Discovering High Entropy Alloy Electrocatalysts in Vast Composition Spaces with Multiobjective Optimization.

High entropy alloys (HEAs) are a highly promising class of materials for electrocatalysis as their unique active site distributions break the scaling relations that limit the activity of conventional transition metal catalysts. Existing Bayesian optimization (BO)-based virtual screening approaches focus on catalytic activity as the sole objective and correspondingly tend to identify promising materials that are unlikely to be entropically stabilized. Here, we overcome this limitation with a multiobjective BO framework for HEAs that simultaneously targets activity, cost-effectiveness, and entropic stabilization. With diversity-guided batch selection further boosting its data efficiency, the framework readily identifies numerous promising candidates for the oxygen reduction reaction that strike the balance between all three objectives in hitherto unchartered HEA design spaces comprising up to 10 elements.

Implicit Solvation Methods for Catalysis at Electrified Interfaces.

Implicit solvation is an effective, highly coarse-grained approach in atomic-scale simulations to account for a surrounding liquid electrolyte on the level of a continuous polarizable medium. Originating in molecular chemistry with finite solutes, implicit solvation techniques are now increasingly used in the context of first-principles modeling of electrochemistry and electrocatalysis at extended (often metallic) electrodes. The prevalent ansatz to model the latter electrodes and the reactive surface chemistry at them through slabs in periodic boundary condition supercells brings its specific challenges. Foremost this concerns the difficulty of describing the entire double layer forming at the electrified solid-liquid interface (SLI) within supercell sizes tractable by commonly employed density functional theory (DFT). We review liquid solvation methodology from this specific application angle, highlighting in particular its use in the widespread ab initio thermodynamics approach to surface catalysis. Notably, implicit solvation can be employed to mimic a polarization of the electrode's electronic density under the applied potential and the concomitant capacitive charging of the entire double layer beyond the limitations of the employed DFT supercell. Most critical for continuing advances of this effective methodology for the SLI context is the lack of pertinent (experimental or high-level theoretical) reference data needed for parametrization.

Constant potential energetics of metallic and semiconducting electrodes: A benchmark study on 2D materials.

Grand-canonical (GC) constant-potential methods within an implicit solvent environment provide a general approach to compute the potential-dependent energetics at electrified solid-liquid interfaces with first-principles density-functional theory. Here, we use a mindfully chosen set of 27 isostructural 2D metal halides MX2 to analyze the variation of this energetics when the electronic structure changes from metallic to semiconducting and insulating state. Apart from expectable changes due to the opening up of the electronic bandgap, the calculations also show an increasing sensitivity to the numerical Brillouin zone integration and electronic smearing, which imposes computational burdens in practice. We rationalize these findings within the picture of the total interfacial capacitance arising from a series connection of the electrochemical double-layer capacitance and the so-called quantum capacitance resulting from the filling of electronic states inside the electrode. For metals, the electrochemical double-layer capacitance dominates at all potentials, and the entire potential drop takes place in the electrolyte. For semiconductors, the potential drop occurs instead fully or partially inside the electrode at potentials within or just outside the bandgap. For 2D semiconductors, the increased sensitivity to numerical parameters then results from the concomitantly increased contribution of the quantum capacitance that is harder to converge. Fortunately, this understanding motivates a simple extension of the CHE + DL approximation for metals, which provides the approximate GC energetics of 2D semiconductors using only quantities that can be obtained from computationally undemanding calculations at the point of zero charge and a generic double-layer capacitance.

Small basis set density functional theory method for cost-efficient, large-scale condensed matter simulations.

We present an efficient first-principles based method geared toward reliably predicting the structures of solid materials across the Periodic Table. To this end, we use a density functional theory baseline with a compact, near-minimal min+s basis set, yielding low computational costs and memory demands. Since the use of such a small basis set leads to systematic errors in chemical bond lengths, we develop a linear pairwise correction, available for elements Z = 1-86 (excluding the lanthanide series), parameterized for use with the Perdew-Burke-Ernzerhof exchange-correlation functional. We demonstrate the reliability of this corrected approach for equilibrium volumes across the Periodic Table and the transferability to differently coordinated environments and multi-elemental crystals. We examine relative energies, forces, and stresses in geometry optimizations and molecular dynamics simulations.

Correction: Photoelectron angular distributions as sensitive probes of surfactant layer structure at the liquid-vapor interface.

Correction for 'Photoelectron angular distributions as sensitive probes of surfactant layer structure at the liquid-vapor interface' by Rémi Dupuy et al., Phys. Chem. Chem. Phys., 2022, 24, 4796-4808, https://doi.org/10.1039/D1CP05621B.

Cavity formation at metal-water interfaces.

The free energy cost of forming a cavity in a solvent is a fundamental concept in rationalizing the solvation of molecules and ions. A detailed understanding of the factors governing cavity formation in bulk solutions has inter alia enabled the formulation of models that account for this contribution in coarse-grained implicit solvation methods. Here, we employ classical molecular dynamics simulations and multistate Bennett acceptance ratio free energy sampling to systematically study cavity formation at a wide range of metal-water interfaces. We demonstrate that the obtained size- and position-dependence of cavitation energies can be fully rationalized by a geometric Gibbs model, which considers that the creation of the metal-cavity interface necessarily involves the removal of interfacial solvent. This so-called competitive adsorption effect introduces a substrate dependence to the interfacial cavity formation energy that is missed in existing bulk cavitation models. Using expressions from scaled particle theory, this substrate dependence is quantitatively reproduced by the Gibbs model through simple linear relations with the adsorption energy of a single water molecule. Besides providing a better general understanding of interfacial solvation, this paves the way for the derivation and efficient parametrization of more accurate interface-aware implicit solvation models needed for reliable high-throughput calculations toward improved electrocatalysts.

q-pac: A Python package for machine learned charge equilibration models.

Many state-of-the art machine learning (ML) interatomic potentials are based on a local or semi-local (message-passing) representation of chemical environments. They, therefore, lack a description of long-range electrostatic interactions and non-local charge transfer. In this context, there has been much interest in developing ML-based charge equilibration models, which allow the rigorous calculation of long-range electrostatic interactions and the energetic response of molecules and materials to external fields. The recently reported kQEq method achieves this by predicting local atomic electronegativities using Kernel ML. This paper describes the q-pac Python package, which implements several algorithmic and methodological advances to kQEq and provides an extendable framework for the development of ML charge equilibration models.

A fuzzy classification framework to identify equivalent atoms in complex materials and molecules.

The nature of an atom in a bonded structure-such as in molecules, in nanoparticles, or in solids, at surfaces or interfaces-depends on its local atomic environment. In atomic-scale modeling and simulation, identifying groups of atoms with equivalent environments is a frequent task, to gain an understanding of the material function, to interpret experimental results, or to simply restrict demanding first-principles calculations. However, while routine, this task can often be challenging for complex molecules or non-ideal materials with breaks in symmetries or long-range order. To automatize this task, we here present a general machine-learning framework to identify groups of (nearly) equivalent atoms. The initial classification rests on the representation of the local atomic environment through a high-dimensional smooth overlap of atomic positions (SOAP) vector. Recognizing that not least thermal vibrations may lead to deviations from ideal positions, we then achieve a fuzzy classification by mean-shift clustering within a low-dimensional embedded representation of the SOAP points as obtained through multidimensional scaling. The performance of this classification framework is demonstrated for simple aromatic molecules and crystalline Pd surface examples.

Interpreting ultrafast electron transfer on surfaces with a converged first-principles Newns-Anderson chemisorption function.

We study the electronic coupling between an adsorbate and a metal surface by calculating tunneling matrix elements Had directly from first principles. For this, we employ a projection of the Kohn-Sham Hamiltonian upon a diabatic basis using a version of the popular projection-operator diabatization approach. An appropriate integration of couplings over the Brillouin zone allows the first calculation of a size-convergent Newns-Anderson chemisorption function, a coupling-weighted density of states measuring the line broadening of an adsorbate frontier state upon adsorption. This broadening corresponds to the experimentally observed lifetime of an electron in the state, which we confirm for core-excited Ar*(2p3/2-14s) atoms on a number of transition metal (TM) surfaces. Yet, beyond just lifetimes, the chemisorption function is highly interpretable and encodes rich information on orbital phase interactions on the surface. The model thus captures and elucidates key aspects of the electron transfer process. Finally, a decomposition into angular momentum components reveals the hitherto unresolved role of the hybridized d-character of the TM surface in the resonant electron transfer and elucidates the coupling of the adsorbate to the surface bands over the entire energy scale.

wfl Python toolkit for creating machine learning interatomic potentials and related atomistic simulation workflows.

Predictive atomistic simulations are increasingly employed for data intensive high throughput studies that take advantage of constantly growing computational resources. To handle the sheer number of individual calculations that are needed in such studies, workflow management packages for atomistic simulations have been developed for a rapidly growing user base. These packages are predominantly designed to handle computationally heavy ab initio calculations, usually with a focus on data provenance and reproducibility. However, in related simulation communities, e.g., the developers of machine learning interatomic potentials (MLIPs), the computational requirements are somewhat different: the types, sizes, and numbers of computational tasks are more diverse and, therefore, require additional ways of parallelization and local or remote execution for optimal efficiency. In this work, we present the atomistic simulation and MLIP fitting workflow management package wfl and Python remote execution package ExPyRe to meet these requirements. With wfl and ExPyRe, versatile atomic simulation environment based workflows that perform diverse procedures can be written. This capability is based on a low-level developer-oriented framework, which can be utilized to construct high level functionality for user-friendly programs. Such high level capabilities to automate machine learning interatomic potential fitting procedures are already incorporated in wfl, which we use to showcase its capabilities in this work. We believe that wfl fills an important niche in several growing simulation communities and will aid the development of efficient custom computational tasks.

Low-dimensional heterostructures for advanced electrocatalysis: an experimental and computational perspective.

Low dimensional electrocatalytic heterostructures have recently attracted significant attention in the catalysis community due to their highly tuneable interfaces and exciting electronic features, opening up new possibilities for effective nanometric control of both the charge carriers and energetic states of several intermediate catalytic species. In-depth understanding of electrocatalytic routes at the interface between two or more low-dimensional nanostructures has triggered the development of heterostructure nanocatalysts with extraordinary properties for water splitting reactions, NRR and CO2RR. This tutorial review provides an overview of the most recent advances in synthetic strategies for 0D-1D, 0D-2D, and 2D-2D nanoheterostructures, discussing key aspects of their electrocatalytic performances from experimental and computational perspectives as well as their applications towards the development of overall water splitting and Zn-air battery devices.

Adsorption Enthalpies for Catalysis Modeling through Machine-Learned Descriptors.

Heterogeneous catalysts are rather complex materials that come in many classes (e.g., metals, oxides, carbides) and shapes. At the same time, the interaction of the catalyst surface with even a relatively simple gas-phase environment such as syngas (CO and H2) may already produce a wide variety of reaction intermediates ranging from atoms to complex molecules. The starting point for creating predictive maps of, e.g., surface coverages or chemical activities of potential catalyst materials is the reliable prediction of adsorption enthalpies of all of these intermediates. For simple systems, direct density functional theory (DFT) calculations are currently the method of choice. However, a wider exploration of complex materials and reaction networks generally requires enthalpy predictions at lower computational cost.The use of machine learning (ML) and related techniques to make accurate and low-cost predictions of quantum-mechanical calculations has gained increasing attention lately. The employed approaches span from physically motivated models over hybrid physics-ΔML approaches to complete black-box methods such as deep neural networks. In recent works we have explored the possibilities for using a compressed sensing method (Sure Independence Screening and Sparsifying Operator, SISSO) to identify sparse (low-dimensional) descriptors for the prediction of adsorption enthalpies at various active-site motifs of metals and oxides. We start from a set of physically motivated primary features such as atomic acid/base properties, coordination numbers, or band moments and let the data and the compressed sensing method find the best algebraic combination of these features. Here we take this work as a starting point to categorize and compare recent ML-based approaches with a particular focus on model sparsity, data efficiency, and the level of physical insight that one can obtain from the model.Looking ahead, while many works to date have focused only on the mere prediction of databases of, e.g., adsorption enthalpies, there is also an emerging interest in our field to start using ML predictions to answer fundamental science questions about the functioning of heterogeneous catalysts or perhaps even to design better catalysts than we know today. This task is significantly simplified in works that make use of scaling-relation-based models (volcano curves), where the model outcome is determined by only one or two adsorption enthalpies and which consequently become the sole target for ML-based high-throughput screening or design. However, the availability of cheap ML energetics also allows going beyond scaling relations. On the basis of our own work in this direction, we will discuss the additional physical insight that can be achieved by integrating ML-based predictions with traditional catalysis modeling techniques from thermal and electrocatalysis, such as the computational hydrogen electrode and microkinetic modeling, as well as the challenges that lie ahead.

CO2-Activation by size-selected tantalum cluster cations (Ta1-16+): thermalization governing reaction selectivity.

The reactions of tantalum cluster cations of different sizes toward carbon dioxide are studied in an ion trap under multi-collisional conditions. For all sizes studied, consecutive reactions with several CO2 molecules are observed. This reveals two different pathways, namely oxide formation and the pickup of an entire molecule. Supported by calculations of the thermochemistry of TanO+ formation upon reaction with CO2, changes in the branching ratios at a particular cluster size are related to heat effects due to the vibrational heat capacity of the clusters and the exothermicity of the reaction.

Photoelectron angular distributions as sensitive probes of surfactant layer structure at the liquid-vapor interface.

The characterization of liquid-vapor interfaces at the molecular level is an important underpinning for a basic understanding of fundamental heterogeneous processes in many areas, such as atmospheric science. Here we use X-ray photoelectron spectroscopy to study the adsorption of a model surfactant, octanoic acid, at the water-gas interface. In particular, we examine the information contained in photoelectron angular distributions and show that information about the relative depth of molecules and functional groups within molecules can be obtained from these measurements. Focusing on the relative location of carboxylate (COO-) and carboxylic acid (COOH) groups at different solution pH, the former is found to be immersed deeper into the liquid-vapor interface, which is confirmed by classical molecular dynamics simulations. These results help establish photoelectron angular distributions as a sensitive tool for the characterization of molecules at the liquid-vapor interface.

Regularized second-order correlation methods for extended systems.

Second-order Møller-Plesset perturbation theory (MP2) constitutes the simplest form of many-body wavefunction theory and often provides a good compromise between efficiency and accuracy. There are, however, well-known limitations to this approach. In particular, MP2 is known to fail or diverge for some prototypical condensed matter systems like the homogeneous electron gas (HEG) and to overestimate dispersion-driven interactions in strongly polarizable systems. In this paper, we explore how the issues of MP2 for metallic, polarizable, and strongly correlated periodic systems can be ameliorated through regularization. To this end, two regularized second-order methods (including a new, size-extensive Brillouin-Wigner approach) are applied to the HEG, the one-dimensional Hubbard model, and the graphene-water interaction. We find that regularization consistently leads to improvements over the MP2 baseline and that different regularizers are appropriate for the various systems.

Surface-Mediated Ring-Opening and Porphyrin Deconstruction via Conformational Distortion.

The breakdown of macrocyclic compounds is of utmost importance in manifold biological and chemical processes, usually proceeding via oxygenation-induced ring-opening reactions. Here, we introduce a surface chemical route to selectively break a prototypical porphyrin species, cleaving off one pyrrole unit and affording a tripyrrin derivative. This pathway, operational in an ultrahigh vacuum environment at moderate temperature is enabled by a distinct molecular conformation achieved via the specific interaction between the porphyrin and its copper support. We provide an atomic-level characterization of the surface-anchored tripyrrin, its reaction intermediates, and byproducts by bond-resolved atomic force microscopy, unequivocally identifying the molecular skeletons. The ring-opening is rationalized by the distortion reducing the macrocycle's stability. Our findings open a route to steer ring-opening reactions by conformational design and to study intriguing tetrapyrrole catabolite analogues on surfaces.

Mapping Materials and Molecules.

The visualization of data is indispensable in scientific research, from the early stages when human insight forms to the final step of communicating results. In computational physics, chemistry and materials science, it can be as simple as making a scatter plot or as straightforward as looking through the snapshots of atomic positions manually. However, as a result of the "big data" revolution, these conventional approaches are often inadequate. The widespread adoption of high-throughput computation for materials discovery and the associated community-wide repositories have given rise to data sets that contain an enormous number of compounds and atomic configurations. A typical data set contains thousands to millions of atomic structures, along with a diverse range of properties such as formation energies, band gaps, or bioactivities.It would thus be desirable to have a data-driven and automated framework for visualizing and analyzing such structural data sets. The key idea is to construct a low-dimensional representation of the data, which facilitates navigation, reveals underlying patterns, and helps to identify data points with unusual attributes. Such data-intensive maps, often employing machine learning methods, are appearing more and more frequently in the literature. However, to the wider community, it is not always transparent how these maps are made and how they should be interpreted. Furthermore, while these maps undoubtedly serve a decorative purpose in academic publications, it is not always apparent what extra information can be garnered from reading or making them.This Account attempts to answer such questions. We start with a concise summary of the theory of representing chemical environments, followed by the introduction of a simple yet practical conceptual approach for generating structure maps in a generic and automated manner. Such analysis and mapping is made nearly effortless by employing the newly developed software tool ASAP. To showcase the applicability to a wide variety of systems in chemistry and materials science, we provide several illustrative examples, including crystalline and amorphous materials, interfaces, and organic molecules. In these examples, the maps not only help to sift through large data sets but also reveal hidden patterns that could be easily missed using conventional analyses.The explosion in the amount of computed information in chemistry and materials science has made visualization into a science in itself. Not only have we benefited from exploiting these visualization methods in previous works, we also believe that the automated mapping of data sets will in turn stimulate further creativity and exploration, as well as ultimately feed back into future advances in the respective fields.

Static and dynamic water structures at interfaces: A case study with focus on Pt(111).

An accurate atomistic treatment of aqueous solid-liquid interfaces necessitates the explicit description of interfacial water ideally via ab initio molecular dynamics simulations. Many applications, however, still rely on static interfacial water models, e.g., for the computation of (electro)chemical reaction barriers and focus on a single, prototypical structure. In this work, we systematically study the relation between density functional theory-derived static and dynamic interfacial water models with specific focus on the water-Pt(111) interface. We first introduce a general construction protocol for static 2D water layers on any substrate, which we apply to the low index surfaces of Pt. Subsequently, we compare these with structures from a broad selection of reference works based on the Smooth Overlap of Atomic Positions descriptor. The analysis reveals some structural overlap between static and dynamic water ensembles; however, static structures tend to overemphasize the in-plane hydrogen bonding network. This feature is especially pronounced for the widely used low-temperature hexagonal ice-like structure. In addition, a complex relation between structure, work function, and adsorption energy is observed, which suggests that the concentration on single, static water models might introduce systematic biases that are likely reduced by averaging over consistently created structural ensembles, as introduced here.

Data-efficient iterative training of Gaussian approximation potentials: Application to surface structure determination of rutile IrO2 and RuO2.

Machine-learning interatomic potentials, such as Gaussian Approximation Potentials (GAPs), constitute a powerful class of surrogate models to computationally involved first-principles calculations. At a similar predictive quality but significantly reduced cost, they could leverage otherwise barely tractable extensive sampling as in global surface structure determination (SSD). This efficiency is jeopardized though, if an a priori unknown structural and chemical search space as in SSD requires an excessive number of first-principles data for the GAP training. To this end, we present a general and data-efficient iterative training protocol that blends the creation of new training data with the actual surface exploration process. Demonstrating this protocol with the SSD of low-index facets of rutile IrO2 and RuO2, the involved simulated annealing on the basis of the refining GAP identifies a number of unknown terminations even in the restricted sub-space of (1 × 1) surface unit cells. Particularly in an O-poor environment, some of these, then metal-rich terminations, are thermodynamically most stable and are reminiscent of complexions as discussed for complex ceramic materials.

Zeolite-Stabilized Di- and Tetranuclear Molybdenum Sulfide Clusters Form Stable Catalytic Hydrogenation Sites.

Supercages of faujasite (FAU)-type zeolites serve as a robust scaffold for stabilizing dinuclear (Mo2 S4 ) and tetranuclear (Mo4 S4 ) molybdenum sulfide clusters. The FAU-encaged Mo4 S4 clusters have a distorted cubane structure similar to the FeMo-cofactor in nitrogenase. Both clusters possess unpaired electrons on Mo atoms. Additionally, they show identical catalytic activity per sulfide cluster. Their catalytic activity is stable (>150 h) for ethene hydrogenation, while layered MoS2 structures deactivate significantly under the same reaction conditions.