When atomic-scale resolution is not enough: Spatial effects in in situ model catalyst studies

We investigate transport effects in in situ studies of defined model catalysts using a multi-scale modeling approach integrating first-principles kinetic Monte Carlo simulations into a fluid dynamical treatment. We specifically address two isothermal flow setups: i) a channel flow with the gas-stream approaching the single crystal from the side, as is representative for reactor scanning tunneling microscopy experiments; and ii) a stagnation flow with perpendicular impingement. Using the CO oxidation at RuO2 (110) as showcase we obtain substantial variations in the gas-phase pressures between the inlet and the catalyst surface. In the channel geometry the mass transfer limitations lead furthermore to pronounced lateral changes in surface composition across the catalyst surface. This prevents the aspired direct relation between activity and catalyst structure. For the stagnation flow the lateral variations are restricted to the edges of the catalyst. This allows to access the desired structure-activity relation using a simple model.Comment: 22 pages, 7 figure

Nearest-Neighbor Interaction Systems in the Tensor-Train Format

Low-rank tensor approximation approaches have become an important tool in the scientific computing community. The aim is to enable the simulation and analysis of high-dimensional problems which cannot be solved using conventional methods anymore due to the so-called curse of dimensionality. This requires techniques to handle linear operators defined on extremely large state spaces and to solve the resulting systems of linear equations or eigenvalue problems. In this paper, we present a systematic tensor-train decomposition for nearest-neighbor interaction systems which is applicable to a host of different problems. With the aid of this decomposition, it is possible to reduce the memory consumption as well as the computational costs significantly. Furthermore, it can be shown that in some cases the rank of the tensor decomposition does not depend on the network size. The format is thus feasible even for high-dimensional systems. We will illustrate the results with several guiding examples such as the Ising model, a system of coupled oscillators, and a CO oxidation model

CO Oxidation on a Pd(100)

A stagnation flow reactor has been designed and characterized for both experimental and modeling studies of single-crystal model catalysts in heterogeneous catalysis. Using CO oxidation over a Pd(100) single crystal as a showcase, we have employed planar laser-induced fluorescence (PLIF) to visualize the CO2 distribution over the catalyst under reaction conditions and subsequently used the 2D spatially resolved gas phase data to characterize the stagnation flow reactor. From a comparison of the experimental data and the stagnation flow model, it was found that characteristic stagnation flow can be achieved with the reactor. Furthermore, the combined stagnation flow/PLIF/modeling approach makes it possible to estimate the turnover frequency (TOF) of the catalytic surface from the measured CO2 concentration profiles above the surface and to predict the CO2, CO and O2 concentrations at the surface under reaction conditions

A Fuzzy Classification Framework to Identify Equivalent Atoms in Complex Materials and Molecules

The nature of an atom in a bonded structure -- such as in molecules, in nanoparticles or solids, at surfaces or interfaces -- depends on its local atomic environment. In atomic-scale modeling and simulation, identifying groups of atoms with equivalent environments is a frequent task, to gain an understanding of the material function, to interpret experimental results or to simply restrict demanding first-principles calculations. While routine, this task can often be challenging for complex molecules or non-ideal materials with breaks of symmetries or long-range order. To automatize this task, we here present a general machine-learning framework to identify groups of (nearly) equivalent atoms. The initial classification rests on the representation of the local atomic environment through a high-dimensional smooth overlap of atomic positions (SOAP) vector. Recognizing that not least thermal vibrations may lead to deviations from ideal positions, we then achieve a fuzzy classification by mean-shift clustering within a low-dimensional embedded representation of the SOAP points as obtained through multidimensional scaling. The performance of this classification framework is demonstrated for simple aromatic molecules and crystalline Pd surface examples.Comment: Accepted manuscript in Journal of Chemical Physics. Repositories of the package (DECAF): DOI:10.17617/3.U7VKBM or https://gitlab.mpcdf.mpg.de/klai/deca

Examination of the concept of degree of rate control by first-principles kinetic Monte Carlo simulations

The conceptual idea of degree of rate control (DRC) approaches is to identify the "rate limiting step" in a complex reaction network by evaluating how the overall rate of product formation changes when a small change is made in one of the kinetic parameters. We examine two definitions of this concept by applying it to first-principles kinetic Monte Carlo simulations of the CO oxidation at RuO2(110). Instead of studying experimental data we examine simulations, because in them we know the surface structure, reaction mechanism, the rate constants, the coverage of the surface and the turn-over frequency at steady state. We can test whether the insights provided by the DRC are in agreement with the results of the simulations thus avoiding the uncertainties inherent in a comparison with experiment. We find that the information provided by using the DRC is non-trivial: It could not have been obtained from the knowledge of the reaction mechanism and of the magnitude of the rate constants alone. For the simulations the DRC provides furthermore guidance as to which aspects of the reaction mechanism should be treated accurately and which can be studied by less accurate and more efficient methods. We therefore conclude that a sensitivity analysis based on the DRC is a useful tool for understanding the propagation of errors from the electronic structure calculations to the statistical simulations in first-principles kinetic Monte Carlo simulations.Comment: 27 pages including 5 figures; related publications can be found at http://www.fhi-berlin.mpg.de/th/th.htm

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

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 RuO2(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

Kinetic Trapping of Charge-Transfer Molecules at Metal Interfaces

Despite the common expectation that conjugated organic molecules on metals adsorb in a flat-lying layer, several recent studies have found coverage-dependent transitions to upright-standing phases, which exhibit notably different physical properties. In this work, we argue that from an energetic perspective, thermodynamically stable upright-standing phases may be more common than hitherto thought. However, for kinetic reasons, this phase may often not be observed experimentally. Using first-principles kinetic Monte Carlo simulations, we find that the structure with lower molecular density is (almost) always formed first, reminiscent of Ostwald’s rule of stages. The phase transitions to the upright-standing phase are likely to be kinetically hindered under the conditions typically used in surface science. The simulation results are experimentally confirmed for the adsorption of tetracyanoethylene on Cu(111) using infrared and X-ray photoemission spectroscopy. Investigating both the role of the growth conditions and the energetics of the interface, we find that the time for the phase transition is determined mostly by the deposition rate and, thus, is mostly independent of the nature of the molecule

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

Many problems in computational materials science and chemistry require the evaluation of expensive functions with locally rapid changes, such as the turn-over frequency of first principles kinetic Monte Carlo models for heterogeneous catalysis. Because of the high computational cost, it is often desirable to replace the original with a surrogate model, e.g., for use in coupled multiscale simulations. The construction of surrogates becomes particularly challenging in high-dimensions. Here, we present a novel version of the modified Shepard interpolation method which can overcome the curse of dimensionality for such functions to give faithful reconstructions even from very modest numbers of function evaluations. The introduction of local metrics allows us to take advantage of the fact that, on a local scale, rapid variation often occurs only across a small number of directions. Furthermore, we use local error estimates to weigh different local approximations, which helps avoid artificial oscillations. Finally, we test our approach on a number of challenging analytic functions as well as a realistic kinetic Monte Carlo model. Our method not only outperforms existing isotropic metric Shepard methods but also state-of-the-art Gaussian process regression