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An Introduction to Kinetic Monte Carlo Simulations of Surface Reactions pp 73–119Cite as

How to Get Kinetic Parameters

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Part of the book series: Lecture Notes in Physics ((LNP,volume 856))

Abstract

This chapter shows how rate constants can either be calculated or be derived from experimental results. Calculating rate constants involves determining the initial and the transition state of a process, the energies of these states, and their partition functions. We show that the general expression for the partition functions can often be simplified when a degree of freedom is a vibration, a rotation, or a free translation. Recipes can be given for how to combine partition functions to get rate constants for processes like Langmuir–Hinshelwood and Eley–Rideal reactions, adsorption and desorption, and diffusion. The phenomenological or macroscopic equation is the essential equation to get rate constants from experiments. It is shown how to use it for simple desorption, simple and dissociative adsorption, uni- and bimolecular reactions, and diffusion. Lateral interactions can affect rate constants substantially, but because they are relatively weak, special attention needs to be given to the reliability of calculations of these interactions. Cross validation and Bayesian model selection are discussed in relation to the cluster expansion for these interactions.

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Notes

  1. 1.

    If one determines the activation energy E act by a linear regression of a set of rate constants at different temperatures, then this energy is not exactly equal to E bar+E zp. This is because the factors \((k_{\mathrm{B}}T/h)(\tilde{Q}^{\ddagger}/\tilde{Q})\) also give a small contribution to E act. See the discussion at the end of Sect. 4.2.2.

  2. 2.

    Strictly speaking this is not always true. There may be a factor in the quantum version that is absent in the classical one, and that is related to the statistics of identical particles. See for example the geometry factor in Eqs. (4.22) and (4.23).

  3. 3.

    There are actually two more factors [7]. There is the partition function of the electronic states Q el and the partition function of the spins of the nuclei Q nucl. We will ignore both. The electronic ground state defines the potential energy of the system, so the partition function is defined only by the summation in Eq. (4.11). As the electronic excitation energies are, except for rare case, much larger than the thermal energy, we get Q el=1. The spin state of the nuclei generally does not change during a reaction. So its partition functions for the transition and initial state cancel in the expression for the rate constant, and can therefore be ignored.

  4. 4.

    Note that below room temperature this expression should not be used for molecular hydrogen. The rotational excitations for this molecule are so high, that the high-temperature approximation only becomes valid at higher temperatures.

  5. 5.

    It may be that there is a very low barrier for diffusion of the adsorbed molecule. In that case the partition function of the initial or transition state will have a 2D translational partition function for the center of mass motion as a factor. See the example of CO desorption in Sect. 4.4.6.

  6. 6.

    Parts of Sect. 4.5.4 have been reprinted with permission from A.P.J. Jansen, C. Popa, Bayesian approach to the calculation of lateral interactions: NO/Rh(111), Phys. Rev. B 78, 085404 (2008). Copyright 2008, American Physical Society.

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  1. ST/SKA, Eindhoven University of Technology, Eindhoven, Netherlands

    A. P. J. Jansen

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Jansen, A.P.J. (2012). How to Get Kinetic Parameters. In: An Introduction to Kinetic Monte Carlo Simulations of Surface Reactions. Lecture Notes in Physics, vol 856. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29488-4_4

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