A general method for spatially coarse-graining Metropolis Monte Carlo simulations onto a lattice

Liu, Xiao; Seider, Warren D.; Sinno, Talid

doi:10.1063/1.4794686

Cited by 4 publications

(1 citation statement)

References 53 publications

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“…The Metropolis MC algorithm is employed to perform structure optimization. The general algorithm is well described in the literature. − The probability of a structure at a fixed n to be in configuration is defined as where is the Boltzmann constant, T is the temperature, and is a normalization constant to ensure over all accessible configurations. The acceptance criterion is based on the relation between probabilities before and after an MC move assuming all moves are symmetric: …”

Section: Methodsmentioning

confidence: 99%

Finite-Temperature Structures of Supported Subnanometer Catalysts InferredviaStatistical Learning and Genetic Algorithm-Based Optimization

Wang

Hensen

et al. 2020

ACS Nano

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Single-atom catalysts (SACs) minimize noble metal utilization and can alter the activity and selectivity of supported metal nanoparticles. However, the morphology of active centers, including single atoms and subnanometer clusters of a few atoms, remains elusive due to experimental challenges. The computational cost to describe numerous cluster shapes and sizes makes direct first-principles calculations impractical. We present a computational framework to enable structure determination for single-atom and subnanometer cluster catalysts. As a case study, we obtained the low-energy structures of Pd n (n = 1−21) clusters supported on CeO 2 (111), which are critical components of automobile three-way catalysts. Trained on density functional theory data, a three-dimensional cluster expansion is established using statistical learning to describe the Hamiltonian and predict energies of supported Pd n clusters of any structure. Low-energy stable and metastable structures are identified using a Metropolis Monte Carlo-based genetic algorithm in the canonical ensemble at 300 K. We observe that supported single atoms sinter to form bilayer clusters, and large cluster isomers share similarities in both shape and energy. The findings elucidate the significance of the support and microstructure on cluster stability. We discovered a simple surrogate structure−energy model, where the energy per atom scales with the square root of the average first coordination number, which can be used to estimate energies and compare the stability of clusters. Our framework, applicable to any metal/support system, fills an important methodological gap to predict the stability of supported metal catalysts in the subnanometer regime.

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Section: Methodsmentioning

confidence: 99%

Finite-Temperature Structures of Supported Subnanometer Catalysts InferredviaStatistical Learning and Genetic Algorithm-Based Optimization

Wang

Hensen

et al. 2020

ACS Nano

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Coarse-grained Monte Carlo simulations of non-equilibrium systems

Liu

Crocker

Sinno

2013

The Journal of Chemical Physics

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We extend the scope of a recent method for generating coarse-grained lattice Metropolis Monte Carlo simulations [X. Liu, W. D. Seider, and T. Sinno, Phys. Rev. E 86, 026708 (2012); and J. Chem. Phys. 138, 114104 (2013)] from continuous interaction potentials to non-equilibrium situations. The original method has been shown to satisfy detailed balance at the coarse scale and to provide a good representation of various equilibrium properties in both atomic and molecular systems. However, we show here that the original method is inconsistent with non-equilibrium trajectories generated by full-resolution Monte Carlo simulations, which, under certain conditions, have been shown to correspond to Langevin dynamics. The modified coarse-grained method is generated by simultaneously biasing the forward and backward transition probability for every possible move, thereby preserving the detailed balance of the original method. The resulting coarse-grained Monte Carlo simulations are shown to provide trajectories that are consistent with overdamped Langevin (Smoluchowski) dynamics using a sequence of simple non-equilibrium examples. We first consider the purely diffusional spreading of a Gaussian pulse of ideal-gas particles and then include an external potential to study the influence of drift. Finally, we validate the method using a more general situation in which the particles interact via a Lennard-Jones interparticle potential.

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Analysis of the lattice kinetic Monte Carlo method in systems with external fields

Lee

Sinno

2016

The Journal of Chemical Physics

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The lattice kinetic Monte Carlo (LKMC) method is studied in the context of Brownian particles subjected to drift forces, here principally represented by external fluid flow. LKMC rate expressions for particle hopping are derived that satisfy detailed balance at equilibrium while also providing correct dynamical trajectories in advective-diffusive situations. Error analyses are performed for systems in which collections of particles undergo Brownian motion while also being advected by plug and parabolic flows. We demonstrate how the flow intensity, and its associated drift force, as well as its gradient, each impact the accuracy of the method in relation to reference analytical solutions and Brownian dynamics simulations. Finally, we show how a non-uniform grid that everywhere retains full microscopic detail may be employed to increase the computational efficiency of lattice kinetic Monte Carlo simulations of particles subjected to drift forces arising from the presence of external fields.

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A general method for spatially coarse-graining Metropolis Monte Carlo simulations onto a lattice

Cited by 4 publications

References 53 publications

Finite-Temperature Structures of Supported Subnanometer Catalysts InferredviaStatistical Learning and Genetic Algorithm-Based Optimization

Finite-Temperature Structures of Supported Subnanometer Catalysts InferredviaStatistical Learning and Genetic Algorithm-Based Optimization

Coarse-grained Monte Carlo simulations of non-equilibrium systems

Analysis of the lattice kinetic Monte Carlo method in systems with external fields

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