Unity Bond Index-quadratic Exponential Potential Research Articles

Hierarchical Multiscale Mechanism Development for Methane Partial Oxidation and Reforming and for Thermal Decomposition of Oxygenates on Rh

A thermodynamically consistent C1 microkinetic model is developed for methane partial oxidation and reforming and for oxygenate (methanol and formaldehyde) decomposition on Rh via a hierarchical multiscale methodology. Sensitivity analysis is employed to identify the important parameters of the semiempirical unity bond index quadratic exponential potential (UBI-QEP) method and these parameters are refined using quantum mechanical density functional theory. With adjustment of only two pre-exponentials in the CH4 oxidation subset, the C1 mechanism captures a multitude of catalytic partial oxidation (CPOX) and reforming experimental data as well as thermal decomposition of methanol and formaldehyde. We validate the microkinetic model against high-pressure, spatially resolved CPOX experimental data. Distinct oxidation and reforming zones are predicted to exist, in agreement with experiments, suggesting that hydrogen is produced from reforming of methane by H2O formed in the oxidation zone. CO is produced catalytically by partial oxidation up to moderately high pressures, with water-gas shift taking place in the gas-phase at sufficiently high pressures resulting in reduction of CO selectivity.

A thermodynamically consistent surface reaction mechanism for CO oxidation on Pt

The thermodynamic inconsistency of catalytic combustion reaction mechanisms has been a long-standing, fundamental, and practical problem. Here, we develop a thermodynamically consistent catalytic reaction mechanism for CO oxidation on Pt. First, we propose a modification of the bond index of the unity bond index–quadratic exponential potential (UBI-QEP) semiempirical framework for calculation of the activation energy of the Langmuir–Hinshelwood-type bimolecular surface reaction between co-adsorbed CO ∗ and O ∗ . Thermodynamic consistency is then ensured in the reaction mechanism by combining the semiempirical UBI-QEP theory, statistical mechanics, and constraint-based optimization against experimental data. Atmospheric pressure ignition and ultrahigh vacuum molecular beam experiments are selected as targets for optimization. The optimized mechanism is validated against redundant experiments, including temperature-programmed desorption, temperature-programmed reaction, and molecular beam experiments. Our microkinetic model is able to capture multiple types of data while being thermodynamically consistent over a wide range of conditions.

UBI-QEP Analysis for the Mechanism of Fischer-Tropsch Synthesis

The unity bond index-quadratic exponential potential(UBI-QEP) model is used to evaluate the heat of chemisorption of adsorbed species and activation barriers for the elementary reactions in the mechanisms for Fischer-Tropsch synthesis (FTS) reaction over a model catalyst Co(0001), including carbide mechanism, hydroxycarbene mechanism, and Co insertion mechanism. It is demonstrated that the reaction pathway for the formation of hydrocarbons proposed in the carbide mechanism is energetically favorable. The insertion of CO is the pathway for the formation of oxygenations. Dissociation of adsorbed CO and hydrogenation of C(subscript ads) have higher activation barriers than other elementary steps in the reaction pathway. The energetically preferred pathway to initiate the carbon chain growth is via insertion of CH(subscript 2, ads) intermediate into the carbon-metal bond of CH(subscript 3, ads) or CH(subscript 2, ads) group. The activation barrier for termination of carbon chain propagation by β-H elimination is lower than hydrogenation. The olefins and oxygenates in the primary products during FTS are apt to conduct the secondary reaction via readsorption on the catalyst surface because of its low active energies. Compared with Fe/W(110), the activation barriers for CH(subscript x, ads) hydrogenations and CH(subscript 2, ads) insertion are lower on Co(0001), which results in higher selectivity of methane and more yield of heavy hydrocarbons.

A kinetic Monte Carlo/UBI-QEP model of O2 adsorption on fcc (111) metal surfaces

The previously developed kinetic Monte Carlo model of molecular oxygen adsorption on fcc (1 0 0) metal surfaces has been extended to fcc (1 1 1) surfaces. The model treats uniformly all elementary steps of the process—O2 adsorption, dissociation, recombination, desorption, and atomic oxygen hopping—at various coverages and temperatures. The model employs the unity bond index—quadratic exponential potential (UBI-QEP) formalism to calculate coverage-dependent energetics (atomic and molecular binding energies and activation barriers of elementary steps) and a Metropolis-type algorithm including the Arrhenius-type reaction rates to calculate coverage- and temperature-dependent features, particularly the adsorbate distribution over the surface. Optimal values of non-energetic model parameters (the spatial constraint, a travel distance of “hot” atoms, attempt frequencies of elementary steps) have been chosen. Proper modifications of the fcc (1 0 0) model have been made to reflect structural differences in the fcc (1 1 1) surface, in particular the presence of two different hollow sites (fcc and hcp). Detailed simulations were performed for molecular oxygen adsorption on Ni(1 1 1). We found that at very low coverages, only O2 adsorption and dissociation were effective, while O2 desorption and O2 and O diffusion practically did not occur. At a certain O + O2 coverage, the O2 dissociation becomes the fastest process with a rate one–two orders of magnitude higher than adsorption. Dissociation continuously slows down due to an increase in the activation energy of dissociation and due to the exhaustion of free sites. The binding energies of both molecular and atomic oxygen decrease with coverage, and this leads to greater mobility of atomic oxygen and more pronounced desorption of molecular oxygen. Saturation is observed when the number of adsorbed molecules becomes approximately equal to the number of desorbed molecules. Simulated coverage dependences of the sticking probability and of the atomic binding energy are in reasonable agreement with experimental data. From comparison with the results of the previous work, it appears that the binding energy profiles for Ni(1 1 1) and Ni(1 0 0) have similar shapes, although at any coverage the absolute values of the oxygen binding energy are higher for the (1 0 0) surface. For metals other than Ni, particularly Pt, the model projections were found to be too parameter-dependent and therefore less certain. In such cases further model developments are needed, and we briefly comment on this situation.

The Role of Adsorbate–Adsorbate Interactions in the Rate Controlling Step and the Most Abundant Reaction Intermediate of NH3Decomposition on Ru

N–N adsorbate–adsorbate interactions on a Ru(0001) surface are first estimated using quantum mechanical density functional theory (DFT) calculations, and subsequently incorporated, for the first time, in a detailed microkinetic model for NH3 decomposition on Ru using the unity bond index-quadratic exponential potential (UBI–QEP) method. DFT simulations indicate that the cross N–H interactions are relatively small. Microkinetic model predictions are compared to ultra-high vacuum temperature programmed desorption and atmospheric fixed bed reactor data. The microkinetic model with N–N interactions captures the experimental features quantitatively. It is shown that the N–N interactions significantly alter the rate determining step, the most abundant reaction intermediate, and the maximum N*-coverage, compared to mechanisms that ignore adsorbate–adsorbate interactions.

Monte Carlo modeling of O2 adsorption kinetics on unreconstructed fcc(100) surfaces of metals using UBI?QEP coverage-dependent energetics

We have developed a Monte Carlo (MC) model of dissociative molecular oxygen adsorption on unreconstructed fcc(1 0 0) metal surfaces. The model explicitly and uniformly considers elementary steps/events including adsorption (trapping), dissociation, diffusion (hopping), recombination, and desorption. The unity bond index–quadratic exponential potential (UBI–QEP) formalism was used to calculate the energetics (atomic O and molecular O 2 binding energies, enthalpies and activation barriers), and the kinetic formalism of the MC modeling makes use of Arrhenius-type reaction rates and the Metropolis-type algorithm. The coverage-dependent UBI–QEP formalism was substantially refined, which included the use of (a) hollow sites for atomic oxygen as the only stable ones, (b) rescaling the atomic binding energies due to metal sharing A–M–A, (c) the spatial constraint k , and (d) hot atom traveling distance v . In the kinetic simulations, the preexponential factors were assumed to be proportional to the attempt frequency of the events. The explored coverage range was from 0 to 0.30 ML (monolayer), and the temperature range was from 100 to 700 K. The model makes it possible to calculate a multitude of coverage-dependent parameters of the process, in particular binding energies of molecular and atomic oxygen, the normalized O 2 sticking probability, and the amount and mutual arrangement of neighbors in an overlayer. With inclusion of very weak (<1 kcal/mol) lateral attractive nnn A–A interactions, the model also enables simulations of the development of p(2 × 2)-O and c(2 × 2)-O domains from disordered phases, generating the snapshots of the overlayer structures. The Ni(1 0 0) surface, for which the detailed experimental data on O 2 dissociative adsorption are available, was used as a model system. Practically all model projections, including those concerning the O 2 and O coverages and their binding energies, normalized sticking probabilities, and the overlayer structures, are in good agreement with experimental data. Moreover, the simulated sticking probabilities may be more relevant to the intrinsic Ni(1 0 0) surface behavior because the deviation from the experimental curve at high coverages (>0.25 ML) appears to be due to the formation of the NiO phase. The trends for the binding energies were also modeled for unreconstructed fcc(1 0 0) surfaces of Cu, Ag, and Pd. Because relevant experimental data are scarce, the model results are mostly projections to be verified by experiment.

Monte Carlo modeling of O 2 adsorption kinetics on unreconstructed fcc(1 0 0) surfaces of metals using UBI–QEP coverage-dependent energetics

We have developed a Monte Carlo (MC) model of dissociative molecular oxygen adsorption on unreconstructed fcc(1 0 0) metal surfaces. The model explicitly and uniformly considers elementary steps/events including adsorption (trapping), dissociation, diffusion (hopping), recombination, and desorption. The unity bond index–quadratic exponential potential (UBI–QEP) formalism was used to calculate the energetics (atomic O and molecular O 2 binding energies, enthalpies and activation barriers), and the kinetic formalism of the MC modeling makes use of Arrhenius-type reaction rates and the Metropolis-type algorithm. The coverage-dependent UBI–QEP formalism was substantially refined, which included the use of (a) hollow sites for atomic oxygen as the only stable ones, (b) rescaling the atomic binding energies due to metal sharing A–M–A, (c) the spatial constraint k, and (d) hot atom traveling distance v. In the kinetic simulations, the preexponential factors were assumed to be proportional to the attempt frequency of the events. The explored coverage range was from 0 to 0.30 ML (monolayer), and the temperature range was from 100 to 700 K. The model makes it possible to calculate a multitude of coverage-dependent parameters of the process, in particular binding energies of molecular and atomic oxygen, the normalized O 2 sticking probability, and the amount and mutual arrangement of neighbors in an overlayer. With inclusion of very weak (<1 kcal/mol) lateral attractive nnn A–A interactions, the model also enables simulations of the development of p(2 × 2)-O and c(2 × 2)-O domains from disordered phases, generating the snapshots of the overlayer structures. The Ni(1 0 0) surface, for which the detailed experimental data on O 2 dissociative adsorption are available, was used as a model system. Practically all model projections, including those concerning the O 2 and O coverages and their binding energies, normalized sticking probabilities, and the overlayer structures, are in good agreement with experimental data. Moreover, the simulated sticking probabilities may be more relevant to the intrinsic Ni(1 0 0) surface behavior because the deviation from the experimental curve at high coverages (>0.25 ML) appears to be due to the formation of the NiO phase. The trends for the binding energies were also modeled for unreconstructed fcc(1 0 0) surfaces of Cu, Ag, and Pd. Because relevant experimental data are scarce, the model results are mostly projections to be verified by experiment.

INVESTIGATION OF THE ENERGETICS OF THE DECOMPOSITION OF AZOMETHANE ON Pd(111): THE UBI–QEP APPROACH

The method of unity bond index–quadratic exponential potential (UBI–QEP) is employed to derive the energetic parameters associated with the steps of the pathway which we propose for the catalytic decomposition of azomethane on the Pd (111) surface. According to the energy calculations, azomethane adsorbs molecularly in trans-configuration and then decomposes to CH 3 N with no activation energy. The reaction continues by tilting and dehydrogenation to the products ( H 2 and HCN). The calculated activation energies at various surface coverages perfectly account for the variation of relative yields of H 2 and HCN with changing of the coverage of azomethane. According to the calculations, desorption of molecular azomethane at high surface coverage occurs, which is in excellent agreement with experimental data.

Thermodynamic Consistency in Microkinetic Development of Surface Reaction Mechanisms

The foundation of microkinetic analysis over 10 years ago has drastically changed the way of parametrization of rates of surface-catalyzed reactions. In the initial stages of development, some parameters arose from experimental data whereas others were fitted to experimental data. Semiempirical and first principles quantum mechanical and statistical mechanics simulations nowadays are powerful tools in estimating kinetic parameters. However, even in best cases, some tuning of parameters is typically necessary for quantitative model predictions. During this process, parameters of reaction mechanisms may violate thermodynamics. Here we review thermodynamic constraints of reaction networks and derive expressions applicable to surface reactions. We present three examples of ethylene hydrogenation, ammonia synthesis, and hydrogen oxidation to assess the thermodynamic validity of literature mechanisms. Various methods to ensure thermodynamic consistency are discussed and demonstrated with a specific example of H2 oxidation on Pt. The use of semiempirical techniques, such as the bond order conservation (BOC), known also as unity bond index-quadratic exponential potential (UBI-QEP) or Polanyi free energy relations, and first principles density functional theory (DFT), in conjunction with fitting of experimental data is discussed. Finally, mechanisms compatible with Surface CHEMKIN are proposed.

Investigation of the Energetics of the Reactions of NH2 Species with Hydrogen and NO on the Pt(100) Surface by the Method of UBI-QEP

The formation of NH 2, ads and its further reactions with hydrogen and NO on the Pt(100) surface were previously studied by the methods of HREELS and TPR, in order to understand the role of amino species in the mechanism of the NO + H 2 reaction. In this work the method of unity bond index – quadratic exponential potential (UBI-QEP) has been employed to rationalize the experimental findings by calculating the energies associated with the envisaged routes of reactions. It is concluded that the activation energy of formation of NH 2, ads is higher than water production. The simplicity of recombinative desorption of N2 is due to the decrease of its activation energy because of the destabilizing effect of O ads and NO ads. The rate-determining step of explosive surface reaction in the saturated coadsorption layer of NH 2, ads and NOads is dissociation of NO ads. Autocatalytic acceleration of the explosive reactions is due to the decrease of activation energy of the rds by increasing the number adsorption vacant sites. H 2 O is produced via two different processes with different activation energies. NH 3 is produced via several paths.

Monte Carlo modeling of UBI-QEP coverage-dependent atomic chemisorption

The unity bond index-quadratic exponential potential (UBI-QEP) method is used to determine the equilibrium coverage-dependent atomic binding energies and overlayer structures for fcc(1 1 1) and (1 0 0) surfaces by Monte Carlo simulations. We modify the current UBI-QEP formalism to include changes in the total energy of the overlayer under adsorption and desorption of atoms, which gives a more accurate description of the reaction enthalpy and desorption activation barrier. Preferred coordination modes are found to be coverage-dependent and typically change with coverage as: (a) only hollow site occupancy; (b) hollow and bridge site occupancy with metal coordination remaining equal to unity; (c) bridge site occupancy with mono- and di-coordinated metal atoms. Although hops to the atop sites are allowed, their population is very rarely seen in the equilibrium state at any coverage. The results of Monte Carlo simulations are compared with the earlier projections made for various local coverage situations. Within the scope of comparability, the agreement is good. Some ad hoc modifications are mentioned, and possible applications of the results are discussed.

The UBI–QEP treatment of polyatomic molecules without bond-energy partitioning

Bond-energy partitioning in polyatomic molecules is a mathematical construct realizing intuitive chemical reasoning but having no physical justification. The bond order conservation–Morse potential method [1,2] and its generalization as the unity bond index–quadratic exponential potential (UBI–QEP) method [3,4] treat polyatomic molecules as quasi-diatomic and often use some bond-energy partitioning, which creates conceptual and numerical uncertainty. We present a new UBI–QEP formalism to calculate binding energies of polyatomic molecules without bond-energy partitioning. We discuss the types of molecules best suited for the new treatment and the nature and values of the relevant parameters. Examples include both symmetric molecules such as ethylene, acetylene and hydrazine and non-symmetric molecules such as nitrous oxide on various metal fcc(1 1 1) surfaces. The calculated binding energies were compared with those obtained by the previous UBI–QEP formulas (using some bond-energy partitioning). The older and new UBI–QEP values typically were found to be close. The scarcity of appropriate experimental data prevents a systematic comparison in order to decide where each approximation can be used most efficiently. One thing is certain, however, that the new UBI–QEP formalism, conceptually superior and quantitatively more reasonable than the older ones, expands opportunities of the practitioners.

Monte Carlo and UBI–QEP Modeling of the Coverage-Dependent Binding Energy for Atomic Adsorbates on the (111) and (100) Transition Metal Surfaces

Using the unity bond index–quadratic exponential potential (UBI–QEP) formalism and the Monte Carlo method, functions are obtained that describe the dependence of the binding energies of atomic adsorbates on the single crystal surface coverage for the models of random adsorption, models with a site choice and site preference, models with neighbor exclusion, and models with diffusion assistance.

The generalized UBI-QEP method for modeling the energetics of reactions on transition metal surfaces

The unity bond index––quadratic exponential potential (UBI-QEP) method is generalized to include any number of bond indices in the UBI constraint. The energy and bond index expressions are given that are completely general and not limited with respect to the number of bond indices that are allowed to participate in the UBI constraint. A procedure is described and illustrated for the generalization of the potential energy parameters by fitting to observable thermodynamic data. Applications and criteria for the applicability of the UBI-QEP method are discussed and a screening test for the applicability of the method is presented.

Ab initio gas-phase bond energies of CNH x isomers and the reactivity and stability of aminomethylidyne (CNH 2) on metal surfaces: UBI-QEP analysis

Energetics of reactions involving CNH 2 as an intermediate on Fe, Ni, Pd, and Cu surfaces were determined with the unity bond index-quadratic exponential potential (UBI-QEP) method. The gas-phase bond energy parameters of CNH x isomers that are needed for the UBI-QEP treatment were obtained from high quality ab initio calculations. The results show that CN can dimerize to C 2N 2 on Pd and Cu, but the dimerization is difficult on Fe, and the polymerization of CNH 2 is difficult. The N–H bond in CNH 2 is more easily cleaved than the C–N bond, and CNH 2 can be dissociated into CNH+H on Fe, Ni, Pd, and Cu surfaces, although it may remain on Pd and Cu metal surfaces due to CN and HCN hydrogenation. CNH 2 hydrogenation leads to the formation of HCN, NH 3, H 2, and CH 4 on those metal surfaces. The difficulty in breaking the C–N bond in CNH x isomers increases on the metal surfaces according to: Fe<Ni<Pd<Cu. The H-assisted C–N bond scission in some CNH x isomers on Fe, Ni, Pd, and Cu surfaces is discussed.

On the Energetics of nh 3 Adsorption and Decomposition on nb(100) Surface : a ubi-qep Study

The energetics of the adsorption and decomposition of ammonia on Nb(100) surface was investigated by the method of unity bond index-quadratic exponential potential (UBI-QEP). The experimental as well as theoretically derived atomic heats of adsorptions were used as the input data and the results were compared with the findings of local density functional theory (LDFT) and non-local density functional theory (NLDFT). The method was capable of correctly predicting the fragmentation of ammonia on 4-fold hollow sites on the surface of Nb(100) and magnitudes of the heats of adsorptions and activation energies were more realistic.

Hydrogen transfer in hydrocarbon conversions over transition metal surfaces

Hydrogen-transfer steps are a poorly studied and rarely proposed class of elementary reactions in heterogeneous catalysis over metal surfaces. In these steps, a hydrogen atom that is attached to the carbon in one surface species transfers to a carbon atom of another species. Unity bond index–quadratic exponential potential (UBI–QEP) calculations of the activation energies for three model surfaces representing substrates with strong, weak, and intermediate chemisorption abilities, combined with UBI–QEP/DFT data for the Pt(1 1 1) surface, suggest that there is no great energetic impediment to these steps. Therefore, they should not be arbitrarily ignored when building mechanisms of hydrocarbon conversions over metal surfaces. Moreover, kinetics simulations show that conditions are possible under which one-step hydrogen transfer is faster than the two-step process with the formation of adsorbed hydrogen.

Oxidation of methanol on platinum, ruthenium and mixed Pt–M metals (M=Ru, Sn): a theoretical study

A relativistic density-functional study of the dehydrogenation of CH 3OH and H 2O on pure platinum, ruthenium, and mixed Pt–M (M=Ru, Sn) metals is reported. Cluster models of Pt n M 10− n were used to simulate the metal surfaces. Calculated adsorption energies of a series of intermediate species agree well with available experimental values. Reaction energies for the elementary steps involved are determined and their activation energies estimated by the analytic unity bond index–quadratic exponential potential (UBI-QEP) formula of Shustorovich and Sellers [Surf. Sci. Rep. 31 (1998) 1]. On pure platinum, the dehydrogenation of surface-adsorbed methanol, CH 3OH s, is energetically favorable, with a hydrogen atom first stripped off the carbon end. However, the dehydrogenation of H 2O s to OH s, crucial in oxidative removal of poisoning CO, has the highest activation energy ( E ∗) among all of the reaction steps. Dehydrogenation of H 2O s on pure ruthenium is considerably more favorable than on pure platinum, but the combination reaction, CO s+OH s→COOH s, for the oxidative removal of CO s by OH s possesses the highest E ∗. On mixed Pt–M metals, the effect of M is to promote the formation of OH s and a combined effect of platinum and M atoms favors oxidative removal of CO s and formation of COOH s. The relative importance of a ‘ligand effect’ versus a bifunctional mechanism for oxidative removal of CO s is discussed. A ligand effect plays some role in the oxidation of CO on Pt–Ru, but it is unimportant on Pt–Sn.

Enumeration and discrimination of mechanisms in heterogeneous catalysis based on response reactions and unity bond index–quadratic exponential potential (UBI–QEP) method

The problem of a complete enumeration of a unique set of overall reactions and the corresponding mechanisms from a given set of elementary reactions is discussed in terms of the recently introduced concept of response reactions. A simple algorithm for the systematic generation of direct overall reactions and direct mechanisms from the given set of elementary reactions is presented. Further, based on energetic characteristics of the surface elementary reactions, i.e. the enthalpy changes and activation energy barriers, calculated by using the unity bond index–quadratic exponential potential (UBI–QEP) method, a qualitative procedure for the selection of energetically the most favorable direct mechanisms is proposed. These theoretical considerations are illustrated by a detailed analysis of the mechanism of methanol synthesis on copper catalyst.

CO 2-reforming of methane on transition metal surfaces

The mechanisms of CO 2-reforming of methane on Cu(111), Ni(111), Pd(111), Pt(111), Rh(111), Ru(001), Ir(111) and Fe(110) have been investigated by the the unity bond index-quadratic exponential potential (UBI-QEP) method. This method was named as the bond order conservation Morse potential (BOC-MP) approach before, but it has been generalized and renamed now. The heats of chemisorption ( Q) for all involved adspecies, activation barriers (Δ E) and enthalpy changes (Δ H) for forward and reverse reactions were evaluated. The calculations indicated that both the dissociation of CH 4 and the dissociation of CO 2 are rate-determining steps and that they are promoted by each other. A small amount of OH radical may account for the lower activity for the CO 2-reforming of methane. The activity sequence of catalysts is Fe>Ni>Rh>Ru>Ir>Pd>Pt>Cu. The most appropriate catalyst for CO 2-reforming is Ru. The most suitable non-noble catalyst is Ni.