fields. Multi-dimensional free energy landscapes were reduced to bi-dimensional maps through the non-linear dimensionality reduction algorithm sketch-map to identify the energetically stable conformers and their interconnection paths. Quantum chemical calculations were then performed on the minimum free energy structures. Our procedure returned the low energy conformations observed experimentally in the gas phase with rotational spectroscopy [M. E. Sanz et al., Phys. Chem. Chem. Phys. 12, 3573 (2010)]. Moreover, it provided information on higher energy conformers not accessible to experiments and on the conformers in water. The comparison between different force-fields and quantum chemical data highlighted the importance of the underlying potential energy surface to accurately capture energy rankings. The combination of force-field based metadynamics, sketch-map analysis, and quantum chemical calculations was able to produce an exhaustive conformational exploration in a range of significant free energies that complements the experimental data. Similar protocols can be applied to larger peptides with complex conformational landscapes and would greatly benefit from the next generation of accurate force-fields.

The effect of chemical ordering and lattice mismatch on structural transitions in phase segregating nanoalloys.

We elucidate the effect of lattice mismatch and chemical ordering on structural transitions in bimetallic nanoalloys of ∼1.5 nm. We show that collective screw dislocation motions happen in small mismatch shell@core systems while strongly mismatched ones favour incomplete outer shell rearrangements. Cooperative transitions can also become hindered when the chemical ordering breaks the geometrical symmetry. Escaping from an unfavourable morphological basin occurs first via re-arrangements of the geometry and then changes towards a better chemical pattern. We observe that the chemical re-ordering mechanisms are independent of system composition and stoichiometry but hinge on the initial and final chemical arrangements.

Controlling Structural Transitions in AuAg Nanoparticles through Precise Compositional Design.

We present a study of the transitional pathways between high-symmetry structural motifs for AgAu nanoparticles, with a specific focus on controlling the energetic barriers through chemical design. We show that the barriers can be altered by careful control of the elemental composition and chemical arrangement, with core@shell and vertex-decorated arrangements being specifically influential on the barrier heights. We also highlight the complexity of the potential and free energy landscapes for systems where there are low-symmetry geometric motifs that are energetically competitive to the high-symmetry arrangements. In particular, we highlight that some core@shell arrangements preferentially transition through multistep restructuring of low-symmetry truncated octahedra and rosette-icosahedra, instead of via the more straightforward square-diamond transformations, due to lower energy barriers and competitive energetic minima. Our results have promising implications for the continuing efforts in bespoke nanoparticle design for catalytic and plasmonic applications.