A practical approach to the sensitivity analysis for kinetic Monte Carlo simulation of heterogeneous catalysis

Abstract

Lattice kinetic Monte Carlo simulations have become a vital tool for predictive quality atomistic understanding of complex surface chemical reaction kinetics over a wide range of reaction conditions. In order to expand their practical value in terms of giving guidelines for the atomic level design of catalytic systems, it is very desirable to readily evaluate a sensitivity analysis for a given model. The result of such a sensitivity analysis quantitatively expresses the dependency of the turnover frequency, being the main output variable, on the rate constants entering the model. In the past, the application of sensitivity analysis, such as degree of rate control, has been hampered by its exuberant computational effort required to accurately sample numerical derivatives of a property that is obtained from a stochastic simulation method. In this study, we present an efficient and robust three-stage approach that is capable of reliably evaluating the sensitivity measures for stiff microkinetic models as we demonstrate using the CO oxidation on RuO(110) as a prototypical reaction. In the first step, we utilize the Fisher information matrix for filtering out elementary processes which only yield negligible sensitivity. Then we employ an estimator based on the linear response theory for calculating the sensitivity measure for non-critical conditions which covers the majority of cases. Finally, we adapt a method for sampling coupled finite differences for evaluating the sensitivity measure for lattice based models. This allows for an efficient evaluation even in critical regions near a second order phase transition that are hitherto difficult to control. The combined approach leads to significant computational savings over straightforward numerical derivatives and should aid in accelerating the nano-scale design of heterogeneous catalysts.

Local-metrics error-based Shepard interpolation as surrogate for highly non-linear material models in high dimensions

“…The reduced version of the model employed here was introduced by Gelß et al 41 and is obtained by excluding all processes involving br sites. It has been shown that chemical kinetics is mainly controlled by the cus sites [42][43][44] and that the reduced model reproduces the results of the full model quantitatively for many reaction conditions. 41 Being computationally cheap, the reduced model can be evaluated for a large number of different input parameter values, which makes it a valuable test problem for our interpolation method.…”

“…III B 2, we needed 10 000 results for reference, which with more complex multi-species models could cost vast amounts of computational time. On the other hand, the RuO 2 CO oxidation model has been characterized in detail both in (p CO , p O 2 , T )-space 40,[46][47][48][49] and in rate constant space [42][43][44] and its behavior is well understood. This makes it ideal for testing new theoretical developments such as the one presented here.…”

“…Such values lay close to the anticipated (second order) phase transition. 44 We define the limits of the interpolation domain such as to encompass a change in each of the rate constants of four orders of magnitude in total (i.e., two orders of magnitude higher and lower than the default, cf. Table I).…”

A Practical Guide to Surface Kinetic Monte Carlo Simulations

“…A positive (negative) DRC signifies that the reaction rate will increase (decrease) when increasing k I , whereas a value of zero signifies that the reaction rate is insensitive to variations in k I . The DRCs follow a sum rule, which states that the sum of all DRCs is equal to one (Meskine et al, 2009; Hoffmann et al, 2017). A single non-zero DRC equal to one then signifies a single rate-limiting step in the reaction mechanism, while in general several steps can be rate-limiting at the same time.…”

“…Relying instead on a finite-difference sampling, very long simulation times are typically required to reduce the statistical error sufficiently (Meskine et al, 2009). A more efficient three-stage approach has recently been proposed (Hoffmann et al, 2017), which allows for the direct sampling of sensitivity measures from a single KMC trajectory.…”