A practical approach to the sensitivity analysis for kinetic Monte Carlo simulation of heterogeneous catalysis

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.

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.

A Practical Guide to Surface Kinetic Monte Carlo Simulations

This review article is intended as a practical guide for newcomers to the field of kinetic Monte Carlo (KMC) simulations, and specifically to lattice KMC simulations as prevalently used for surface and interface applications. We will provide worked out examples using the kmos code, where we highlight the central approximations made in implementing a KMC model as well as possible pitfalls. This includes the mapping of the problem onto a lattice and the derivation of rate constant expressions for various elementary processes. Example KMC models will be presented within the application areas surface diffusion, crystal growth and heterogeneous catalysis, covering both transient and steady-state kinetics as well as the preparation of various initial states of the system. We highlight the sensitivity of KMC models to the elementary processes included, as well as to possible errors in the rate constants. For catalysis models in particular, a recurrent challenge is the occurrence of processes at very different timescales, e.g., fast diffusion processes and slow chemical reactions. We demonstrate how to overcome this timescale disparity problem using recently developed acceleration algorithms. Finally, we will discuss how to account for lateral interactions between the species adsorbed to the lattice, which can play an important role in all application areas covered here.

Systematic Enumeration of Elementary Reaction Steps in Surface Catalysis

The direct synthesis of complex chemicals from simple precursors (such as syngas) is one of the main objectives of current research in heterogeneous catalysis. To rationally design catalytic materials for this purpose, it is essential to identify the critical elementary reaction steps that ultimately determine a catalyst's activity and selectivity with respect to a desired product. Unfortunately, the number of potentially relevant elementary steps is in the thousands, even for relatively simple target species like ethanol. The challenge of identifying the critical steps is thus akin to finding the proverbial needle in a haystack. Recently, a model-reduction scheme has been proposed, which tackles this problem by prescreening the barriers of all potential reactions with computationally inexpensive approximations. Although this route appears highly promising, it raises the question of how the starting point of the model-reduction process can be determined. In this contribution, we present a systematic method for enumerating all intermediates and elementary reactions relevant to a chemical process of interest. Using this approach, we construct reaction networks for C,H,O-containing systems consisting of up to four non-hydrogen atoms (more than 1 million reactions). Importantly, the scheme goes beyond simple bond-breaking reactions and allows considering rearrangement and transfer reactions as well. The presented reaction networks thus cover the chemistry of syngas-based processes (and beyond) to an unprecedented scale.

SQERT-T: alleviating kinetic Monte Carlo (KMC)-stiffness in transient KMC simulations

Lattice based kinetic Monte Carlo (KMC) is often used for simulating the dynamics of systems at a supramolecular scale, based on molecular scale transitions. A common challenge in KMC simulations is rapid 'back-and-forth' reactions, which dominate the events executed during simulations and inhibit the ability for simulations to reach longer time scales. Such processes are fast frivolous processes (FFPs) and are one manifestation of a phenomenon referred to as KMC-stiffness. Here, an algorithm for staggered quasi-equilibrium rank-based throttling geared towards transient kinetics (SQERT-T) is presented. Within the SQERT-T methodology, a pace-restrictor reaction and an FFP floor are utilized along with throttling of the process transition rate constants to accelerate the KMC simulations while still retaining sufficient time resolution for sampling of the data. KMC simulations were performed for CO oxidation over RuO₂(1 1 0) and over RuO₂(1 1 1), and the results were compared to experimental data obtained using RuO₂ powders. The experiments and simulations were for transient conditions: the system was subjected to a temperature program which included temperatures in the range of 363 to 453 K. The timescales that were achieved during the KMC simulations in this study would not have been accessible without KMC acceleration, and were enabled by the use of SQERT-T.

Addressing global uncertainty and sensitivity in first-principles based microkinetic models by an adaptive sparse grid approach

In the last decade, first-principles-based microkinetic modeling has been developed into an important tool for a mechanistic understanding of heterogeneous catalysis. A commonly known, but hitherto barely analyzed issue in this kind of modeling is the presence of sizable errors from the use of approximate Density Functional Theory (DFT). We here address the propagation of these errors to the catalytic turnover frequency (TOF) by global sensitivity and uncertainty analysis. Both analyses require the numerical quadrature of high-dimensional integrals. To achieve this efficiently, we utilize and extend an adaptive sparse grid approach and exploit the confinement of the strongly non-linear behavior of the TOF to local regions of the parameter space. We demonstrate the methodology on a model of the oxygen evolution reaction at the Co₃O₄ (110)-A surface, using a maximum entropy error model that imposes nothing but reasonable bounds on the errors. For this setting, the DFT errors lead to an absolute uncertainty of several orders of magnitude in the TOF. We nevertheless find that it is still possible to draw conclusions from such uncertain models about the atomistic aspects controlling the reactivity. A comparison with derivative-based local sensitivity analysis instead reveals that this more established approach provides incomplete information. Since the adaptive sparse grids allow for the evaluation of the integrals with only a modest number of function evaluations, this approach opens the way for a global sensitivity analysis of more complex models, for instance, models based on kinetic Monte Carlo simulations.

Beyond mean-field approximations for accurate and computationally efficient models of on-lattice chemical kinetics

Modeling the kinetics of surface catalyzed reactions is essential for the design of reactors and chemical processes. The majority of microkinetic models employ mean-field approximations, which lead to an approximate description of catalytic kinetics by assuming spatially uncorrelated adsorbates. On the other hand, kinetic Monte Carlo (KMC) methods provide a discrete-space continuous-time stochastic formulation that enables an accurate treatment of spatial correlations in the adlayer, but at a significant computation cost. In this work, we use the so-called cluster mean-field approach to develop higher order approximations that systematically increase the accuracy of kinetic models by treating spatial correlations at a progressively higher level of detail. We further demonstrate our approach on a reduced model for NO oxidation incorporating first nearest-neighbor lateral interactions and construct a sequence of approximations of increasingly higher accuracy, which we compare with KMC and mean-field. The latter is found to perform rather poorly, overestimating the turnover frequency by several orders of magnitude for this system. On the other hand, our approximations, while more computationally intense than the traditional mean-field treatment, still achieve tremendous computational savings compared to KMC simulations, thereby opening the way for employing them in multiscale modeling frameworks.

Local-metrics error-based Shepard interpolation as surrogate for highly non-linear material models in high dimensions

Many problems in computational materials science and chemistry require the evaluation of expensive functions with locally rapid changes, such as the turn-over frequency of first principles kinetic Monte Carlo models for heterogeneous catalysis. Because of the high computational cost, it is often desirable to replace the original with a surrogate model, e.g., for use in coupled multiscale simulations. The construction of surrogates becomes particularly challenging in high-dimensions. Here, we present a novel version of the modified Shepard interpolation method which can overcome the curse of dimensionality for such functions to give faithful reconstructions even from very modest numbers of function evaluations. The introduction of local metrics allows us to take advantage of the fact that, on a local scale, rapid variation often occurs only across a small number of directions. Furthermore, we use local error estimates to weigh different local approximations, which helps avoid artificial oscillations. Finally, we test our approach on a number of challenging analytic functions as well as a realistic kinetic Monte Carlo model. Our method not only outperforms existing isotropic metric Shepard methods but also state-of-the-art Gaussian process regression.