Efficient Monte Carlo methods for the simulation of catalytic surface reactions

Lukkien, Johan J.; Segers, Jpl John; Hilbers, Paj Peter; Gelten, RJ; Jansen, Apj Tonek

doi:10.1103/physreve.58.2598

Cited by 217 publications

(221 citation statements)

References 22 publications

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“…For example, the probability that a given molecule of A reacts with a given molecule of B in a small time dt is k 1 7 uses this approach; that is, it picks random molecules of A and B and sees whether they react.) Previous work on efficient simulation 4 focused on surface processes, where reactions may take place on a large matrix of (x, y) positions. The current work focuses on reactions in solution, for which position is not important, and one can group by molecule type.…”

Section: Theoretical and Computational Backgroundmentioning

confidence: 99%

“…(An equivalent way of saying the same thing is 'if the dependency graph is sparse.') Lukkien et al 4 discuss ways to improve the Direct Method and the First Reaction Method (a more detailed treatment can be found in Segers 12 ). Their improved First Reaction Method, which we shall call the Absolute Time First Reaction Method, consists of switching from relative to absolute times and using a standard priority queue.…”

Section: Definition 5 An Indexed Priority Queue Consists Of (A) a Trmentioning

confidence: 99%

“…The discussion thus far has been somewhat abstract and calls for an example. Figure 7b, the tree structure for a 1 4 , so stop and let µ be "4".…”

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confidence: 99%

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Efficient Exact Stochastic Simulation of Chemical Systems with Many Species and Many Channels

2000

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There are two fundamental ways to view coupled systems of chemical equations: as continuous, represented by differential equations whose variables are concentrations, or as discrete, represented by stochastic processes whose variables are numbers of molecules. Although the former is by far more common, systems with very small numbers of molecules are important in some applications (e.g., in small biological cells or in surface processes). In both views, most complicated systems with multiple reaction channels and multiple chemical species cannot be solved analytically. There are exact numerical simulation methods to simulate trajectories of discrete, stochastic systems, (methods that are rigorously equivalent to the Master Equation approach) but these do not scale well to systems with many reaction pathways. This paper presents the Next Reaction Method, an exact algorithm to simulate coupled chemical reactions that is also efficient: it (a) uses only a single random number per simulation event, and (b) takes time proportional to the logarithm of the number of reactions, not to the number of reactions itself. The Next Reaction Method is extended to include timedependent rate constants and non-Markov processes and is applied to a sample application in biology (the lysis/lysogeny decision circuit of lambda phage). The performance of the Next Reaction Method on this application is compared with one standard method and an optimized version of that standard method.

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Section: Theoretical and Computational Backgroundmentioning

confidence: 99%

Section: Definition 5 An Indexed Priority Queue Consists Of (A) a Trmentioning

confidence: 99%

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Efficient Exact Stochastic Simulation of Chemical Systems with Many Species and Many Channels

2000

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“…The preexponential factor is assumed to be constant with coverage. The simulations were carried out using the computer program CARLOS, 4 which is a general purpose program that admits specification of the adlayer, the species, and the microscopic steps as input.…”

Section: B Theoretical Detailsmentioning

confidence: 99%

“…3,4 This allows for modeling of lateral interactions, local reconstructions, and diffusion of adsorbates. Our interest is to describe the kinetics of surface reactions on highly covered surfaces by including lateral interactions on a local basis.…”

Section: Introductionmentioning

confidence: 99%

Quantification of lateral repulsion between coadsorbed CO and N on Rh(100) using temperature-programmed desorption, low-energy electron diffraction, and Monte Carlo simulations

Bavel

Hopstaken

Curulla

et al. 2003

The Journal of Chemical Physics

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Temperature programmed desorption of CO coadsorbed with atomic N on Rh͑100͒, reveals both long-and short-range interactions between adsorbed CO and N. For CO desorption from Rh͑100͒ at low coverage we find an activation energy E a of 137Ϯ2 kJ/mol and a preexponential factor of 10 13.8Ϯ0.2 s Ϫ1 . Coadsorption with N partially blocks CO adsorption and destabilizes CO by lowering E a for CO desorption. Destabilization at low N coverage is explained by long-range electronic modification of the Rh͑100͒ surface. At high N and CO coverage, we find evidence for a short-range repulsive lateral interaction between CO ads and N ads in neighboring positions. We derive a pairwise repulsive interaction CO-N NN ϭ19 kJ/mol for CO coadsorbed to a c͑2ϫ2͒ arrangement of N atoms. This has important implications for the lateral distribution of coadsorbed CO and N at different adsorbate coverages. Regarding the different lateral interactions and mobility of adsorbates, we propose a structural model which satisfactorily explains the observed effects of atomic N on the desorption of CO. Dynamic Monte Carlo simulations were used to verify the experimentally obtained value for the CO-N interaction, by using the kinetic parameters and interaction energy derived from the temperature-programmed desorption experiments.

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Numerical simulations of electrocatalytic processes

Koper

2010

Handbook of Fuel Cells

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Recent developments in the computer simulation of electrocatalytic processes are discussed. The type of computer simulation chosen for a particular application depends on the time scale of the process and the level of molecular detail desired. Quantum‐chemical electronic structure calculations utilizing the density functional formalism give information about the details of the chemical bonding of molecules at surfaces. Application of the bonding of carbon monoxide to transition metal surfaces and alloys is described, including the role of the electric field. The link to macroscopically measurable kinetics, like voltammetry, can be made by resorting to Dynamic Monte Carlo methods. In this method, reaction events are mapped on to a lattice‐gas model of the catalyst surface and the statistical mechanics is solved exactly by Monte Carlo simulation algorithms. The reactant parameters can either be obtained from first‐principles quantum chemical calculations, or be adjusted so as to mimic as closely as possible the experimental results. An example of this method as applied to the oxidation of CO on platinum–ruthenium alloys is discussed.

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Efficient Monte Carlo methods for the simulation of catalytic surface reactions

Cited by 217 publications

References 22 publications

Efficient Exact Stochastic Simulation of Chemical Systems with Many Species and Many Channels

Efficient Exact Stochastic Simulation of Chemical Systems with Many Species and Many Channels

Quantification of lateral repulsion between coadsorbed CO and N on Rh(100) using temperature-programmed desorption, low-energy electron diffraction, and Monte Carlo simulations

Numerical simulations of electrocatalytic processes

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