A Practical Guide to Surface Kinetic Monte Carlo Simulations

First-Principles Studies on the Atomistic Properties of Metallic Magnesium as Anode Material in Magnesium-Ion Batteries

Rechargeable magnesium-ion batteries (MIBs) are a promising alternative to commercial lithium-ion batteries (LIBs). They are safer to handle, environmentally more friendly, and provide a five-time higher volumetric capacity (3832 mAh cm^-3 ) than commercialized LIBs. However, the formation of a passivation layer on metallic Mg electrodes is still a major challenge towards their commercialization. Using density functional theory (DFT), the atomistic properties of metallic magnesium, mainly well-selected self-diffusion processes on perfect and imperfect Mg surfaces were investigated to better understand the initial surface growth phenomena. Subsequently, rate constants and activation temperatures of crucial diffusion processes on Mg(0001) and Mg(10 1 ‾ 1) were determined, providing preliminary insights into the surface kinetics of metallic Mg electrodes. The obtained DFT results provide a data set for parametrizing a force field for metallic Mg or performing kinetic Monte-Carlo simulations.

Coupling of mitochondrial population evolution to microtubule dynamics in fission yeast cells: a kinetic Monte Carlo study

Mitochondrial populations in cells are maintained by cycles of fission and fusion events. Perturbation of this balance has been observed in several diseases such as cancer and neurodegeneration. In fission yeast cells, the association of mitochondria with microtubules inhibits mitochondrial fission [Mehta et al., J. Biol. Chem., 2019, 294, 3385], illustrating the intricate coupling between mitochondria and the dynamic population of microtubules within the cell. In order to understand this coupling, we carried out kinetic Monte Carlo (KMC) simulations to predict the evolution of mitochondrial size distributions for different cases; wild-type cells, cells with short and long microtubules, and cells without microtubules. Comparisons are made with mitochondrial distributions reported in experiments with fission yeast cells. Using experimentally determined mitochondrial fission and fusion frequencies, simulations implemented without the coupling of microtubule dynamics predicted an increase in the mean number of mitochondria, equilibrating within 50 s. The mitochondrial length distribution in these models also showed a higher occurrence of shorter mitochondria, implying a greater tendency for fission, similar to the scenario observed in the absence of microtubules and cells with short microtubules. Interestingly, this resulted in overestimating the mean number of mitochondria and underestimating mitochondrial lengths in cells with wild-type and long microtubules. However, coupling mitochondria's fission and fusion events to the microtubule dynamics effectively captured the mitochondrial number and size distributions in wild-type and cells with long microtubules. Thus, the model provides greater physical insight into the temporal evolution of mitochondrial populations in different microtubule environments, allowing one to study both the short-time evolution as observed in the experiments (<5 minutes) as well as their transition towards a steady-state (>15 minutes). Our study illustrates the critical role of microtubules in mitochondrial dynamics and coupling microtubule growth and shrinkage dynamics is critical to predicting the evolution of mitochondrial populations within the cell.

Kinetic Monte Carlo simulations for heterogeneous catalysis: Fundamentals, current status, and challenges

Kinetic Monte Carlo (KMC) simulations in combination with first-principles (1p)-based calculations are rapidly becoming the gold-standard computational framework for bridging the gap between the wide range of length scales and time scales over which heterogeneous catalysis unfolds. 1p-KMC simulations provide accurate insights into reactions over surfaces, a vital step toward the rational design of novel catalysts. In this Perspective, we briefly outline basic principles, computational challenges, successful applications, as well as future directions and opportunities of this promising and ever more popular kinetic modeling approach.

Simulations to Cover the Waterfront for Iron Oxide Catalysis

Hematite has been widely studied for catalytic water splitting, but the role of the interactions between catalytic sites is unknown. In this paper, we calculate the oxygen evolution reaction free energies and the surface adsorption distribution using a combination of density functional theory and Monte Carlo simulations to "cover the waterfront," or cover a wide range of properties with a simulation of the hematite surface under working conditions. First, we show that modeling noninteracting catalytic sites provides a poor explanation of hematite's slow reaction kinetics. The interactions between the catalytic site may hinder catalysis through the strong interactions of *OH2 and *OOH intermediates, which cause the reaction to revert back to the *O intermediate. Hence, neighboring interactions may be a possible reason for the abundant, experimentally observed *O intermediate on the surface. This study demonstrates how neighboring sites impact the energy required for catalytic steps, thus providing new avenues to improve catalysis by controlling neighboring site interactions.

Kinetically Corrected Monte Carlo-Molecular Dynamics Simulations of Solid Electrolyte Interphase Growth

We present a kinetic approach to the Monte Carlo-molecular dynamics (MC-MD) method for simulating reactive liquids using nonreactive force fields. A graphical reaction representation allows definition of reactions of arbitrary complexity, including their local solvation environment. Reaction probabilities and molecular dynamics (MD) simulation times are derived from ab initio calculations. Detailed validation is followed by studying the development of the solid electrolyte interphase (SEI) in lithium-ion batteries. We reproduce the experimentally observed two-layered structure on graphite, with an inorganic layer close to the anode and an outer organic layer. This structure develops via a near-shore aggregation mechanism.

Kinetic Monte Carlo simulations of the dry reforming of methane catalyzed by the Ru (0001) surface based on density functional theory calculations

This study shows the main pathways for the DRM reaction and the competitive RWGS reaction upon changing reaction conditions, displaying the importance of including lateral–lateral interactions to describe the reaction in agreement with the experiment.

Diffusion Barriers for Carbon Monoxide on the Cu(001) Surface Using Many-Body Perturbation Theory and Various Density Functionals

First-principles calculations play a key role in understanding the interactions of molecules with transition-metal surfaces and the energy profiles for catalytic reactions. However, many of the commonly used density functionals are not able to correctly predict the surface energy as well as the adsorption site preference for a key molecule such as CO, and it is not clear to what extent this shortcoming influences the prediction of reaction or diffusion pathways. Here, we report calculations of carbon monoxide diffusion on the Cu(001) surface along the [100] and [110] pathways, as well as the surface energy of Cu(001), and CO-adsorption energy and compare the performance of the Perdew-Burke-Ernzerhof (PBE), PBE + D2, PBE + D3, RPBE, Bayesian error estimation functional with van der Waals correlation (BEEF-vdW), HSE06 density functionals, and the random phase approximation (RPA), a post-Hartree-Fock method based on many-body perturbation theory. We critically evaluate the performance of these methods and find that RPA appears to be the only method giving correct site preference, overall barrier, adsorption enthalpy, and surface energy. For all of the other methods, at least one of these properties is not correctly captured. These results imply that many density functional theory (DFT)-based methods lead to qualitative and quantitative errors in describing CO interaction with transition-metal surfaces, which significantly impacts the description of diffusion pathways. It is well conceivable that similar effects exist when surface reactions of CO-related species are considered. We expect that the methodology presented here will be used to get more detailed insights into reaction pathways for CO conversion on transition-metal surfaces in general and Cu in particular, which will allow us to better understand the catalytic and electrocatalytic reactions involving CO-related species.

Accessing Structural, Electronic, Transport and Mesoscale Properties of Li-GICs via a Complete DFTB Model with Machine-Learned Repulsion Potential

Lithium-graphite intercalation compounds (Li-GICs) are the most popular anode material for modern lithium-ion batteries and have been subject to numerous studies—both experimental and theoretical. However, the system is still far from being consistently understood in detail across the full range of state of charge (SOC). The performance of approaches based on density functional theory (DFT) varies greatly depending on the choice of functional, and their computational cost is far too high for the large supercells necessary to study dilute and non-equilibrium configurations which are of paramount importance for understanding a complete charging cycle. On the other hand, cheap machine learning methods have made some progress in predicting, e.g., formation energetics, but fail to provide the full picture, including electrostatics and migration barriers. Following up on our previous work, we deliver on the promise of providing a complete and affordable simulation framework for Li-GICs. It is based on density functional tight binding (DFTB), which is fitted to dispersion-corrected DFT data using Gaussian process regression (GPR). In this work, we added the previously neglected lithium–lithium repulsion potential and extend the training set to include superdense Li-GICs (LiC_6−x; x>0) and lithium metal, allowing for the investigation of dendrite formation, next-generation modified GIC anodes, and non-equilibrium states during fast charging processes in the future. For an extended range of structural and energetic properties—layer spacing, bond lengths, formation energies and migration barriers—our method compares favorably with experimental results and with state-of-the-art dispersion-corrected DFT at a fraction of the computational cost. We make use of this by investigating some larger-scale system properties—long range Li–Li interactions, dielectric constants and domain-formation—proving our method’s capability to bring to light new insights into the Li-GIC system and bridge the gap between DFT and meso-scale methods such as cluster expansions and kinetic Monte Carlo simulations.

Self-reproducing catalytic micelles as nanoscopic protocell precursors

Protocells at life's origin are often conceived as bilayer-enclosed precursors of life, whose self-reproduction rests on the early advent of replicating catalytic biopolymers. This Perspective describes an alternative scenario, wherein reproducing nanoscopic lipid micelles with catalytic capabilities were forerunners of biopolymer-containing protocells. This postulate gains considerable support from experiments describing micellar catalysis and autocatalytic proliferation, and, more recently, from reports on cross-catalysis in mixed micelles that lead to life-like steady-state dynamics. Such results, along with evidence for micellar prebiotic compatibility, synergize with predictions of our chemically stringent computer-simulated model, illustrating how mutually catalytic lipid networks may enable micellar compositional reproduction that could underlie primal selection and evolution. Finally, we highlight studies on how endogenously catalysed lipid modifications could guide further protocellular complexification, including micelle to vesicle transition and monomer to biopolymer progression. These portrayals substantiate the possibility that protocellular evolution could have been seeded by pre-RNA lipid assemblies.

Computational pharmaceutics - A new paradigm of drug delivery

In recent decades pharmaceutics and drug delivery have become increasingly critical in the pharmaceutical industry due to longer time, higher cost, and less productivity of new molecular entities (NMEs). However, current formulation development still relies on traditional trial-and-error experiments, which are time-consuming, costly, and unpredictable. With the exponential growth of computing capability and algorithms, in recent ten years, a new discipline named "computational pharmaceutics" integrates with big data, artificial intelligence, and multi-scale modeling techniques into pharmaceutics, which offered great potential to shift the paradigm of drug delivery. Computational pharmaceutics can provide multi-scale lenses to pharmaceutical scientists, revealing physical, chemical, mathematical, and data-driven details ranging across pre-formulation studies, formulation screening, in vivo prediction in the human body, and precision medicine in the clinic. The present paper provides a comprehensive and detailed review in all areas of computational pharmaceutics and "Pharma 4.0", including artificial intelligence and machine learning algorithms, molecular modeling, mathematical modeling, process simulation, and physiologically based pharmacokinetic (PBPK) modeling. We not only summarized the theories and progress of these technologies but also discussed the regulatory requirements, current challenges, and future perspectives in the area, such as talent training and a culture change in the future pharmaceutical industry.

Infrequent metadynamics study of rare-event electrostatic channeling

The efficiency of cascade reactions, which consist of multiple chemical transformations that occur in a single pot without purification steps, is limited by the transport efficiency of intermediates between adjacent steps. Electrostatic channeling is a proven strategy for intermediate transfer in natural chemical cascades, but implementation into artificial cascades remains a challenge. Here, we combine infrequent metadynamics (InMetaD), umbrella sampling (US), and kinetic Monte Carlo (KMC) models to computationally study the transfer mechanism of glucose-6-phosphate (G6P) on a poly-arginine peptide bridging hexokinase (HK) and glucose-6-dehydrogenase (G6PDH). Transport of G6P by hopping in the presence of poly-arginine peptides is shown to be a rare event, and InMetaD is used to compute the hopping activation energy. US simulations capture the configurational change in the desorption process and enable the determination of the desorption energy. Parameterized by these results, a KMC model is used to estimate transport efficiency for the bridged enzyme complex. Results are compared to a similar complex using a poly-lysine bridge, using kinetic lag time as a metric. Even at a high ionic strength of 120 mM, poly-arginine peptides may be capable of more efficient transport as compared to poly-lysine, with a predicted lag time of 6 seconds for poly-arginine, compared to a previously reported lag time of 59 seconds for poly-lysine. This work indicates that poly-arginine peptides may be an improved bridge structure for electrostatic channeling of anionic intermediates.

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.

When Fluxionality Beats Size Selection: Acceleration of Ostwald Ripening of Sub-Nano Clusters

Size selection was demonstrated to suppress Ostwald ripening of supported catalytic nanoparticles. When the supported clusters are subnanometer in size and highly fluxional, such as Pt clusters on the rutile TiO₂ (110) surface, this paradigm breaks down, and the established theory of sintering needs a revision. At temperatures characteristic of catalysis (i.e. 700 K), sub-nano clusters thermally populate many low-energy metastable isomers. As these isomers all have different geometric and electronic structures, and thus, formation and dissociation energies (in lieu of surface energy), Ostwald ripening is not suppressed, despite the size-selection. However, some clusters arise as magic numbers in terms of sintering stability at the ensemble level. Acceleration of sintering by metastable species persists though weakens in polydisperse cluster systems. We propose a competing pathways theory for sintering, which at the atomistic level describes the found size-specific sintering behavior.

Toward alcohol synthesis from CO hydrogenation on Cu(111)-supported MoS2 - predictions from DFT+KMC

In the quest for cheap and efficient catalysts for alcohol synthesis from syngas, a material of interest is single-layer MoS₂ owing to its low cost, abundancy, and flexible structure. Because of the inertness of its basal plane, however, it is essential to find ways that make it catalytically active. Herein, by means of density functional theory based calculations of reaction pathways and activation energy barriers and accompanying kinetic Monte Carlo simulations, we show that while S vacancy row structures activate the MoS₂ basal plane, further enhancement of chemical activity and selectivity can be achieved by interfacing the MoS₂ layer with a metallic support. When defect-laden MoS₂ is grown on Cu(111), there is not only an increase in the active region (surface area of active sites) but also charge transfer from Cu to MoS₂, resulting in a shift of the Fermi level such that the frontier states (d orbitals of the exposed Mo atoms) appear close to it, making the MoS₂/Cu(111) system ready for catalytic activity. Our calculated thermodynamics of reaction pathways lead to the conclusion that the Cu(111) substrate promotes both methanol and ethanol as the products, while kinetic Monte Carlo simulations suggest a high selectivity toward the formation of ethanol.

The role of oxygenated species in the catalytic self-coupling of MeOH on O pre-covered Au(111)

The oxidation of alcohols plays a central role in the valorisation of biomass, in particular when performed with a non-toxic oxidant such as O₂. Aerobic oxidation of methanol on gold has attracted attention lately and the main steps of its mechanism have been described experimentally. However, the exact role of O and OH on each elementary step and the effect of the interactions between adsorbates are still not completely understood. Here we investigate the mechanism of methanol oxidation to HCOOCH₃ and CO₂. We use Density Functional Theory (DFT) to assess the energetics of the underlying pathways, and subsequently build lattice kinetic Monte Carlo (kMC) models of increasing complexity, to elucidate the role of different oxygenates. Detailed comparisons of our simulation results with experimental temperature programmed desorption (TPD) spectra enable us to validate the mechanism and identify rate determining steps. Crucially, taking into account dispersion (van der Waals forces) and adsorbate-adsorbate lateral interactions are both important for reproducing the experimental data.

Off-Lattice Monte-Carlo Approach for Studying Nucleation and Evaporation Phenomena at the Molecular Scale

Droplet nucleation and evaporation are ubiquitous in nature and many technological applications, such as phase-change cooling and boiling heat transfer. So far, the description of these phenomena at the molecular scale has posed challenges for modelling with most of the models being implemented on a lattice. Here, we propose an off-lattice Monte-Carlo approach combined with a grid that can be used for the investigation of droplet formation and evaporation. We provide the details of the model, its implementation as Python code, and results illustrating its dependence on various parameters. The method can be easily extended for any force-field (e.g., coarse-grained, all-atom models, and external fields, such as gravity and electric field). Thus, we anticipate that the proposed model will offer opportunities for a wide range of studies in various research areas involving droplet formation and evaporation and will also form the basis for further method developments for the molecular modelling of such phenomena.

Lattice model for self-folding at the microscale

Three-dimensional shell-like structures can be obtained spontaneously at the microscale from the self-folding of 2D templates of rigid panels. At least for simple structures, the motion of each panel is consistent with a Brownian process and folding occurs through a sequence of binding events, where pairs of panels meet at a specific closing angle. Here, we propose a lattice model to describe the dynamics of self-folding. As an example, we study the folding of a pyramid of N lateral faces. We combine analytical and numerical Monte Carlo simulations to find how the folding time depends on the number of faces, closing angle, and initial configuration. Implications for the study of more complex structures are discussed.

Factors correlating to enhanced surface diffusion in metallic glasses

The enhancement of surface diffusion (D_S) over the bulk (D_V) in metallic glasses (MGs) is well documented and likely to strongly influence the properties of glasses grown by vapor deposition. Here, we use classical molecular dynamics (MD) simulations to identify different factors influencing the enhancement of surface diffusion in MGs. MGs have a simple atomic structure and belong to the category of moderately fragile glasses that undergo pronounced slowdown of bulk dynamics with cooling close to the glass transition temperature (T_g). We observe that D_S exhibits a much more moderate slowdown compared to D_V when approaching T_g, and D_S/D_V at T_g varies by two orders of magnitude among the MGs investigated. We demonstrate that both the surface energy and the fraction of missing bonds for surface atoms show good correlation to D_S/D_V, implying that the loss of nearest neighbors at the surface directly translates into higher mobility, unlike the behavior of network-bonded and hydrogen-bonded organic glasses. Fragility, a measure of the slowdown of bulk dynamics close to T_g, also correlates to D_S/D_V, with more fragile systems having larger surface enhancement of mobility. The deviations observed in the fragility-D_S/D_V relationship are shown to be correlated to the extent of segregation or depletion of the mobile element at the surface. Finally, we explore the relationship between the diffusion pre-exponential factor (D₀) and the activation energy (Q) and compare it to a ln(D₀)-Q correlation previously established for bulk glasses, demonstrating similar correlations from MD as in the experiments and that the surface and bulk have very similar ln(D₀)-Q correlations.

Graph analysis of proton conduction pathways in scandium-doped barium zirconate

Understanding the relationship between the acceptor dopant size and proton conductivity in barium zirconate, BaZrO₃, is important for maximizing efficiency in this promising fuel cell material. While proton conduction pathways with larger Y_Zr ^' and smaller Al_Zr ^' defects have been explored, proton pathways with Sc_Zr ^', a defect of comparable size to the replaced ion, have not been investigated using centrality measures, periodic pathway searches, and kinetic Monte Carlo (KMC). Centrality measures in BaSc_0.125Zr_0.875O₃ highlight a trapping region by Sc_Zr ^' and scattered high centrality regions on undoped planes. Connected long-range high centrality regions are found mainly in undoped planes for BaAl_0.125Zr_0.875O₃ and in the dopant planes for BaY_0.125Zr_0.875O₃. The best long-range proton conduction periodic pathways in Al_Zr ^' and Sc_Zr ^' systems travel between dopant planes, while those for yttrium-doped BaZrO₃ remained on dopant planes. KMC trajectories at 1000 K show long-range proton conduction barriers of 0.86 eV, 0.52 eV, and 0.25 eV for Al_Zr ^', Sc_Zr ^', and Y_Zr ^' systems, respectively. Long-range periodic conduction highway limiting barrier averages correlate well with the connectivity of the most central regions in each system but ignore diffusion around the dopant and through other high centrality regions. BaSc_0.125Zr_0.875O₃ shows an intermediate overall conduction barrier limited by trapping, which earlier experiments and simulations suggest that it can be mitigated with increased oxygen vacancy concentration.

Theoretical insights into C-H bond activation of methane by transition metal clusters: the role of anharmonic effects

In heterogeneous catalysis, the determination of active phases has been a long-standing challenge, as materials' properties change under operational conditions (i.e. temperature (T) and pressure (p) in an atmosphere of reactive molecules). As a first step towards materials design for methane activation, we study the T and p dependence of the composition, structure, and stability of metal oxide clusters in a reactive atmosphere at thermodynamic equilibrium using a prototypical model catalyst having wide practical applications: free transition metal (Ni) clusters in a combined oxygen and methane atmosphere. A robust methodological approach is employed, where the starting point is systematic scanning of the potential energy surface (PES) to obtain the global minimum structures using a massively parallel cascade genetic algorithm (cGA) at the hybrid density functional level. The low energy clusters are further analyzed to estimate their thermodynamic stability at realistic T, p O2 and p CH4 using ab initio atomistic thermodynamics (aiAT). To incorporate the anharmonicity in the vibrational free energy contribution to the configurational entropy, we evaluate the excess free energy of the clusters numerically by a thermodynamic integration method with ab initio molecular dynamics (aiMD) simulation inputs. By analyzing a large dataset, we show that the conventional harmonic approximation miserably fails for this class of materials, and capturing the anharmonic effects on the vibration free energy contribution is indispensable. The latter has a significant impact on detecting the activation of the C-H bond, while the harmonic infrared spectrum fails to capture this, due to the wrong prediction of the vibrational modes.

DFTB Modeling of Lithium-Intercalated Graphite with Machine-Learned Repulsive Potential

Lithium ion batteries have been a central part of consumer electronics for decades. More recently, they have also become critical components in the quickly arising technological fields of electric mobility and intermittent renewable energy storage. However, many fundamental principles and mechanisms are not yet understood to a sufficient extent to fully realize the potential of the incorporated materials. The vast majority of concurrent lithium ion batteries make use of graphite anodes. Their working principle is based on intercalation, the embedding and ordering of (lithium-) ions in two-dimensional spaces between the graphene sheets. This important process, it yields the upper bound to a battery's charging speed and plays a decisive role in its longevity, is characterized by multiple phase transitions, ordered and disordered domains, as well as nonequilibrium phenomena, and therefore quite complex. In this work, we provide a simulation framework for the purpose of better understanding lithium-intercalated graphite and its behavior during use in a battery. To address large system sizes and long time scales required to investigate said effects, we identify the highly efficient, but semiempirical density functional tight binding (DFTB) as a suitable approach and combine particle swarm optimization (PSO) with the machine learning (ML) procedure Gaussian process regression (GPR) as implemented in the recently developed GPrep package for DFTB repulsion fitting to obtain the necessary parameters. Using the resulting parametrization, we are able to reproduce experimental reference structures at a level of accuracy which is in no way inferior to much more costly ab initio methods. We finally present structural properties and diffusion barriers for some exemplary system states.

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.

Comparison of Queueing Data-Structures for Kinetic Monte Carlo Simulations of Heterogeneous Catalysts

On-lattice kinetic Monte Carlo (KMC) is a computational method used to simulate (among others) physicochemical processes on catalytic surfaces. The KMC algorithm propagates the system through discrete configurations by selecting (with the use of random numbers) the next elementary process to be simulated, e.g., adsorption, desorption, diffusion, or reaction. An implementation of such a selection procedure is the first-reaction method in which all realizable elementary processes are identified and assigned a random occurrence time based on their rate constant. The next event to be executed will then be the one with the minimum interarrival time. Thus, a fast and efficient algorithm for selecting the most imminent process and performing all of the necessary updates on the list of realizable processes post execution is of great importance. In the current work, we implement five data-structures to handle the elementary process queue during a KMC run: an unsorted list, a binary heap, a pairing heap, a one-way skip list, and finally, a novel two-way skip list with a mapping array specialized for KMC simulations. We also investigate the effect of compiler optimizations on the performance of these data-structures on three benchmark models, capturing CO oxidation, a simplified water gas shift mechanism, and a temperature-programmed desorption run. Excluding the least efficient and impractical for large-problems unsorted list, we observe a 3× speedup of the binary or pairing heaps (most efficient) compared to the one-way skip list (least efficient). Compiler optimizations deliver a speedup of up to 1.8×. These benchmarks provide valuable insight into the importance of, often-overlooked, implementation-related aspects of KMC simulations, such as the queueing data-structures. Our results could be particularly useful in guiding the choice of data-structures and algorithms that would minimize the computational cost of large-scale simulations.

SuSMoST: Surface Science Modeling and Simulation Toolkit

We present to the scientific community the Surface Science Modeling and Simulation Toolkit (SuSMoST), which includes a number of utilities and implementations of statistical physics algorithms and models. With SuSMoST it is possible to predict or explain the structure and thermodynamic properties of adsorption layers. SuSMoST automatically builds formal graph and tensor-network models based on atomic description of adsorption complexes and helps to do ab initio calculations of interactions between adsorbed species. Using methods of various nature SuSMoST generates representative samples of adsorption layers and computes its thermodynamic quantities such as mean energy, coverage, density, and heat capacity. From these data one can plot phase diagrams of adsorption systems, assess thermal stability of self-assembled structures, simulate thermal desorption spectra, and so forth.

A Caching Scheme To Accelerate Kinetic Monte Carlo Simulations of Catalytic Reactions

Kinetic Monte Carlo (KMC) simulations have been instrumental in advancing our fundamental understanding of heterogeneously catalyzed reactions, with particular emphasis on structure sensitivity, ensemble effects, and the interplay between adlayer structure and adsorbate-adsorbate lateral interactions in shaping the observed kinetics. Yet, the computational cost of KMC remains high, thereby motivating the development of acceleration schemes that would improve the simulation efficiency. We present an exact such scheme, which implements a caching algorithm along with shared-memory parallelization to improve the computational performance of simulations incorporating long-range adsorbate-adsorbate lateral interactions. This scheme is based on caching information about the energetic interaction patterns associated with the products of each possible lattice process (adsorption, desorption, reaction etc.). Thus, every time a reaction occurs ("ongoing reaction"), it enables fast updates of the rate constants of "affected reactions", i.e., possible reactions in the region of influence of the "ongoing reaction". Benchmarks on KMC simulations of NO_x oxidation/reduction, yielded acceleration factors of up to 20, when comparing single-thread runs without caching to runs on 16 threads with caching, for simulations with a cluster expansion Hamiltonian that incorporates up to 8th-nearest-neighbor interactions.

The Exploration of Chemical Reaction Networks

Modern computational chemistry has reached a stage at which massive exploration into chemical reaction space with unprecedented resolution with respect to the number of potentially relevant molecular structures has become possible. Various algorithmic advances have shown that such structural screenings must and can be automated and routinely carried out. This will replace the standard approach of manually studying a selected and restricted number of molecular structures for a chemical mechanism. The complexity of the task has led to many different approaches. However, all of them address the same general target, namely to produce a complete atomistic picture of the kinetics of a chemical process. It is the purpose of this overview to categorize the problems that should be targeted and to identify the principal components and challenges of automated exploration machines so that the various existing approaches and future developments can be compared based on well-defined conceptual principles.

Fingerprint Voltammograms of Copper Single Crystals under Alkaline Conditions: A Fundamental Mechanistic Analysis

A critical step toward the systematic development of electrocatalysts is the determination of the microscopic structure and processes at the electrified solid/electrolyte interface. The major challenges toward this end for experiment and computations are achieving sufficient cleanliness and modeling the complexity of electrochemical systems, respectively. In this sense, benchmarks of well-defined model systems are sparse. This work presents a rigorous joint experimental-theoretical study on the single-crystal (SC) Cu/aqueous interface. Within typical computational uncertainties, we find quantitative agreement between simulated and experimentally measured voltammograms, which allows us to unequivocally identify the *OH adsorption feature in the fingerprint region of Cu(110), Cu(100), and Cu(111) SCs under alkaline conditions. We find the inclusion of hydrogen evolution reaction kinetics in the theoretical model to be crucial for an accurate steady-state description that gives rise to a negligible H* coverage. A purely thermodynamic description of the H* coverage through a Pourbaix analysis would incorrectly lead to a H* adsorption peak. The presented results establish a fundamental benchmark for all electrochemical applications of Cu.

Dynamic vs static behaviour of a supported nanoparticle with reaction-induced catalytic sites in a lattice model

Modern literature shows a rapidly growing interest to the supported nanocatalysts with dynamic behaviour under reaction conditions. This new frontier of heterogeneous catalysis is recognized as one of the most challenging and worthy of consideration from all possible angles. In this context, a previously suggested lattice model is used to get an insight, by means of kinetic Monte Carlo, into the influence of the mobility of reaction-induced catalytic sites of a two-dimensional supported nanoparticle on the system behaviour. The results speak in favour of feasibility of dynamic nanocatalysts with self-organized structures capable of robust functioning. This approach, from the macroscopic end, is believed to be a useful complement to ever developing experimental and first principle approaches.

Kinetic Monte-Carlo Simulation of Methane Steam Reforming over a Nickel Surface

A kinetic Monte-Carlo model was developed in order to simulate the methane steam reforming and kinetic behavior of this reaction. There were 34 elementary step reactions that were used, based on the Langmuir–Hinshelwood mechanism, over a nickel catalyst. The simulation was investigated at a mole fraction of methane between 0.1 and 0.9, temperature of 600 to 1123 K, and total pressure of up to 40 bar. The simulated results were collected at a steady state and were compared with the previously reported experiments. The fractional coverages of the adsorbed species and the production rates of H2, CO, and CO2 were evaluated, and the effects of the reaction temperature, feed concentration, and total pressure of reactants were also investigated. The simulation results showed a similar trend with previous experimental results, and suggested the appropriate conditions for this reaction, which were a total pressure of 10 bar, with the mole fraction of methane in a range of 0.4–0.5.

Efficient Implementation of Cluster Expansion Models in Surface Kinetic Monte Carlo Simulations with Lateral Interactions: Subtraction Schemes, Supersites, and the Supercluster Contraction

While lateral interaction models for reactions at surfaces have steadily gained popularity and grown in terms of complexity, their use in chemical kinetics has been impeded by the low performance of current kinetic Monte Carlo (KMC) algorithms. The origins of the additional computational cost in KMC simulations with lateral interactions are traced back to the more elaborate cluster expansion Hamiltonian, the more extensive rate updating, and to the impracticality of rate-catalog-based algorithms for interacting adsorbate systems. Favoring instead site-based algorithms, we propose three ways to reduce the cost of KMC simulations: (1) representing the lattice energy by a smaller Supercluster Hamiltonian without loss of accuracy, (2) employing the subtraction schemes for updating key quantities in the simulation that undergo only small, local changes during a reaction event, and (3) applying efficient search algorithms from a set of established methods (supersite approach). The cost of the resulting algorithm is fixed with respect to the number of lattice sites for practical lattice sizes and scales with the square of the range of lateral interactions. The overall added cost of including a complex lateral interaction model amounts to less than a factor 3. Practical issues in implementation due to finite numerical accuracy are discussed in detail, and further suggestions for treating long-range lateral interactions are made. We conclude that, while KMC simulations with complex lateral interaction models are challenging, these challenges can be overcome by modifying the established variable step-size method by employing the supercluster, subtraction, and supersite algorithms (SSS-VSSM). © 2019 Wiley Periodicals, Inc.