Optimizing core-shell nanoparticle catalysts with a genetic algorithm

Inverse Design for Coating Parameters in Nano-Film Growth Based on Deep Learning Neural Network and Particle Swarm Optimization Algorithm

The NN (neural network)-PSO (particle swarm optimization) method is demonstrated to be able to inversely extract the coating parameters for the multilayer nano-films through a simulation case and two experimental cases to verify its accuracy and robustness. In the simulation case, the relative error (RE) between the average layer values and the original one was less than 3.45% for 50 inverse designs. In the experimental anti-reflection (AR) coating case, the mean thickness values of the inverse design results had a RE of around 5.05%, and in the Bragg reflector case, the RE was less than 1.03% for the repeated inverse simulations. The method can also be used to solve the single-solution problem of a tandem neural network in the inverse process.

Computational Discovery of Transition-metal Complexes: From High-throughput Screening to Machine Learning

Transition-metal complexes are attractive targets for the design of catalysts and functional materials. The behavior of the metal-organic bond, while very tunable for achieving target properties, is challenging to predict and necessitates searching a wide and complex space to identify needles in haystacks for target applications. This review will focus on the techniques that make high-throughput search of transition-metal chemical space feasible for the discovery of complexes with desirable properties. The review will cover the development, promise, and limitations of "traditional" computational chemistry (i.e., force field, semiempirical, and density functional theory methods) as it pertains to data generation for inorganic molecular discovery. The review will also discuss the opportunities and limitations in leveraging experimental data sources. We will focus on how advances in statistical modeling, artificial intelligence, multiobjective optimization, and automation accelerate discovery of lead compounds and design rules. The overall objective of this review is to showcase how bringing together advances from diverse areas of computational chemistry and computer science have enabled the rapid uncovering of structure-property relationships in transition-metal chemistry. We aim to highlight how unique considerations in motifs of metal-organic bonding (e.g., variable spin and oxidation state, and bonding strength/nature) set them and their discovery apart from more commonly considered organic molecules. We will also highlight how uncertainty and relative data scarcity in transition-metal chemistry motivate specific developments in machine learning representations, model training, and in computational chemistry. Finally, we will conclude with an outlook of areas of opportunity for the accelerated discovery of transition-metal complexes.

Photonic-dispersion neural networks for inverse scattering problems

Inferring the properties of a scattering objective by analyzing the optical far-field responses within the framework of inverse problems is of great practical significance. However, it still faces major challenges when the parameter range is growing and involves inevitable experimental noises. Here, we propose a solving strategy containing robust neural-networks-based algorithms and informative photonic dispersions to overcome such challenges for a sort of inverse scattering problem-reconstructing grating profiles. Using two typical neural networks, forward-mapping type and inverse-mapping type, we reconstruct grating profiles whose geometric features span hundreds of nanometers with nanometric sensitivity and several seconds of time consumption. A forward-mapping neural network with a parameters-to-point architecture especially stands out in generating analytical photonic dispersions accurately, featured by sharp Fano-shaped spectra. Meanwhile, to implement the strategy experimentally, a Fourier-optics-based angle-resolved imaging spectroscopy with an all-fixed light path is developed to measure the dispersions by a single shot, acquiring adequate information. Our forward-mapping algorithm can enable real-time comparisons between robust predictions and experimental data with actual noises, showing an excellent linear correlation (R2 > 0.982) with the measurements of atomic force microscopy. Our work provides a new strategy for reconstructing grating profiles in inverse scattering problems.

Data Science in Chemical Engineering: Applications to Molecular Science

Chemical engineering is being rapidly transformed by the tools of data science. On the horizon, artificial intelligence (AI) applications will impact a huge swath of our work, ranging from the discovery and design of new molecules to operations and manufacturing and many areas in between. Early adoption of data science, machine learning, and early examples of AI in chemical engineering has been rich with examples of molecular data science-the application tools for molecular discovery and property optimization at the atomic scale. We summarize key advances in this nascent subfield while introducing molecular data science for a broad chemical engineering readership. We introduce the field through the concept of a molecular data science life cycle and discuss relevant aspects of five distinct phases of this process: creation of curated data sets, molecular representations, data-driven property prediction, generation of new molecules, and feasibility and synthesizability considerations.

Finite-Temperature Structures of Supported Subnanometer Catalysts Inferred via Statistical Learning and Genetic Algorithm-Based Optimization

Single-atom catalysts (SACs) minimize noble metal utilization and can alter the activity and selectivity of supported metal nanoparticles. However, the morphology of active centers, including single atoms and subnanometer clusters of a few atoms, remains elusive due to experimental challenges. The computational cost to describe numerous cluster shapes and sizes makes direct first-principles calculations impractical. We present a computational framework to enable structure determination for single-atom and subnanometer cluster catalysts. As a case study, we obtained the low-energy structures of Pd_n (n = 1-21) clusters supported on CeO₂(111), which are critical components of automobile three-way catalysts. Trained on density functional theory data, a three-dimensional cluster expansion is established using statistical learning to describe the Hamiltonian and predict energies of supported Pd_n clusters of any structure. Low-energy stable and metastable structures are identified using a Metropolis Monte Carlo-based genetic algorithm in the canonical ensemble at 300 K. We observe that supported single atoms sinter to form bilayer clusters, and large cluster isomers share similarities in both shape and energy. The findings elucidate the significance of the support and microstructure on cluster stability. We discovered a simple surrogate structure-energy model, where the energy per atom scales with the square root of the average first coordination number, which can be used to estimate energies and compare the stability of clusters. Our framework, applicable to any metal/support system, fills an important methodological gap to predict the stability of supported metal catalysts in the subnanometer regime.

Progress in Computational and Machine-Learning Methods for Heterogeneous Small-Molecule Activation

The chemical conversion of small molecules such as H₂ , H₂ O, O₂ , N₂ , CO₂ , and CH₄ to energy and chemicals is critical for a sustainable energy future. However, the high chemical stability of these molecules poses grand challenges to the practical implementation of these processes. In this regard, computational approaches such as density functional theory, microkinetic modeling, data science, and machine learning have guided the rational design of catalysts by elucidating mechanistic insights, identifying active sites, and predicting catalytic activity. Here, the theory and methodologies for heterogeneous catalysis and their applications for small-molecule activation are reviewed. An overview of fundamental theory and key computational methods for designing catalysts, including the emerging data science techniques in particular, is given. Applications of these methods for finding efficient heterogeneous catalysts for the activation of the aforementioned small molecules are then surveyed. Finally, promising directions of the computational catalysis field for further outlooks are discussed, focusing on the challenges and opportunities for new methods.

Synthetic Biology: A Solution for Tackling Nanomaterial Challenges

Bioengineers have mastered practical techniques for tuning a biomaterial's properties with only limited information on the relationship between the material's structure and function. These techniques have been quintessential to engineering proteins, which are most often riddled with ill-defined structure-function relationships. In this Perspective, we review bioengineering approaches aimed at overcoming the elusive protein structure-function relation. We extend these principles to engineering synthetic nanomaterials, specifically applying the underlying theory to optical sensors based on single-stranded DNA-wrapped single-walled carbon nanotubes (ssDNA-SWCNTs). Bioengineering techniques such as directed evolution, computational design, and noncanonical synthesis are reviewed in the broader context of nanomaterials engineering. We further provide an order-of-magnitude analysis of empirical approaches that rely on random or guided searches for designing new nanomaterials. The underlying concepts presented in these approaches can be further extended to a broad range of engineering fields confronted with empirical design strategies, including catalysis, metal-organic frameworks (MOFs), pharmaceutical dosing, and optimization algorithms.

Predicting metal-metal interactions. II. Accelerating generalized schemes through physical insights

Operando-computational frameworks that integrate descriptors for catalyst stability within catalyst screening paradigms enable predictions of rates and selectivity on chemically faithful representations of nanoparticles under reaction conditions. These catalyst stability descriptors can be efficiently predicted by density functional theory (DFT)-based models. The alloy stability model, for example, predicts the stability of metal atoms in nanoparticles with site-by-site resolution. Herein, we use physical insights to present accelerated approaches of parameterizing this recently introduced alloy-stability model. These accelerated approaches meld quadratic functions for the energy of metal atoms in terms of the coordination number with linear correlations between model parameters and the cohesive energies of bulk metals. By interpolating across both the coordination number and chemical space, these accelerated approaches shrink the training set size for 12 fcc p- and d-block metals from 204 to as few as 24 DFT calculated total energies without sacrificing the accuracy of our model. We validate the accelerated approaches by predicting adsorption energies of metal atoms on extended surfaces and 147 atom cuboctahedral nanoparticles with mean absolute errors of 0.10 eV and 0.24 eV, respectively. This efficiency boost will enable a rapid and exhaustive exploration of the vast material space of transition metal alloys for catalytic applications.

Deep Learning for the Inverse Design of Mid-Infrared Graphene Plasmons

We theoretically investigate the plasmonic properties of mid-infrared graphene-based metamaterials and apply deep learning of a neural network for the inverse design. These artificial structures have square periodic arrays of graphene plasmonic resonators deposited on dielectric thin films. Optical spectra vary significantly with changes in structural parameters. To validate our theoretical approach, we carry out finite difference time domain simulations and compare computational results with theoretical calculations. Quantitatively good agreements among theoretical predictions, simulations, and previous experiments allow us to employ this proposed theoretical model to generate reliable data for training and testing deep neural networks. By merging the pre-trained neural network with the inverse network, we implement calculations for inverse design of the graphene-based metameterials. We also discuss the limitation of the data-driven approach.

Computational screening of M/Cu core/shell nanoparticles and their applications for the electro-chemical reduction of CO2 and CO

To improve the catalytic activity of copper nanoparticles (Cu NPs) in the electro-chemical catalysis of the CO2 reduction reactions (CO2RRs), the formation and use of core/shell nanoparticles (CSNPs) with Cu as the shell composite may be an effective way. Using Cu79 NP as the representative, we performed computational screening and confirmed four Mx@Cu79-x CSNPs that can stably exist. Then, the catalytic performance of the screened CSNPs was tested through first-principles calculations. The free energy profiles indicate that Fe19@Cu60 is more desirable for CO2RR catalysis due to its high selectivity for CO rather than HCOOH at a low potential. Moreover, when it electro-catalyzes CO2 into CH4, the Fe19@Cu60 CSNP exhibits much lower limiting potential (-0.58 V) compared with pure Cu79 NP (-0.86 V) or the Cu (211) surface (-0.70 V). Taking the cost into consideration, the Fe19@Cu60 CSNP is highly recommended as a promising electro-catalyst for CO2RRs. In addition, when CO is taken as the initial reactant to be reduced, all the screened CSNPs exhibit lower limiting potentials than Cu79 NP. From the view of material design, the significant weakening of CO binding originating from the change in the d-band center could be the reason why the formation of a core/shell structure will enhance the catalytic performance of Cu NPs in CO reduction.

Search for Catalysts by Inverse Design: Artificial Intelligence, Mountain Climbers, and Alchemists

In silico catalyst design is a grand challenge of chemistry. Traditional computational approaches have been limited by the need to compute properties for an intractably large number of possible catalysts. Recently, inverse design methods have emerged, starting from a desired property and optimizing a corresponding chemical structure. Techniques used for exploring chemical space include gradient-based optimization, alchemical transformations, and machine learning. Though the application of these methods to catalysis is in its early stages, further development will allow for robust computational catalyst design. This review provides an overview of the evolution of inverse design approaches and their relevance to catalysis. The strengths and limitations of existing techniques are highlighted, and suggestions for future research are provided.

A coordination-based model for transition metal alloy nanoparticles

We present a simple approach for predicting the relative energies of bimetallic nanoparticles spanning a wide-ranging combinatorial space, using only the identity and nearest-neighbor coordination number of individual metal atoms as independent parameters. By performing straightforward metal atom adsorption calculations on surface slab models, we parameterize expressions for the energy of metal atoms as a function of their coordination number in 21 bimetallic pairings of fcc metals. We rigorously establish the transferability of our model by predicting relative energies of a series of nanoparticles across a large number of morphologies, sizes, atomic compositions, and arrangements. The model is particularly accurate in predicting atomic rearrangements at or near the metal surfaces, which is essential for its potential applications when studying segregation phenomena or dynamic processes in heterogeneous catalysis. By rapidly forecasting site stabilities with atomic specificity across generic structural and compositional features, our model is able to reverse engineer thermodynamically feasible motifs of active sites in bimetallic nanoparticles through robust property ⇔ structure relations.

Nanophotonic particle simulation and inverse design using artificial neural networks

We propose a method to use artificial neural networks to approximate light scattering by multilayer nanoparticles. We find that the network needs to be trained on only a small sampling of the data to approximate the simulation to high precision. Once the neural network is trained, it can simulate such optical processes orders of magnitude faster than conventional simulations. Furthermore, the trained neural network can be used to solve nanophotonic inverse design problems by using back propagation, where the gradient is analytical, not numerical.

(Multi-)Metallic Cluster Growth

This review article provides a survey of contemporary investigations on main group metal cluster formation, addressing homo- and heterometallic clusters (including small numbers of transition metal atoms), with or without an external ligand shell, thereby excluding clusters with non-metal atoms as bridging ligands. Most of the studies reflected herein represent insights into the formation of intermediates from the starting material, or the final cluster formation from established intermediates. In rare cases, the entire process was suggested as a result of comprehensive, multi-method elucidations. The article is to be understood as a state-of-the-art report, as the subject matter is currently a rising field of research, which is still in its infancy, despite some early activities that date back to the 1980s. At the same time, the article intends to point toward both the importance and the feasibility of according studies, in order to encourage researchers to gain even more knowledge in this field. Only deep understanding of cluster formation will allow for design, and ultimately control, of their syntheses, with the long-term goal of their optimization and purposeful application in catalysis or novel material synthesis.

A Computational Framework for Material Design

A computational framework is proposed that enables the integration of experimental and computational data, a variety of user-selected models, and a computer algorithm to direct a design optimization. To demonstrate this framework, a sample design of a ternary Ni-Al-Cr alloy with a high work-to-necking ratio is presented. This design example illustrates how CALPHAD phase-based, composition and temperature-dependent phase equilibria calculations and precipitation models are coupled with models for elastic and plastic deformation to calculate the stress-strain curves. A genetic algorithm then directs the search within a specific set of composition and processing constraints for the ideal composition and processing profile to optimize the mechanical properties. The initial demonstration of the framework provides a potential solution to initiate the material design process in a large space of composition and processing conditions. This framework can also be used in similar material systems or adapted for other material classes.

Understanding the atomic-level process of CO-adsorption-driven surface segregation of Pd in (AuPd)147 bimetallic nanoparticles

When the elements that compose bimetallic catalysts interact asymmetrically with reaction feedstock, the surface concentration of the bimetallic catalysts and the morphology of the reaction center evolve dynamically as a function of environmental factors such as the partial pressure of the triggering molecule. Relevant experimental and theoretical findings of the dynamic structural evolution of bimetallic catalysts under the reaction conditions are emerging, thus enabling the design of more consistent, reliable, and efficient bimetallic catalysts. In an initial attempt to provide an atomic-level understanding of the adsorption-induced structural evolution of bimetallic nanoparticles (NPs) under CO oxidation conditions, we used density functional theory to study the details of CO-adsorption-driven Pd surface segregation in (AuPd)₁₄₇ bimetallic NPs. The strong CO affinity of Pd provides a driving force for Pd surface segregation. We found that the vertex site of the NP becomes a gateway for the initial Pd-Au swapping and the subsequent formation of an internal vacancy. This self-generated internal vacancy easily diffuses inside the NP and activates Pd-Au swapping pathways in the (100) NP facet. Our results reveal how the surface and internal concentrations of bimetallic NPs respond immediately to changes in the reaction conditions. Our findings should aid in the rational design of highly active and versatile bimetallic catalysts by considering the environmental factors that systematically affect the structure of bimetallic catalysts under the reaction conditions.

Core@shell, Au@TiOx nanoparticles by gas phase synthesis

Herein, gas phase synthesis and characterization of multifunctional core@shell, Au@TiOx nanoparticles have been reported. The nanoparticles were produced via a one-step process using a multiple-ion cluster source under a controlled environment that guaranteed the purity of the nanoparticles. The growth of the Au cores (6 nm diameter) is stopped when they pass through the Ti plasma where they are covered by an ultra-thin (1 nm thick) and homogeneous titanium shell that is oxidized in-flight before the soft-landing of the nanoparticles. The Au cores were found to be highly crystalline with icosahedral (44%) and decahedral (66%) structures, whereas the shell, mainly composed of TiO2 (79%), was not ordered. The highly electrical insulating behaviour of the titanium oxide shell was confirmed by the charging effect produced during X-ray photoemission spectroscopy.

Discovery and Optimization of Materials Using Evolutionary Approaches

Materials science is undergoing a revolution, generating valuable new materials such as flexible solar panels, biomaterials and printable tissues, new catalysts, polymers, and porous materials with unprecedented properties. However, the number of potentially accessible materials is immense. Artificial evolutionary methods such as genetic algorithms, which explore large, complex search spaces very efficiently, can be applied to the identification and optimization of novel materials more rapidly than by physical experiments alone. Machine learning models can augment experimental measurements of materials fitness to accelerate identification of useful and novel materials in vast materials composition or property spaces. This review discusses the problems of large materials spaces, the types of evolutionary algorithms employed to identify or optimize materials, and how materials can be represented mathematically as genomes, describes fitness landscapes and mutation operators commonly employed in materials evolution, and provides a comprehensive summary of published research on the use of evolutionary methods to generate new catalysts, phosphors, and a range of other materials. The review identifies the potential for evolutionary methods to revolutionize a wide range of manufacturing, medical, and materials based industries.

A basin-hopping Monte Carlo investigation of the structural and energetic properties of 55- and 561-atom bimetallic nanoclusters: the examples of the ZrCu, ZrAl, and CuAl systems

We report a basin-hopping Monte Carlo investigation within the embedded-atom method of the structural and energetic properties of bimetallic ZrCu, ZrAl, and CuAl nanoclusters with 55 and 561 atoms. We found that unary Zr55, Zr561, Cu55, Cu561, Al55, and Al561 systems adopt the well known compact icosahedron (ICO) structure. The excess energy is negative for all systems and compositions, which indicates an energetic preference for the mixing of both chemical species. The ICO structure is preserved if a few atoms of the host system are replaced by different species, however, the composition limit in which the ICO structure is preserved depends on both the host and new chemical species. Using several structural analyses, three classes of structures, namely ideal ICO, nearly ICO, and distorted ICO structures, were identified. As the amounts of both chemical species change towards a more balanced composition, configurations far from the ICO structure arise and the dominant structures are nearly spherical, which indicates a strong minimization of the surface energy by decreasing the number of atoms with lower coordination on the surface. The average bond lengths follow Vegard's law almost exactly for ZrCu and ZrAl, however, this is not the case for CuAl. Furthermore, the radial distribution allowed us to identify the presence of an onion-like behavior in the surface of the 561-atom CuAl nanocluster with the Al atoms located in the outermost surface shell, which can be explained by the lower surface energies of the Al surfaces compared with the Cu surfaces. In ZrCu and ZrAl the radial distribution indicates a nearly homogeneous distribution for the chemical species, however, with a slightly higher concentration of Al atoms on the ZrAl surface, which can also be explained by the lower surface energy.

Understanding of multimetallic cluster growth

The elucidation of formation mechanisms is mandatory for understanding and planning of synthetic routes. For (bio-)organic and organometallic compounds, this has long been realized even for very complicated molecules, whereas the formation of ligand-free inorganic molecules has widely remained a black box to date. This is due to poor structural relationships between reactants and products and the lack of structurally related intermediates—due to the comparably high coordination flexibility of involved atoms. Here we report on investigations of the stepwise formation of multimetallic clusters, based on a series of crystal structures and complementary quantum-chemical studies of (Ge₂As₂)²⁻, (Ge₇As₂)²⁻, [Ta@Ge₆As₄]³⁻, [Ta@Ge₈As₄]³⁻ and [Ta@Ge₈As₆]³⁻. The study makes use of efficient quantum-chemical tools, enabling the first detailed screening of the energy hypersurface along the formation of ligand-free inorganic species for a semi-quantitative picture. The results can be generalized for an entire family of multimetallic clusters.

Elucidation of formation mechanisms of inorganic cluster compounds is challenging due to the high coordination flexibility of the atoms involved. Here, the authors combine crystallographic and quantum-chemical studies to probe the energy hypersurface of a series of multimetallic clusters.

Ligand-field theory-based analysis of the adsorption properties of ruthenium nanoparticles

The experimental design of improved nanocatalysts is usually based on shape control and is surface-ligand dependent. First-principle calculations can guide their design, both in terms of activity and selectivity, provided that theoretical descriptors can be defined and used in a prescreening process. As a consequence of the Sabatier principle and of the Brønsted-Evans-Polanyi relationship, an important prerequisite before optimizing the catalytic properties of nanoparticles is the knowledge of the selective adsorption strengths of reactants at their surface. We report here adsorption energies of X (H, CH3) and L (PH3, CO) ligands at the surface of bare ruthenium nanoclusters Run (n = 55 and 147) calculated at the DFT level. Their dependence on the topology of the adsorption sites as well as on the size and shape of the nanoparticles (NPs) is rationalized with local descriptors derived from the so-called d-band center model. Defining the descriptors involves the determination of the energy of effective d atomic orbitals for each surface atom. Such a ligand field theory-like model is in close relation with frontier molecular orbital theory, a cornerstone of rational chemical synthesis. The descriptors are depicted as color maps which straightforwardly yield possible reactivity spots. The adsorption map of a large spherical hcp cluster (Ru288) nicely confirms the remarkable activity of steps, the so-called B5 sites. The predictive character of this conceptual DFT approach should apply to other transition metal NPs and it could be a useful guide to the design of efficient nanocatalysts bearing sites with a specific activity.

Path Integral Computation of Quantum Free Energy Differences Due to Alchemical Transformations Involving Mass and Potential

Thermodynamic integration, perturbation theory, and λ-dynamics methods were applied to path integral molecular dynamics calculations to investigate free energy differences due to "alchemical" transformations. Several estimators were formulated to compute free energy differences in solvable model systems undergoing changes in mass and/or potential. Linear and nonlinear alchemical interpolations were used for the thermodynamic integration. We find improved convergence for the virial estimators, as well as for the thermodynamic integration over nonlinear interpolation paths. Numerical results for the perturbative treatment of changes in mass and electric field strength in model systems are presented. We used thermodynamic integration in ab initio path integral molecular dynamics to compute the quantum free energy difference of the isotope transformation in the Zundel cation. The performance of different free energy methods is discussed.