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Journal of Chemical Physics / Volume 134 / Issue 21 / ARTICLES / Theoretical Methods and Algorithms

J. Chem. Phys. 134, 214115 (2011); http://dx.doi.org/10.1063/1.3596751 (13 pages)

A graph-theoretical kinetic Monte Carlo framework for on-lattice chemical kinetics

Michail Stamatakis and Dionisios G. Vlachos

Department of Chemical Engineering, University of Delaware, Newark, Delaware 19716, USA

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(Received 3 March 2011; accepted 12 May 2011; published online 7 June 2011)

Existing kinetic Monte Carlo (KMC) frameworks for the simulation of adsorption, desorption, diffusion, and reaction on a lattice often assume that each participating species occupies a single site and represent elementary events involving a maximum of two sites. However, these assumptions may be inadequate, especially in the case of complex chemistries, involving multidentate species or complex coverage and neighboring patterns between several lattice sites. We have developed a novel approach that employs graph-theoretical ideas to overcome these challenges and treat easily complex chemistries. As a benchmark, the Ziff-Gulari-Barshad system is simulated and comparisons of the computational times of the graph-theoretical KMC and a simpler KMC approach are made. Further, to demonstrate the capabilities of our framework, the water-gas shift chemistry on Pt(111) is simulated.

© 2011 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. METHODS
    1. Lattice representation
    2. State of the system
    3. Elementary step representation
    4. Mapping to lattice processes
    5. Event statistics
    6. Pseudocode
  3. COMPUTATIONAL RESULTS AND DISCUSSION
    1. Ziff-Gulari-Barshad model system
    2. Water-gas shift on Pt(111)
  4. CONCLUSIONS

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KEYWORDS and PACS

Keywords

adsorption, desorption, diffusion, graph theory, Monte Carlo methods, platinum, reaction kinetics theory, surface chemistry

PACS

  • 82.20.Db

    Transition state theory and statistical theories of rate constants

  • 82.65.+r

    Surface and interface chemistry; heterogeneous catalysis at surfaces

  • 68.43.Nr

    Desorption kinetics

  • 02.10.Ox

    Combinatorics; graph theory

  • 02.50.Ng

    Distribution theory and Monte Carlo studies

  • 68.43.Mn

    Adsorption kinetics

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3596751

PUBLICATION DATA

ISSN

0021-9606 (print)  
1089-7690 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

For access to fully linked references, you need to log in.
    M. Silverberg, A. Ben-Shaul, and F. Rebentrost, J. Chem. Phys. 83(12), 6501 (1985)JCPSA6000083000012006501000001.

    M. Silverberg and A. Ben-Shaul, J. Chem. Phys. 87(5), 3178 (1987)JCPSA6000087000005003178000001.

    K. Reuter and M. Scheffler, Phys. Rev. B 73(4), 045433 (2006).

    J. J. Lukkien, J. P. L. Segers, P. A. J. Hilbers, R. J. Gelten, and A. P. J. Jansen, Phys. Rev. E 58(2), 2598 (1998).

    R. M. Ziff, E. Gulari, and Y. Barshad, Phys. Rev. Lett. 56(24), 2553 (1986).

    P. Hänggi, P. Talkner, and M. Borkovec, Rev. Mod. Phys. 62, 251 (1990).


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