Efficient Implementation of Cluster Expansion Models in Surface Kinetic Monte Carlo Simulations with Lateral Interactions: Subtraction Schemes,Supersites, and the Supercluster Contraction

While lateral interaction models for reactions at surfaces have steadily gained popularity and grown in terms of complexity, their use in chemical kinetics has been impeded by the low performance of current kinetic Monte Carlo (KMC) algorithms. The origins of the additional computational cost in KMC simulations with lateral interactions are traced back to the more elaborate cluster expansion Hamiltonian, the more extensive rate updating, and to the impracticality of rate-catalog-based algorithms for interacting adsorbate systems. Favoring instead site-based algorithms, we propose three ways to reduce the cost of KMC simulations: (1) representing the lattice energy by a smaller Supercluster Hamiltonian without loss of accuracy, (2) employing the subtraction schemes for updating key quantities in the simulation that undergo only small, local changes during a reaction event, and (3) applying efficient search algorithms from a set of established methods (supersite approach). The cost of the resulting algorithm is fixed with respect to the number of lattice sites for practical lattice sizes and scales with the square of the range of lateral interactions. The overall added cost of including a complex lateral interaction model amounts to less than a factor 3. Practical issues in implementation due to finite numerical accuracy are discussed in detail, and further suggestions for treating long-range lateral interactions are made. We conclude that, while KMC simulations with complex lateral interaction models are challenging, these challenges can be overcome by modifying the established variable step-size method by employing the supercluster, subtraction, and supersite algorithms (SSS-VSSM). © 2019 Wiley Periodicals, Inc.     

The influence of defects on the morphology of Si (111) etched in NH4F

We have implemented a kinetic Monte Carlo (KMC) simulation to study the effects of wafer miscut and wafer defects on the morphologies of Si (111) surfaces etched in NH4F. Although a conventional KMC simulation reproduced previously published results, it failed to produce the morphologies observed in our experiments. By introducing both dopant sites and lattice defect sites into the model, we are able to simulate samples having different dopant elements and densities as well as different defect concentrations. Using the modified KMC simulation, the simulated surface morphologies agree well with the morphologies observed in our experiments. The enhanced model also gives insights to the formation mechanism for multiple level stacking pits, a notable morphology on the etched surfaces of samples with very small miscut angles.     

The enhanced extended phenomenological kinetics method to deal with timescale disparity problem among different reaction pathways

Kinetic Monte Carlo method can provide valuable mechanistic insights for catalytic systems. Nonetheless, it suffers from the notorious problem of timescale disparity due to the existence of the complex catalytic network that consists of fast events and slow events. Previously, we have proposed the extended phenomenological kinetics (XPK) method that effectively deals with the timescale disparity problem between diffusion and reaction. However, it remains a great challenge to simulate systems with timescale disparity among different reaction pathways, which is important when selectivity is the major concern. In this study, we implement the enhanced XPK method to address this problem. The new algorithm works by identifying states connected through fast transitions and compressing them into a “superstate” when the chosen states satisfy a local steadystate condition. This state compression algorithm simplifies the reaction network by concealing the fast transitions. The accuracy and efficiency of the algorithm are demonstrated by two model systems: selective catalytic hydrogenation and selective catalytic decomposition. The enhanced XPK method is expected to be beneficial to the kinetic simulations of catalytic systems, especially those with complex reaction networks.     

Kinetic Monte Carlo study of binary diffusion in silicalite

We report a Kinetic Monte Carlo (KMC) study of the diffusion of linear n-hexane (nC6) and 2,2-dimethylbutane (22DMB) mixture in zeolite silicalite. We first investigated the loading dependences of single component self- and corrected diffusivities of nC6 at 300 K. Anisotropic transition rates are implemented to account for the distribution of the molecules within the zeolite framework. Repulsive guest-guest interactions are modeled using the parameter introduced by Reed and Ehrlich (Surf. Sci. 102:588–601, 1981). The results are in good agreement with recent experimental Quasi Elastic Neutron Scattering data of Jobic et al. (J. Phys. Chem. B 110:2195–2201, 2006), although the influence of the adsorption isotherm inflection is not reproduced. The binary diffusion study of nC6/22DMB mixtures was performed by implementing the nC6 transition rates used for the single component study while 22DMB molecules propagate via intersection-intersection hops. This KMC model allows for different saturation capacities and accounts for interactions between molecules by introducing f _ij parameters. Results show the large impact of guest-guest interactions between nC6 and 22DMB on both self- and corrected diffusivities of the two components. Molecule-size effects are found to be predominant near 22DMB saturation capacity. Acceleration/deceleration effects already described in the literature are confirmed.     

Kinetic Monte Carlo study of submonolayer heteroepitaxial growth comparing Cu/Ni and Pt/Ni on Ni(100)

The surface patterns formed during submonolayer Cu/Ni and Pt/Ni heteroepitaxy upon a Ni(100) substrate have been investigated by kinetic Monte Carlo (KMC) simulations. The two-dimensional (2D) KMC simulations are based upon rate constants for a complete nearest-neighbor set of 729 uncorrelated Cu or Pt atoms and/or Ni site-to-site hopping mobilities. The rate constant activation energies are determined by classical-potential total-energy calculations using an embedded-atom method potential function from the literature. We find that diffusion of Cu atoms occurs at a faster rate and Pt atoms at a slower rate than that of Ni atoms on the flat Ni(100) surface, and the initial nucleation and growth patterns of 2D islands and the kinetic versus thermodynamic control of the growth vary as a consequence. In the temperature and deposition time regime in which we work, the Cu/Ni systems show less than random mixing, while the Pt/Ni systems show more than random mixing. The Cu/Ni system has bonding energies that result in a tendency to segregate toward subdomains of pure Ni and Cu, though kinetic effects in the epitaxy trap the development of the system at small subdomain sizes. The Pt/Ni system has bonding energies giving a tendency to intermix completely, while epitaxial kinetic effects modestly interfere with the complete mixing. The kinetically determined island morphologies under various Cu/Ni and Pt/Ni compositions and deposition rates differ substantially over time periods that are long on the deposition time scale, and therefore the island patterns can become frozen in place.     

Kinetic Monte Carlo modeling of chemical reactions coupled with heat transfer

In this paper, we describe two types of effective events for describing heat transfer in a kinetic Monte Carlo (KMC) simulation that may involve stochastic chemical reactions. Simulations employing these events are referred to as KMC-TBT and KMC-PHE. In KMC-TBT, heat transfer is modeled as the stochastic transfer of "thermal bits" between adjacent grid points. In KMC-PHE, heat transfer is modeled by integrating the Poisson heat equation for a short time. Either approach is capable of capturing the time dependent system behavior exactly. Both KMC-PHE and KMC-TBT are validated by simulating pure heat transfer in a rod and a square and modeling a heated desorption problem where exact numerical results are available. KMC-PHE is much faster than KMC-TBT and is used to study the endothermic desorption of a lattice gas. Interesting findings from this study are reported.     

Insights on the role of (dis)order from protein-protein interaction linear free-energy relationships

Protein-protein interactions (PPIs) are remarkably diverse and form the basis for various cellular functions. PPIs can be classified as ordered or disordered; the disordered ones do not have a well-defined structure prior to association, which is an exception to the conventional structure-function relationship. The occurrence of disordered proteins in functional roles is not explained by the conventional structure-function paradigm, and at present there is no clear understanding of the differences between the natures of these two PPIs. In this work, we studied the relationship between the kinetics and thermodynamics in PPIs to provide insights into the latter, with possible implications for the former. Analyzing the experimental data for various protein complexes, we found linear free-energy behavior with a striking kinetic difference between these two types of interactions. Binding affinities of (dis)ordered proteins are correlated with their (association) dissociation rates. Our observation, combined with the correspondence between biological activity and affinity, suggests that selection pressure on the dissociation or association kinetics in a functional context necessitates the presence of (dis)order in the structure.     

Kinetic Monte Carlo simulations of nucleation and growth in electrodeposition

Nucleation and growth during bulk electrodeposition is studied using kinetic Monte Carlo (KMC) simulations. Ion transport in solution is modeled using Brownian dynamics, and the kinetics of nucleation and growth are dependent on the probabilities of metal-on-substrate and metal-on-metal deposition. Using this approach, we make no assumptions about the nucleation rate, island density, or island distribution. The influence of the attachment probabilities and concentration on the time-dependent island density and current transients is reported. Various models have been assessed by recovering the nucleation rate and island density from the current-time transients.     

Spatially adaptive lattice coarse-grained Monte Carlo simulations for diffusion of interacting molecules

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.     

Tracking Explicit Chain Sequence in Kinetic Monte Carlo Simulations

The execution of individual KMC events can become a major computational bottleneck in the simulation of sequences along chains using KMC because of complex data storage schemes required to record the sequence of each chain. The execution of a KMC event can be very time‐consuming because searching, moving, and modifying all the data detailing a chain to reflect the transformation as a result of a chemical reaction event can be computationally expensive. To address this issue, we developed a new data storage scheme for recording sequence, which can significantly improve calculation speed without affecting the information content of the calculations. By using the proposed data storage scheme, the computational time can be reduced significantly from 12 h to 4 min for our test reaction system.

     

Kinetic Monte Carlo simulations of the interaction of oxygen with Pt(111)

The adsorption, dissociation, diffusion, and desorption of oxygen interacting with the Pt(111) surface have been studied using kinetic Monte Carlo simulations. This study has been motivated by uncertainties in the theoretical and the experimental derivations of O(2)Pt(111) reaction barriers. The simulations reproduce all known experimental data within basically one set of parameters, thus yielding microscopic insights into the elementary reaction steps occurring in the interaction of oxygen with Pt(111) and providing reliable estimates for adsorption energies and diffusion and desorption barriers. In particular, we confirm that the distance of oxygen atoms directly after dissociation is caused by ballistic hot atom motion rather than by diffusive motion. We address the equilibrium structure of oxygen atoms at high coverages. At low temperatures, chains of oxygen pairs are formed. We show that this mechanism can be explained by a lowered dissociation in the vicinity of already adsorbed atoms. Finally we discuss the role of the lateral interaction between the oxygen atoms in the oxygen desorption process.     

Kinetic capillary electrophoresis (KCE): a conceptual platform for kinetic homogeneous affinity methods

We propose kinetic capillary electrophoresis (KCE) as a conceptual platform for the development of kinetic homogeneous affinity methods. KCE is defined as the CE separation of species that interact during electrophoresis. Depending on how the interaction is arranged, different KCE methods can be designed. All KCE methods are described by the same mathematics: the same system of partial differential equations with only initial and boundary conditions being different. Every qualitatively unique set of initial and boundary conditions defines a unique KCE method. Here, we (i) present the theoretical bases of KCE, (ii) define four new KCE methods, and (iii) propose a multimethod KCE toolbox as an integrated kinetic technique. Using the KCE toolbox, we were able to, for the first time, observe high-affinity (specific) and low-affinity (nonspecific) interactions within the same protein-ligand pair. The concept of KCE allows for the creation of an expanding toolset of powerful kinetic homogeneous affinity methods, which will find their applications in studies of biomolecular interactions, quantitative analyses, and selecting affinity probes and drug candidates from complex mixtures.     

An off-lattice, self-learning kinetic Monte Carlo method using local environments

We present a method called local environment kinetic Monte Carlo (LE-KMC) method for efficiently performing off-lattice, self-learning kinetic Monte Carlo (KMC) simulations of activated processes in material systems. Like other off-lattice KMC schemes, new atomic processes can be found on-the-fly in LE-KMC. However, a unique feature of LE-KMC is that as long as the assumption that all processes and rates depend only on the local environment is satisfied, LE-KMC provides a general algorithm for (i) unambiguously describing a process in terms of its local atomic environments, (ii) storing new processes and environments in a catalog for later use with standard KMC, and (iii) updating the system based on the local information once a process has been selected for a KMC move. Search, classification, storage and retrieval steps needed while employing local environments and processes in the LE-KMC method are discussed. The advantages and computational cost of LE-KMC are discussed. We assess the performance of the LE-KMC algorithm by considering test systems involving diffusion in a submonolayer Ag and Ag-Cu alloy films on Ag(001) surface.     

Block-localized wavefunction (BLW) method at the density functional theory (DFT) level

The block-localized wavefunction (BLW) approach is an ab initio valence bond (VB) method incorporating the efficiency of molecular orbital (MO) theory. It can generate the wavefunction for a resonance structure or diabatic state self-consistently by partitioning the overall electrons and primitive orbitals into several subgroups and expanding each block-localized molecular orbital in only one subspace. Although block-localized molecular orbitals in the same subspace are constrained to be orthogonal (a feature of MO theory), orbitals between different subspaces are generally nonorthogonal (a feature of VB theory). The BLW method is particularly useful in the quantification of the electron delocalization (resonance) effect within a molecule and the charge-transfer effect between molecules. In this paper, we extend the BLW method to the density functional theory (DFT) level and implement the BLW-DFT method to the quantum mechanical software GAMESS. Test applications to the pi conjugation in the planar allyl radical and ions with the basis sets of 6-31G(d), 6-31+G(d), 6-311+G(d,p), and cc-pVTZ show that the basis set dependency is insignificant. In addition, the BLW-DFT method can also be used to elucidate the nature of intermolecular interactions. Examples of pi-cation interactions and solute-solvent interactions will be presented and discussed. By expressing each diabatic state with one BLW, the BLW method can be further used to study chemical reactions and electron-transfer processes whose potential energy surfaces are typically described by two or more diabatic states.     

Lateral interactions and multi-isotherms: nitrogen recombination from Rh(111)

Lateral adsorbate-adsorbate interactions result in variation of the desorption rate constants with coverage. This effect can be studied in great detail from the shape of a multi-isotherm. To produce the multi-isotherm, the temperature is increased in a (semi)stepwise fashion to some temperature, followed by maintaining this temperature for a prolonged time. Then, the temperature is stepped to a higher value and held constant at this new temperature. This cycle is continued until all of the adsorbates have desorbed. Using a detailed kinetic Monte Carlo model and an optimization algorithm based on Evolutionary Strategy, we are able to reproduce the shape of the experimentally measured multi-isotherm of nitrogen on Rh(111) and obtain the lateral interactions between the nitrogen atoms.     

Kinetic Monte Carlo study of proton binding at the metal oxide/electrolyte interface

The kinetics of proton binding at the metal oxide/electrolyte interface is studied using the kinetic Monte Carlo method. The influence of system properties (surface site density, interfacial dielectric constant, surface energetic heterogeneity) on the equilibrium and kinetic surface coverage is shown. It is shown that the kinetic properties are much more sensitive to lateral interactions than the equilibrium ones. The assumption of energetic heterogeneity rapidly changes the time scales of the processes as well as the time interval between two subsequent elementary processes. In this paper, the atomistic insight into the kinetics of H(+) ion uptake at the metal oxide/electrolyte interface is presented for the first time.     

CO oxidation reaction on Pt(111) studied by the dynamic Monte Carlo method including lateral interactions of adsorbates

The dynamics of adsorbate structures during CO oxidation on Pt(111) surfaces and its effects on the reaction were studied by the dynamic Monte Carlo method including lateral interactions of adsorbates. The lateral interaction energies between adsorbed species were calculated by the density functional theory method. Dynamic Monte Carlo simulations were performed for the oxidation reaction over a mesoscopic scale, where the experimentally determined activation energies of elementary paths were altered by the calculated lateral interaction energies. The simulated results reproduced the characteristics of the microscopic and mesoscopic scale adsorbate structures formed during the reaction, and revealed that the complicated reaction kinetics is comprehensively explained by a single reaction path affected by the surrounding adsorbates. We also propose from the simulations that weakly adsorbed CO molecules at domain boundaries promote the island-periphery specific reaction.     

固体表面吸附分子及其振动——Cu(100)Co-c(2×2)体系的研究

A method is proposed to calculate vibrational frequencies and intensities of an adsorbed molecule system with P2mm or P4 symmetry. The method can be used if the system can be considered as a group of coupled oscillators with one freedom per oscillator. The stretch vibrations and lateral interactions of CO molecules adsorbed on Cu(100) face are studied by means of this method. The calculated results show that the lateral force constants have a strong dependence on interaction range assumed. The size effects on vibrational frequencies of adsorbed system are also examined. The results given here are to be expected.     

The role of molecular interactions and interfaces in diffusion: transport diffusivity and evaluation of the Darken approximation

Kinetic Monte Carlo (KMC) simulations are carried out to directly study diffusion of benzene through thin (37-100 nm) NaX zeolite membranes under a gradient in chemical potential. Nonlinearities in adsorbate loading near the membrane boundaries are shown to arise from the difference in adsorbate density between the zeolite and adjacent fluid phase. Direct extraction of the transport diffusivity from gradient KMC simulations enables testing of the Darken approximation. This rigorous approach reveals limitations of the Darken approximation and, for the first time, the potentially complex nonunique functionality and multiplicity of the transport diffusivity for strongly interacting adsorbates. In the companion paper we explore these nonlinear interfacial effects in the context of permeation through both single-crystal and polycrystalline membranes.