Synchronous relaxation algorithm for parallel kinetic Monte Carlo simulations of thin film growth

Exact distributed kinetic Monte Carlo simulations for on-lattice chemical kinetics: lessons learnt from medium- and large-scale benchmarks

Kinetic Monte Carlo (KMC) simulations have been instrumental in multiscale catalysis studies, enabling the elucidation of the complex dynamics of heterogeneous catalysts and the prediction of macroscopic performance metrics, such as activity and selectivity. However, the accessible length- and time-scales have been a limiting factor in such simulations. For instance, handling lattices containing millions of sites with 'traditional' sequential KMC implementations is prohibitive owing to large memory requirements and long simulation times. We have recently established an approach for exact, distributed, lattice-based simulations of catalytic kinetics which couples the Time-Warp algorithm with the Graph-Theoretical KMC framework, enabling the handling of complex adsorbate lateral interactions and reaction events within large lattices. In this work, we develop a lattice-based variant of the Brusselator system, a prototype chemical oscillator pioneered by Prigogine and Lefever in the late 60s, to benchmark and demonstrate our approach. This system can form spiral wave patterns, which would be computationally intractable with sequential KMC, while our distributed KMC approach can simulate such patterns 15 and 36 times faster with 625 and 1600 processors, respectively. The medium- and large-scale benchmarks thus conducted, demonstrate the robustness of the approach, and reveal computational bottlenecks that could be targeted in further development efforts. This article is part of a discussion meeting issue 'Supercomputing simulations of advanced materials'.

Large-scale benchmarks of the time-warp/graph-theoretical kinetic Monte Carlo approach for distributed on-lattice simulations of catalytic kinetics

Motivated by the need to perform large-scale kinetic Monte Carlo (KMC) simulations, in the context of unravelling complex phenomena such as catalyst reconstruction and pattern formation, we extend the work of Ravipati et al. [S. Ravipati, G. D. Savva, I.-A. Christidi, R. Guichard, J. Nielsen, R. Réocreux and M. Stamatakis, Comput. Phys. Commun., 2022, 270, 108148] in benchmarking the performance of a distributed-computing, on-lattice KMC approach. The latter, implemented in our software package Zacros, combines the graph-theoretical KMC framework with the Time-Warp algorithm for parallel discrete event simulations, and entails dividing the lattice into subdomains, each assigned to a processor. The cornerstone of the Time-Warp algorithm is the state queue, to which snapshots of the simulation state are saved regularly, enabling historical KMC information to be corrected when conflicts occur at subdomain boundaries. Focusing on three model systems, we highlight the key Time-Warp parameters that can be tuned to optimise performance. The frequency of state saving, controlled by the state saving interval, δ_snap, is shown to have the largest effect on performance, which favours balancing the overhead of re-simulating KMC history with that of writing state snapshots to memory. Also important is the global virtual time (GVT) computation interval, Δτ_GVT, which has little direct effect on the progress of the simulation but controls how often the state queue memory can be freed up. We also find that pre-allocating memory for the state queue data structure favours performance. These findings will guide users in maximising the efficiency of Zacros or other distributed KMC software, which is a vital step towards realising accurate, meso-scale simulations 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.

Accelerated kinetic Monte Carlo: A case study; vacancy and dumbbell interstitial diffusion traps in concentrated solid solution alloys

Vacancy and self-interstitial atomic diffusion coefficients in concentrated solid solution alloys can have a non-monotonic concentration dependence. Here, the kinetics of monovacancies and ⟨100⟩ dumbbell interstitials in Ni-Fe alloys are assessed using lattice kinetic Monte Carlo (kMC). The non-monotonicity is associated with superbasins, which impels using accelerated kMC methods. Detailed implementation prescriptions for first passage time analysis kMC (FPTA-kMC), mean rate method kMC (MRM-kMC), and accelerated superbasin kMC (AS-kMC) are given. The accelerated methods are benchmarked in the context of diffusion coefficient calculations. The benchmarks indicate that MRM-kMC underestimates diffusion coefficients, while AS-kMC overestimates them. In this application, MRM-kMC and AS-kMC are computationally more efficient than the more accurate FPTA-kMC. Our calculations indicate that composition dependence of migration energies is at the origin of the vacancy's non-monotonic behavior. In contrast, the difference between formation energies of Ni-Ni, Ni-Fe, and Fe-Fe dumbbell interstitials is at the origin of their non-monotonic diffusion behavior. Additionally, the migration barrier crossover composition-based on the situation where Ni or Fe atom jumps have lower energy barrier than the other one-is introduced. KMC simulations indicate that the interplay between composition dependent crossover of migration energy and geometrical site percolation explains the non-monotonic concentration-dependence of atomic diffusion coefficients.

Scaling-Up Simulations of Diffusion in Microporous Materials

We introduce and demonstrate the coarse-graining of static and dynamical properties of host-guest systems constituted by methane in two different microporous materials. The reference systems are mapped to occupancy-based pore-scale lattice models. Each coarse-grained model is equipped with an appropriate coarse-grained potential and a local dynamical operator, which represents the probability of interpore molecular jumps between different cages. Coarse-grained thermodynamics and dynamics are both defined based on small-scale atomistic simulations of the reference systems. We considered two host materials: the widely studied ITQ-29 zeolite and the LTA-zeolite-templated carbon, which was recently theorized. Our method allows for representing with satisfactory accuracy and a considerably reduced computational effort the reference systems while providing new interesting physical insights in terms of static and diffusive properties.

Kinetic modelling of heterogeneous catalytic systems

The importance of heterogeneous catalysis in modern life is evidenced by the fact that numerous products and technologies routinely used nowadays involve catalysts in their synthesis or function. The discovery of catalytic materials is, however, a non-trivial procedure, requiring tedious trial-and-error experimentation. First-principles-based kinetic modelling methods have recently emerged as a promising way to understand catalytic function and aid in materials discovery. In particular, kinetic Monte Carlo (KMC) simulation is increasingly becoming more popular, as it can integrate several sources of complexity encountered in catalytic systems, and has already been used to successfully unravel the underlying physics of several systems of interest. After a short discussion of the different scales involved in catalysis, we summarize the theory behind KMC simulation, and present the latest KMC computational implementations in the field. Early achievements that transformed the way we think about catalysts are subsequently reviewed in connection to latest studies of realistic systems, in an attempt to highlight how the field has evolved over the last few decades. Present challenges and future directions and opportunities in computational catalysis are finally discussed.

Path factorization approach to stochastic simulations

The computational efficiency of stochastic simulation algorithms is notoriously limited by the kinetic trapping of the simulated trajectories within low energy basins. Here we present a new method that overcomes kinetic trapping while still preserving exact statistics of escape paths from the trapping basins. The method is based on path factorization of the evolution operator and requires no prior knowledge of the underlying energy landscape. The efficiency of the new method is demonstrated in simulations of anomalous diffusion and phase separation in a binary alloy, two stochastic models presenting severe kinetic trapping.

Speeding up simulation of diffusion in zeolites by a parallel synchronous kinetic Monte Carlo algorithm

Understanding the behaviors of molecules in tight confinement is a challenging task. Standard simulation tools like kinetic Monte Carlo have proven to be very effective in the study of adsorption and diffusion phenomena in microporous materials, but they turn out to be very inefficient when simulation time and length scales are extended. In this paper we have explored the possibility of application of a discrete version of the synchronous parallel kinetic Monte Carlo algorithm introduced by Martínez et al. [J. Comput. Phys. 227, 3804 (2008)] to the study of aromatic hydrocarbons diffusion in zeolites. The efficiency of this algorithm is investigated as a function of the number of processors and domain size. We show that with an accurate choice of domains size it is possible to achieve very good efficiencies thus permitting us to effectively extend space and time scales of the simulated system.

Accelerated molecular dynamics simulation of thin-film growth with the bond-boost method

We review the bond-boost method for accelerated molecular dynamics (MD) simulation and we demonstrate its application to kinetic phenomena relevant to thin-film growth. To illustrate various aspects of the method, three case studies are presented. We first illustrate aspects of the bond-boost method in studies of the diffusion of Cu atoms on Cu(001). In these studies, Cu interactions are described using a semi-empirical embedded-atom method potential. We recently extended the bond-boost method to perform accelerated ab initio MD (AIMD) simulations and we present results from preliminary studies in which we applied the bond-boost method in AIMD to uncover diffusion mechanisms of Al adatoms on Al(110). Finally, a problem inherent to many rare-event simulation methods is the 'small-barrier problem', in which the system resides in a group of states connected by small energy barriers and separated from the rest of phase space by large barriers. We developed the state-bridging bond-boost method to address this problem and we discuss its application for studying the diffusion of Co clusters on Cu(001). We discuss the outlook for future applications of the bond-boost method in materials simulation.

Parallel kinetic Monte Carlo simulations of Ag(111) island coarsening using a large database

The results of parallel kinetic Monte Carlo (KMC) simulations of the room-temperature coarsening of Ag(111) islands carried out using a very large database obtained via self-learning KMC simulations are presented. Our results indicate that, while cluster diffusion and coalescence play an important role for small clusters and at very early times, at late time the coarsening proceeds via Ostwald ripening, i.e. large clusters grow while small clusters evaporate. In addition, an asymptotic analysis of our results for the average island size S(t) as a function of time t leads to a coarsening exponent n = 1/3 (where S(t)∼t(2n)), in good agreement with theoretical predictions. However, by comparing with simulations without concerted (multi-atom) moves, we also find that the inclusion of such moves significantly increases the average island size. Somewhat surprisingly we also find that, while the average island size increases during coarsening, the scaled island-size distribution does not change significantly. Our simulations were carried out both as a test of, and as an application of, a variety of different algorithms for parallel kinetic Monte Carlo including the recently developed optimistic synchronous relaxation (OSR) algorithm as well as the semi-rigorous synchronous sublattice (SL) algorithm. A variation of the OSR algorithm corresponding to optimistic synchronous relaxation with pseudo-rollback (OSRPR) is also proposed along with a method for improving the parallel efficiency and reducing the number of boundary events via dynamic boundary allocation (DBA). A variety of other methods for enhancing the efficiency of our simulations are also discussed. We note that, because of the relatively high temperature of our simulations, as well as the large range of energy barriers (ranging from 0.05 to 0.8 eV), developing an efficient algorithm for parallel KMC and/or SLKMC simulations is particularly challenging. However, by using DBA to minimize the number of boundary events, we have achieved significantly improved parallel efficiencies for the OSRPR and SL algorithms. Finally, we note that, among the three parallel algorithms which we have tested here, the semi-rigorous SL algorithm with DBA led to the highest parallel efficiencies. As a result, we have obtained reasonable parallel efficiencies in our simulations of room-temperature Ag(111) island coarsening for a small number of processors (e.g. N(p) = 2 and 4). Since the SL algorithm scales with system size for fixed processor size, we expect that comparable and/or even larger parallel efficiencies should be possible for parallel KMC and/or SLKMC simulations of larger systems with larger numbers of processors.

Parallel kinetic Monte Carlo simulations of two-dimensional island coarsening

The results of parallel kinetic Monte Carlo (KMC) simulations of island coarsening based on a bond-counting model are presented. Our simulations were carried out both as a test of and as an application of the recently developed semirigorous synchronous sublattice (SL) algorithm. By carrying out simulations over long times and for large system sizes the asymptotic coarsening behavior and scaled island-size distribution (ISD) were determined. Our results indicate that while cluster diffusion and coalescence play a role at early and intermediate times, at late times the coarsening proceeds via Ostwald ripening. In addition, we find that the asymptotic scaled ISD is significantly narrower and more sharply peaked than the mean-field theory prediction. The dependence of the scaled ISD on coverage is also studied. Our results demonstrate that parallel KMC simulations can be used to effectively extend the time scale over which realistic coarsening simulations can be carried out. In particular, for simulations of the late stages of coarsening with system size L=1600 and eight processors, a parallel efficiency larger than 80% was obtained. These results suggest that the SL algorithm is likely to be useful in the future in parallel KMC simulations of more complicated models of coarsening.