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In the presence of multiscale dynamics in a reaction network, direct simulation methods become inefficient as they can only advance the system on the smallest scale. This work presents stochastic averaging techniques to accelerate computations for obtaining estimates of expected values and sensitivities with respect to the steady state distribution. A two-time-scale formulation is used to establish bounds on the bias induced by the averaging method. Further, this formulation provides a framework to create an accelerated "averaged" version of most single-scale sensitivity estimation methods. In particular, we propose the use of a centered ergodic likelihood ratio method for steady state estimation and show how one can adapt it to accelerated simulations of multiscale systems. Finally, we develop an adaptive "batch-means" stopping rule for determining when to terminate the micro-equilibration process. [ABSTRACT FROM AUTHOR]

We model N2 desorption on submonolayer bimetallic surfaces consisting of Co clusters on Pt(111) via first-principles density functional theory-based kinetic Monte Carlo simulations. We find that submonolayer structures are essential to rationalize the high activity of these bimetallics in ammonia decomposition. We show that the N2 desorption temperature on Co/Pt(111) is about 100 K higher than that on Ni/Pt(111), despite Co/Pt(111) binding N weaker at low N coverages. Co/Pt(111) has substantially different lateral interactions than single metals and Ni/Pt. The lateral interactions are rationalized with the d-band center theory. The activity of bimetallic catalysts is the result of heterogeneity of binding energies and reaction barriers among sites, and the most active site can differ on various bimetallics. Our results are in excellent agreement with experimental data and demonstrate for the first time that the zero-coverage descriptor, used until now, for catalyst activity is inadequate due not only to lacking lateral interactions but importantly to presence of multiple sites and a complex interplay of thermodynamics (binding energies, occupation) and kinetics (association barriers) on those sites. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We investigate the decomposition of ammonia on bimetallic surfaces prepared by the deposition of a monolayer of Fe, Co, or Cu on a Pt(111) surface computationally and experimentally. We explore the correlation between predicted activities based on the nitrogen binding energies with experimental decomposition activity on these bimetallic and corresponding monometallic surfaces. Through density functional theory calculations and microkinetic modeling, it is predicted that the Fe-Pt-Pt(111) and Co-Pt-Pt(111) surfaces, with a monolayer of Fe or Co on top of Pt(111), are active toward decomposing ammonia. In contrast, the corresponding subsurface configurations, Pt-Fe-Pt(111) and Pt-Co-Pt(111) are inactive. These predictions were confirmed experimentally through temperature programmed desorption experiments. Decomposition was seen at temperatures below 350 K for the Fe-Pt-Pt(111) and Co-Pt-Pt(111) surfaces. For the Cu/Pt(111) system, the surface, subsurface and parent metals were each predicted to be inactive, consistent with experiments, further validating the model predictions. The stability of these bimetallic surfaces in the presence of adsorbed nitrogen is also discussed. [ABSTRACT FROM AUTHOR]

Molecular dynamics (MD) simulations employing embedded atom method potentials and ultrahigh vacuum (UHV) experiments were carried out to study the mixing process between the Ni and Pt atoms in the Ni/Pt(111) bimetallic system. The barrier for a Ni atom to diffuse from the top surface to the subsurface layer is rather high (around 1.7 eV) as calculated using the nudged elastic band (NEB) method. Analysis of the relaxation dynamics of the Ni atoms showed that they undergo diffusive motion through a mechanism of correlated hops. At 600 K, all Ni atoms remain trapped on the top surface due to large diffusion barriers. At 900 K, the majority of Ni atoms diffuse to the second layer and at 1200 K diffusion to the bulk is observed. We also find that smaller Ni coverages and the presence of Pt steps facilitate the Ni-Pt mixing. By simulated annealing simulations, we found that in the mixed state, the Ni fraction oscillates between layers, with the second layer being Ni-richer at equilibrium. The simulation results at multiple time scales are consistent with the experimental data. [ABSTRACT FROM AUTHOR]

On-lattice kinetic Monte Carlo (KMC) simulations have extensively been applied to numerous systems. However, their applicability is severely limited to relatively short time and length scales. Recently, the coarse-grained MC (CGMC) method was introduced to greatly expand the reach of the lattice KMC technique. Herein, we extend the previous spatial CGMC methods to multicomponent species and/or site types. The underlying theory is derived and numerical examples are presented to demonstrate the method. Furthermore, we introduce the concept of homogenization at the stochastic level over all site types of a spatially coarse-grained cell. Homogenization provides a novel coarsening of the number of processes, an important aspect for complex problems plagued by the existence of numerous microscopic processes (combinatorial complexity). As expected, the homogenized CGMC method outperforms the traditional KMC method on computational cost while retaining good accuracy. [ABSTRACT FROM AUTHOR]

The dissociation of hydrogen on a Pt(111) surface covered with a p(2×2) oxygen phase was investigated using quasiclassical, six-dimensional molecular dynamics. The potential energy surface (PES) used in these simulations was obtained by an iterative novelty sampling algorithm. Compared to molecular beam experiments performed under similar conditions, the simulations give an accurate prediction of the reaction probability via a direct dissociation pathway. When compared to previously reported reaction probability curves for the clean Pt(111) surface, we find that the presence of an oxygen overlayer inhibits the direct pathway to hydrogen dissociation. This inhibition is a function of incident energy and cannot be described by a simple site blocking model. An indirect pathway to dissociation, which was observed in experiments, is not properly captured by the PES. Spatially resolved “reaction maps” indicate that the preferred site for hydrogen dissociation on an oxygen covered Pt surface is the top site of the Pt atom farthest from the adsorbed oxygen atom. [ABSTRACT FROM AUTHOR]

We outline a hybrid multiscale approach for the construction of ab initio potential energy surfaces (PESs) useful for performing six-dimensional (6D) classical or quantum mechanical molecular dynamics (MD) simulations of diatomic molecules reacting at single crystal surfaces. The algorithm implements concepts from the corrugation reduction procedure, which reduces energetic variation in the PES, and uses neural networks for interpolation of smoothed ab initio data. A novelty sampling scheme is implemented and used to identify configurations that are most likely to be predicted inaccurately by the neural network. This hybrid multiscale approach, which couples PES construction at the electronic structure level to MD simulations at the atomistic scale, reduces the number of density functional theory (DFT) calculations needed to specify an accurate PES. Due to the iterative nature of the novelty sampling algorithm, it is possible to obtain a quantitative measure of the convergence of the PES with respect to the number of ab initio calculations used to train the neural network. We demonstrate the algorithm by first applying it to two analytic potentials, which model the H2/Pt(111) and H2/Cu(111) systems. These potentials are of the corrugated London-Eyring-Polanyi-Sato form, which are based on DFT calculations, but are not globally accurate. After demonstrating the convergence of the PES using these simple potentials, we use DFT calculations directly and obtain converged semiclassical trajectories for the H2/Pt(111) system at the PW91/generalized gradient approximation level. We obtain a converged PES for a 6D hydrogen-surface dissociation reaction using novelty sampling coupled directly to DFT. These results, in excellent agreement with experiments and previous theoretical work, are compared to previous simulations in order to explore the sensitivity of the PES (and therefore MD) to the choice of exchange and correlation functional. Despite having a lower energetic corrugation in our PES, we obtain a broader reaction probability curve than previous simulations, which is attributed to increased geometric corrugation in the PES and the effect of nonparallel dissociation pathways. [ABSTRACT FROM AUTHOR]

While recently derived continuum mesoscopic equations successfully bridge the gap between microscopic and macroscopic physics, so far they have been derived only for simple lattice models. In this paper, general deterministic continuum mesoscopic equations are derived rigorously via nonequilibrium statistical mechanics to account for multiple interacting surface species and multiple processes on multiple site types and/or different crystallographic planes. Adsorption, desorption, reaction, and surface diffusion are modeled. It is demonstrated that contrary to conventional phenomenological continuum models, microscopic physics, such as the interaction potential, determines the final form of the mesoscopic equation. Models of single component diffusion and binary diffusion of interacting particles on single-type site lattice and of single component diffusion on complex microporous materials’ lattices consisting of two types of sites are derived, as illustrations of the mesoscopic framework. Simplification of the diffusion mesoscopic model illustrates the relation to phenomenological models, such as the Fickian and Maxwell-Stefan transport models. It is demonstrated that the mesoscopic equations are in good agreement with lattice kinetic Monte Carlo simulations for several prototype examples studied. [ABSTRACT FROM AUTHOR]

Monte Carlo (MC) simulation of most spatially distributed systems is plagued by several problems, namely, execution of one process at a time, large separation of time scales of various processes, and large length scales. Recently, a coarse-grained Monte Carlo (CGMC) method was introduced that can capture large length scales at reasonable computational times. An inherent assumption in this CGMC method revolves around a mean-field closure invoked in each coarse cell that is inaccurate for short-ranged interactions. Two new approaches are explored to improve upon this closure. The first employs the local quasichemical approximation, which is applicable to first nearest-neighbor interactions. The second, termed multiscale CGMC method, employs singular perturbation ideas on multiple grids to capture the entire cluster probability distribution function via short microscopic MC simulations on small, fine-grid lattices by taking advantage of the time scale separation of multiple processes. Computational strategies for coupling the fast process at small length scales (fine grid) with the slow processes at large length scales (coarse grid) are discussed. Finally, the binomial τ-leap method is combined with the multiscale CGMC method to execute multiple processes over the entire lattice and provide additional computational acceleration. Numerical simulations demonstrate that in the presence of fast diffusion and slow adsorption and desorption processes the two new approaches provide more accurate solutions in comparison to the previously introduced CGMC method. [ABSTRACT FROM AUTHOR]

Recently, Gillespie introduced the τ-leap approximate, accelerated stochastic Monte Carlo method for well-mixed reacting systems [J. Chem. Phys. 115, 1716 (2001)]. In each time increment of that method, one executes a number of reaction events, selected randomly from a Poisson distribution, to enable simulation of long times. Here we introduce a binomial distribution τ-leap algorithm (abbreviated as BD-τ method). This method combines the bounded nature of the binomial distribution variable with the limiting reactant and constrained firing concepts to avoid negative populations encountered in the original τ-leap method of Gillespie for large time increments, and thus conserve mass. Simulations using prototype reaction networks show that the BD-τ method is more accurate than the original method for comparable coarse-graining in time. © 2005 American Institute of Physics. [ABSTRACT FROM AUTHOR]

While lattice kinetic Monte Carlo (KMC) methods provide insight into numerous complex physical systems governed by interatomic interactions, they are limited to relatively short length and time scales. Recently introduced coarse-grained Monte Carlo (CGMC) simulations can reach much larger length and time scales at considerably lower computational cost. In this paper we extend the CGMC methods to spatially adaptive meshes for the case of surface diffusion (canonical ensemble). We introduce a systematic methodology to derive the transition probabilities for the coarse-grained diffusion process that ensure the correct dynamics and noise, give the correct continuum mesoscopic equations, and satisfy detailed balance. Substantial savings in CPU time are demonstrated compared to microscopic KMC while retaining high accuracy. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Describes a model developed to investigate a gel-to-zeolite transformation as a possible growth mechanism through association and rearrangements of extended precursor structures. Use of continuum time lattice Monte Carlo simulations in the study; Use of model to study the morphology of zeolite L nanocrystals grown from an amorphous microporous precursor gel.

The adsorption of atomic nitrogen on Ni/Pt(111) surface bimetallics has been investigated as a function of the local microstructure of Ni and Pt atoms via density functional theory (DFT) calculations. Microstructures include surface and subsurface Ni atoms on Pt(111) as limiting cases, and also small clusters of Ni in the first and/or second layer of Pt. It is shown that the binding energy of N can be approximated as a perturbation from that on the host metal (Pt) with a linear short-ranged correction from the guest metal (Ni) that accounts for the coordination environment of nitrogen up to the 3rd nearest Ni neighbor. This model is rationalized with the d-band center theory. Coverage effects are also included. The model can be parameterized with a limited number of DFT calculations and applied to other bimetallic catalysts to estimate the coverage dependent binding energy on complex metal microstructures. [ABSTRACT FROM AUTHOR]

We propose non-parametric methods for both local and global sensitivity analysis of chemical reaction models with correlated parameter dependencies. The developed mathematical and statistical tools are applied to a benchmark Langmuir competitive adsorption model on a close packed platinum surface, whose parameters, estimated from quantum-scale computations, are correlated and are limited in size (small data). The proposed mathematical methodology employs gradient-based methods to compute sensitivity indices. We observe that ranking influential parameters depends critically on whether or not correlations between parameters are taken into account. The impact of uncertainty in the correlation and the necessity of the proposed non-parametric perspective are demonstrated. [ABSTRACT FROM AUTHOR]