Automatic Generation of Microkinetic Mechanisms for Heterogeneous

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Automatic Generation of Microkinetic Mechanisms for Heterogeneous Catalysis C. Franklin Goldsmith, and Richard Henry West J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b02133 • Publication Date (Web): 06 Apr 2017 Downloaded from http://pubs.acs.org on April 11, 2017

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The Journal of Physical Chemistry

Automatic Generation of Microkinetic Mechanisms for Heterogeneous Catalysis C. Franklin Goldsmith∗,† and Richard H. West∗,‡ †School of Engineering, Brown University ‡Department of Chemical Engineering, Northeastern University E‐mail: [email protected]; [email protected]

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Abstract A novel approach is presented for generating microkinetic mechanisms in heterogeneous catalysis. The open-source software RMG-Cat automatically develops a detailed list of elementary surface reactions, including thermodynamic properties for the adsorbates and parameterized rate coefficients for the reactions. The software proposes numerous possible surface intermediates and reactions, but it only retains those species that have a sufficiently high rate of formation. RMG-Cat was tested on the dry reforming of methane on nickel. The software correctly found the same set of elementary reactions as in a previously compiled microkinetic mechanism, as well as a few missing reactions. These results demonstrate the potential of this approach for predicting the dominant pathways in heterogeneous catalysis.


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Introduction A major goal in catalysis is to be able to predict the performance of novel materials. Accurate prediction of the reactivity and selectivity of catalytic materials requires a detailed list of elementary surface reactions, or a microkinetic mechanism. 1 The microkinetic mechanism is the critical bridge between the electronic potential energy surface and the catalyst’s performance under industrially relevant conditions. Unlike more traditional models used in kinetics (e.g. pseudo-steady state, quasi-equilibration, irreversibility), microkinetic models do not make a priori assumptions to simplify the chemistry. 2 The advent of accurate, reliable density functional theory (DFT) methods for computing the electronic energy for periodic systems has given scientists the ability to rationalize catalyst performance at the atomic scale. These developments have produced the significant insight, led by Dr. Jens Nørskov and others, that a high-dimensional potential energy surface can be reduced to a lower-dimensional surface. 3–10 These performance descriptors are often referred to as “linear scaling relations”, since, according to the models, the binding energy of an adsorbate scales linearly with the binding energy of the adatom through which it binds, and the activation energy scales linearly with the change in the binding energy upon reaction. These scaling relations not only reduce the time required to generate a microkinetic mechanism, they also explain key trends in catalytic performance for many industrial processes over a wide array of catalysts. 8,9,11–32 Although linear scaling relations have led to major insights into catalyst design, the process of going from these predictors to microkinetic models remains time consuming and error-prone. For a given reactant and material, the scientist must complete a minimum of four tasks: (i) assume/guess which crystalline facet(s) are significant; (ii) assume/guess which elementary reactions are important on that facet, such as adsorption, bond activation, and desorption; (iii) parameterize the corresponding rate coefficients, e.g. an Arrhenius equation for each reaction; and (iv) assemble and solve the coupled differential equations that govern the chemical dynamics. 33–35 To ensure that the model is thermodynamically consistent, the 3 ACS Paragon Plus Environment


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scientist must either compute the reverse rate coefficients in terms of a linear expansion of basis-set reactions, 36 or provide the temperature-dependent free energy for every species in the model. Scaling relations dramatically accelerate step (iii), but the process still requires significant human intervention. An alternative procedure would be to automate the mechanism generation process: the user completes the first task by providing a list of the reactants and the material facets, and the computer completes the remaining three tasks: (i) determine which reactions are important for each surface lattice, (ii) obtain accurate parameterization of the thermodynamic properties and rate coefficients, and (iii) solve the governing equations – without subsequent human intervention. Automated mechanism generation is consistent and thorough: the software does not miss pathways, and the resulting mechanism is thermodynamically consistent. Software that can automatically generate elementary kinetic mechanisms are revolutionizing gas-phase chemistry by predicting the combustion properties and complex interactions of novel biofuels, fuel blends, and additives. 37–53 These codes accomplish in hours what took experienced researchers months or years to accomplish by hand. Automated mechanism generation involves many problems at the intersection of chemistry and computer science. At a minimum, the kineticist must teach the computer how to: 1. Recognize when two or more species in the mechanism are equivalent. 2. Predict all the possible elementary reactions for each species and pair of species. 3. Determine which of the possible reactions are actually important. 4. Estimate accurately all the necessary thermodynamic and kinetic parameters. 5. Ensure that the mechanism is thermodynamically consistent. 6. Include flexibility for new reactants on novel materials. 4 ACS Paragon Plus Environment

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7. Accomplish all of the above in a bug-free manner more quickly than a human. A challenge with automatic mechanism generation is determining which reactions are going to be kinetically significant. Although the final microkinetic mechanism may be sensitive to only a few pathways, these kinetic bottlenecks are seldom known a priori. As the size of the reactant increases, the number of possible elementary reactions grows exponentially. For example, moving from adsorbed methanol to hexanol, the number of possible reactions increases from 50 to 500,000. 34 The number of intermediates and reactions to be considered is vast (e.g. millions for gas-phase combustion of JP-10 Jet Fuel 48 ), so the parameter estimation process must be very fast. If all of these reactions are included, then the resulting mechanism quickly becomes unsolvable and therefore useless. Although one could avoid the combinatorial explosion by truncating the number of expansion steps or iterations, this approach runs the risks of including reactions that are kinetically irrelevant and missing reactions that are kinetically significant. Thus, the central challenge in automatic mechanism generation is more than just teaching the computer how to apply some rules to predict reactions, it must include teaching the computer how to determine which of these reactions is going to be kinetically significant. This selection process should not be biased by the user’s expectation, since the pathways that are dominant on one material may be irrelevant on another material. To address this challenge, the authors have taken existing software that achieves these goals for gas-phase mechanism generation – RMG 53 – and modified it to work for chemical kinetics on surfaces. This offshoot of RMG will be referred to as RMG-Cat. The version described here is archived and freely available online. 54,55



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Methods A complete description of RMG is provided by Gao et al.. The salient features that have been ported over to RMG-Cat are described below, but for a complete description of the underlying software, the reader is referred to Ref. 53 and references therein. An automatic mechanism generator like RMG-Cat requires four main components to function: a unique representation of chemical species; templates and rules to generate reactions; methods to estimate all the thermodynamic and kinetic parameters in the mechanism; and an algorithm to choose which reactions to include in the final mechanism.

Species Representation: Chemical Graph Theory A crucial step in mechanism generation is the representation of chemical species, so as to ensure that the same adsorbate is not represented by two or more distinct names in the mechanism. To accomplish this task, RMG-Cat represents adsorbates using chemical graph theory (ChemGraph), whereby the atoms are represented by nodes, and the bonds are represented by edges. Efficient graph theory algorithms are used for (sub)graph isomorphism detection throughout the code, e.g. to determine when two adsorbates are chemically equivalent, and to decompose molecules into functional groups for parameter estimation. Each adsorbate is represented by an adjacency list, a compact notation to describe the molecular structure in which each row corresponds to an atom in the molecule. This notation can preserve information regarding the bonding, bond order, charge, unpaired electrons, and lone pairs. Presently, the adjacency lists cannot preserve stereochemistry.


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at om ele n m u un en mb pa t er lo ired ne e l fo pair ec. rm al ch ar ge

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H H H C3

1 Ni u0 p0 c0 {2,S} 2 O u0 p2 c0 {1,S}{3,S} 3 C u0 p0 c0 {2,S}{4,S}{5,S}{6,S} 4 H u0 p0 c0 {3,S} 5 H u0 p0 c0 {3,S} 6 H u0 p0 c0 {3,S}

O2 Ni

Ni

1

bonds

Ni

Figure 1: sample adjacency list for methoxy adsorbed on Ni. There is a single (S) bond between atoms 1 and 2, and single bonds between atom pairs (2,3), (3,4), (3,5), and (3,6)

For RMG-Cat, four new bond-types were created to represent the metal-adsorbate bond: single (ıe.g. CH3 *), double (CH2 *), triple (CH*), and quadruple (C*). Figure 1 illustrates the current ChemGraph notation for methoxy adsorbed on Ni(111). The current implementation of chemgraph in RMG-Cat does not distinguish between different binding sites on a given 1

facet; the code assumes that the lowest-energy binding site for a given adsorbate is chosen, which is consistent with the mean-field approach of the kinetics. That said, there is nothing to prevent the code from including binding site as a possible additional column in the adjacency list. The authors are currently working on adding a fifth bond type for physisorbed or van der Waals species (e.g. CH4 *), as well as the possibility of combining bond types to form multi-dentate species (e.g. di-sigma ethylene, CH2 CH2 **).

Thermodynamic Properties Not only must the software be able to represent each species uniquely, but it also must be able to predict the thermodynamic properties of that species, such as binding energies, enthalpy, entropy, and temperature-dependent heat capacity. RMG-Cat accomplishes this task by combining a database of thermochemistry for known species, as well as the ability to predict the thermochemistry for new species that are not in the database. The current database 7 ACS Paragon Plus Environment


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includes 21 adsorbates in Ni(111), listed in Table 1, which were taken from Blaylock et al. for methane steam reforming. For each species, RMG-Cat provides: the enthalpy of formation of the adsorbate, ∆f H ◦ (298 K); the standard-state entropy, S ◦ (298 K); and a polynomial expansion of the heat capacity at constant pressure as a function of temperature, Cp (T ). The thermodynamic properties were computed using the binding energies and normal modes, as provided in Ref. 56, using standard statistical thermodynamic methods. 57 Table 1: List of species in the current thermodynamics database. Adsorbate H* H2 * C* CH* CH2 * O* CH3 * OH* CH4 * H2 O* CO* COH* HCO* CH2 O* CHOH* OO* CH3 O* CH2 OH* CO2 * COOH* CH3 OH*

Metal Ni(111)

In a typical mechanism generation process, RMG-Cat will consider thousands of different adsorbates, even if only 10-100 intermediate species ultimately are retained in the final mechanism. Consequently, RMG-Cat must be able to generate accurate estimates of the thermodynamic properties rapidly, without first pausing to perform an expensive DFT calculation. RMG-Cat accomplishes this task efficiently by combining the ChemGraph functionality described above with Group Additivity, according to which the contribution of each functional group in a molecule contributes a fixed amount to the enthalpy, entropy, and heat capacity. 58–64 When RMG-Cat proposes a new species and confirms that it is not a duplicate of existing species, it first looks in the thermodynamic database to see if it can find an exact match. If it cannot, then it proceeds to estimate it according to the following algorithm: 1. For each species in Table 1, replace any H-atom with a wild card, then determine which species in the table is the closest match for the adsorbate in question. 2. Use a pre-compiled Adsorption Correction for that species. 3. Break the bond between the adsorbate and the metal to form a gas-phase precursor. 8 ACS Paragon Plus Environment

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4. Look up the thermodynamic properties of the gas-phase precursor in a database or estimate them using group additivity (considering additional complications, such as resonantly stabilized isomers, and whether or not the ground electronic state is a singlet or triplet, etc). 5. Determine the adsorbate thermochemistry by adding the pre-compiled adsorption correction to the estimated gas-phase properties.

Xadsorbate = Xgas-phase + ∆Xadsorption ,

X = ∆f H ◦ (298 K) , S ◦ (298 K) , Cp (T )

(1)

The process is summarized in Equation (1). For example, suppose RMG-Cat proposes adsorbed ethyl, CH3 CH2 *. The code first checks to see if this species is in Table 1. Since it is not, it recognizes that CH3 CH2 * is a close match to adsorbed methyl, CH3 *, by treating one of the H-atoms in methyl as a wild card (i.e. the ‘R’ in Figure 2). It then reads from the database the corresponding adsorption correction, or the difference in enthalpy, entropy, and heat capacity between the gas-phase radical CH3 • and the surface adsorbed CH3 *. Next, it removes CH3 CH2 * from the surface and estimates the thermochemistry of the gas-phase radical CH3 CH2 • using group additivity (if it cannot find it in a database). Finally, it adds the adsorption correction to the group additivity value to obtain estimates of the enthalpy, entropy, and heat capacity of CH3 CH2 *. This process is built upon the methods developed by Goldsmith for estimating partition functions for adsorbates. 64 Briefly, the approach assumes that the partition function of the adsorbate can be separated into the conserved modes and the transitional modes. 65–69 The conserved modes correspond to the 3N − 6 internal degrees of freedom of the gas-phase precursor (assuming it is nonlinear), and the transitional modes are the 6 degrees of freedom that describe the motion of the adsorbate relative to the surface.



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qadsorbate ≈

3N −6 Y

qiconserved

i

6 Y

qitransitional

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(2)

i

where qiconserved are the partition functions for the vibrational frequencies of the gas-phase precursor, and qitransitional are the partition functions for the relative motion – typically either a 2D lattice or 2D gas model. 56,57 The model assumes that, although the vibrational frequencies of the precursor do change upon adsorption, the contribution of these changes to the thermodynamic properties is negligible compared to the loss of the 3 external translational and 3 external rotational degrees of freedom and the corresponding gain of 6 new surface modes. Accordingly, the adsorption correction, ∆Xadsorption , in Equation (1) is calculated by

∆Hadsorption = H 6 new modes − 3H translation − 3H rotation + ∆Ebinding

(3a)

∆Sadsorption = S 6 new modes − 3S translation − 3S rotation

(3b)

∆Cp,adsorption = Cp6 new modes − 3Cptranslation − 3Cprotation

(3c)

The corrections for enthalpy and entropy are calculated at 298 K; the corrections for the heat capacity are calculated at the same temperatures as the group additivity values: 300, 400, 500, 600, 800, 1000, and 1500 K. This method has been applied successfully to model high-temperature partial oxidation of methane on platinum. 70 The gas-phase properties that were used for the pre-compiled adsorption corrections for the species in Table 1 were taken from a previously compiled database of DFT frequencies. 71


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R M

H

C

O

N

etc

M

M

M

M

M

C*R4

C*R3

C*R2

C*R

M

M

M

M

RRR R R C C M

M

C* O*R2 M

M

O*R

O*

M

M

R C

RR C

R C

H C

CR C

OR C

H O

CR O

OR O

M

M

M

M

M

M

M

M

M

Figure 2: Hierarchical tree for functional groups for adsorbate thermochemistry. R represents any atom; M is the metal surface site. For each branch in the second level down, the number of vertical lines between M and R is the bond order; the dashed vertical line to the right is for physisorbed or van der Waals complexes. The final row at the bottom indicates that each R can be further refined

The adsorption corrections summarized in Equation (3) are, in effect, a form of group additivity for adsorbate binding groups. These group additive values are arranged in a hierarchical tree-structured database, illustrated in Figure 2, with the most general groups at the top and more specific instances as child nodes. When using the database to estimate thermochemistry for an unknown adsorbate, the tree is climbed from the most specific node until a node is found that has a group value assigned. This way, the best possible estimate is used, but even groups with no training data can be estimated approximately. Once the tree structure is organized, the group additive values for a given node are fitted by linear least squares regression against all the data that falls under that node and its descendants in the tree. 11 ACS Paragon Plus Environment


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This hierarchical tree database of group additive values has been successfully implemented in RMG for gas-phase thermochemistry, 53 reaction kinetics, 72 solvation parameters, 73 transport properties, 74 and most recently transition state geometries. 75

Kinetics Chemical reactions are classified according to “reaction families”. Each family contains: a template to identify when the reaction can occur, a recipe to specify the changes to be made to the molecular graphs, and some rules to determine the reaction rate coefficient. After the graphs are manipulated according to the recipe, they are checked for isomorphism with previously generated molecules to ensure the products are unique and the reactions are not duplicated. RMG-Cat specifies a reaction in a single direction. It assumes that all reactions are reversible, and computes the reverse rate coefficient directly from the forward rate and the equilibrium constant. Consequently, the RMG-Cat mechanisms are always thermodynamically consistent.

H Bond fission recipe: • Break Bond: {*2,S,*3} • Create Bond: {*3,S,*4} • Change Bond: {*1,D,*2}

H H C3 O2

O2

M1 + M4

M1 + M 4

H H H C3

Figure 3: sample reaction recipe for the bond fission of adsorbed methoxy to O* + CH3 * on a generic metal. The reaction breaks the single C–O bond, forms a new single (S) bond between the carbon atom and the metal, and it changes the nature of the oxygen-metal bond to double (D). The code is written in Python and is highly accessible and human readable.


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H-abstraction recipe: • Break Bond: {*2,S,*3} • Create Bond: {*3,S,*5} • Change Bond: {*1,D,*2} • Change Bond: {*4,S,*5}

H

H H C2 3 O5 M1 + M4

H

H C2

H O5 3

M1 + M4

Figure 4: sample reaction recipe for the H-atom transfer between adsorbed methyl and an oxygen adatom to methylene and OH on a generic metal.

RMG contains over 40 distinct families for gas-phase reactions. RMG-Cat now contains three additional reaction families specific to surface chemistry: adsorption/desorption, bond-fission (e.g. Figure 3), and H-abstraction (e.g. Figure 4). Each reaction family is further subdivided. For example, the Adsorption family includes rules for both dissociative and non-dissociated adsorption, with specific rules for the formation of adsorbates with single, double, triple and quadruple bonds. The code represents the rate coefficients for adsorption in terms of sticking coefficients, with built-in subroutines to convert from sticking coefficients to adsorption rate constants, and from adsorption rate constants to desorption rate constants. 76 Although direct reactions between gas-phase species and adsorbates are not presently implemented, Eley-Rideal kinetics will be incorporated soon, as will be physisorption and multi-dentate adsorption. Because the reaction families in the gas-phase RMG are all elementary reactions, it only considers unimolecular and bimolecular reactions; modifications were necessary to allow for dissociative adsorption, since these reactions contain three reactants (a gas-phase molecule and two vacant surface sites). After a reaction has been proposed by a reaction family, RMG-Cat searches a database of reactions to see if it can find an exact match. If the proposed reaction is not in the database, the Arrhenius parameters will be estimated according to a set of rules specific to that reaction family. The rules are arranged in hierarchical tree-structured databases, similar to the thermochemistry described above. The estimation rules, formulated as Brønsted-Evans-Polanyi relationships, are derived automatically from the database of known rate coefficients. 4,8,35 Kinetics and transition states predictions typically use two trees, one for each reactant in 13 ACS Paragon Plus Environment


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bimolecular reactions, and possibly a third for the linking group for intramolecular reactions; the training procedure considers all combinations of each tree. At present, the kinetics database is sparsely populated. As the software develops, more specific values will be added, thereby improving the estimates for novel reactions, and increasingly specific rate rules will be added to the kinetics trees, including coverage dependence. The default rate rule for bond fission is:

k

bond fission

(T ) = A

T Tref

n exp

Ea0 + α∆Hrxn /RT

(4)

A = 1.0 × 1017 m2 /mol-s n = 0.0 [−] Ea0 = 1.92 [eV] (185.3 kJ/mol) α = 0.84 [−]

where the pre-exponential factor was taken from Ref. 77, and the BEP value for the activation energy was taken from Ref. 8. The default rate rule for abstracting a Hydrogen atom from an adsorbate is:

k

H-abstraction

(T ) = A

T Tref

n exp [Ea /RT ]

(5)

A = 1.0 × 1017 m2 /mol-s n = 0.0 [−] Ea = 0.41 [eV] (40 kJ/mol)

where the pre-exponential factor and activation energy were fit from similar values in Ref. 77. RMG-Cat also includes the possibility that functional groups other than a terminal H


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can be abstracted, but that these rate coefficients should be orders of magnitude smaller. For non-H abstraction the default rate rule is:

k

R-abstraction

(T ) = A

T Tref

n exp [Ea /RT ]

(6)

A = 1.0 × 1015 m2 /mol-s n = 0.0 [−] Ea = 0.83 [eV] (80 kJ/mol)

The default sticking coefficients for dissociative and non-dissociative adsorption are:

S0diss. adsorp

(T ) = A

T Tref

n exp [Ea /RT ]

(7)

A = 1.0 × 10−2 [−] n = 0.0 [−] Ea = 0.43 [eV] (41.8 kJ/mol)

S0nondiss. adsorp

(T ) = A

T Tref

n exp [Ea /RT ]

(8)

A = 5.0 × 10−2 [−] n = 0.0 [−] Ea = 0.10 [eV] (10 kJ/mol)

The rate rules have been normalized on a per equivalent reaction site formulation, and RMG-Cat automatically incorporates the reaction path degeneracy into the forward rate



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coefficient. For example, the generic pre-exponential factor for H-abstraction is 1 × 1017 m2 /mol-s. For the reaction C* + CH3 CH2 * → CH* + CH3 CH*, the pre-exponential factor is multiplied by 2, to account for the two equivalent H-atoms on C1 of the adsorbed ethyl, as noted in Table 2. Finally, the user can provide their own set of preferential rate coefficients, or a reaction library. RMG-Cat automatically will use those values first, in lieu of the internal database and estimation process. The user can force RMG-Cat to include all the reactions in the reaction library (a.k.a. a “seed mechanism”), or allow RMG-Cat to determine whether or not a given reaction in the reaction library contributes significantly towards the flux of a species and include only those reactions with a significant contribution. Importantly, the reactions in the user-defined reaction library need not conform to one of the pre-defined reaction families. An example of this functionality will be described in the Demonstration Section below. Our combined decades of experience using automatic mechanism generation for combustion chemistry has taught us that mechanism generation is an iterative process. We anticipate it being used as follows: RMG-Cat predicts a mechanism; sensitivity (or degree or rate control) analysis determines which reactions are critical; 78–89 the rate coefficients for these reactions are computed from first principles, and the new values are both added to the database and used to retrain the rate rules; then the re-trained RMG-Cat is used to predict an improved mechanism.

Mechanism Generation RMG-Cat considers all possible reactions that can be expressed within the reaction family system, without limiting the number of iterations. To avoid an exponential explosion in the number of (potentially irrelevant) species, it includes only those reactions that have a sufficiently high rate of reaction. 38 RMG-Cat divides all the species it considers into two groups: the “core” and the “edge”. The core contains species that are essential to the kinetics 16 ACS Paragon Plus Environment

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of the system; the edge contains species that have been proposed by a reaction, but have not been proven to be kinetically relevant. The process begins with the selection of reactants forming the initial core, as well as the temperature, pressure, and species concentrations. The algorithm follows the fastest pathways, according to the conditions at which the model will be used, and ignores the slow pathways that do not contribute to the overall process. Generate reactions of all core species and estimate parameters

Starting species

Reaction conditions (T, P, Xi)

Run simulations, tracking creation rate of edge species, Rn

Termination tolerance

Are any Rn > Rcritical ?

Add species with max Rn to model core

yes

no Generated mechanism Figure 3: Flow chart to illustrate the rate-based algorithm expansion. The user specifies the reactants (top-left

arrow), temperature, and concentrations (center-left arrow), and the tolerance (lower-left arrow). If Figure 5: the Flow chart pressure, to illustrate the rate-based algorithm for mechanism expansion. any new species is produced at an appreciable rate, the integration routine stops, the species is added to the core, and the process starts over.

Althoughrate-based this algorithmexpansion works exceptionally well for mechanism development, the species The iterative, algorithm is gas-phase described in Figure 5. For each

transition to heterogeneous catalysis may present new scientific challenges, especially for adsorbate-adsorbate interactions, coverage-dependent reaction pathways, and poisoning. In in the mechanism (both core and edge), the net rate of formation is computed: anticipation of these problems, we will track the surface coverage of all edge species, and include their effect on the model once it exceeds a critical threshold, even if their rate of generation is low. RMG-Cat will be able to run multiple reactor models, with the final mechanism as the union of the individual simulations. RMG-Cat will work seamlessly with the open-source code Cantera dNi equations (ODE).87 The initial reaction for solving the system of governing ordinary Ridifferential = (9) dt model used in the integration routine is a zero-dimensional isothermal, isobaric batch reactor, but if an alternative reactor model is desired, then it can be built first in Cantera and then imported into RMG-Cat. where Ni isThis themethod totalofnumber of isspecies i in a given phase (e.g. gas modelingof themoles chemistry inherently a mean-field approximation. The or surface). A advantage of mean-field kinetics is that the system of governing equations can be solved in a characteristic rate is efficient determined the species in the core: in this proposal are at computationally manner,from and many of the systems of interest temperatures sufficiently high that the mean-field approximation is appropriate.4, 88 Furthermore, the implicit Backward Differential Formula (BDF) that is used to solve the stiff ODE’s lends itself naturally to perform local sensitivity analysis.89 Local sensitivity analysis is a numerically efficient procedure that provides insight into the reactions and/or intermediates that control the s 89-97 X in heterogeneous catalysis, this method is commonly referred observable kinetic phenomena; Rdegree Ri2 98-100 species i ∈ core (10) to as Campbell’s char =of rate control. i


11


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 43

The user provides an error tolerance ∈ (0, 1]. For each species j in the edge, if the net rate of formation exceeds the characteristic rate scaled by the error tolerance, i.e. Rj ≥ Rchar , then that species is moved from the edge to the core. When a species is moved from the edge to the core, the simulation starts over. This process continues until a user-specified termination criterion is met and no new species are moved from the edge to the core. The current version of RMG-Cat has two possible termination criteria: a reaction time, or a percent conversion of a reactant. If both are specified, then RMG-Cat will terminate when one of them is met. RMG-Cat currently uses a zero-dimensional, isothermal, isochoric, batch reactor in the integration routine. The state variables are the total number of moles for each species, including gas-phase and surface species. The governing equations are formulated as a system of ordinary differential equations (ODE):

dNi = f (N, t; λ) dt

(11)

where N is the vector of species mole numbers, t is time, and λ is the vector of parameters, such as rate coefficients and thermodynamic properties. To complete the system of equations, the model assumes a reactor volume determined by one mole of gaseous reactants at the specified temperature and pressure (e.g. 2.48 × 10−2 m3 at STP). The user provides a ratio of catalytically active surface area to volume (m−1 ), and a surface site density for the catalyst (mole/m2 ). The system of ODE’s are integrated using PyDAS, 90 which is a Python wrapper for the DASPK integrator for stiff ordinary differential equation. 91


Page 19 of 43

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Other Properties RMG was recently extended to include more heteroatoms, transport properties, phase behavior, and solvation effects. 92–96 These tools have been carried over into RMG-Cat, thereby allowing RMG-Cat to be extended to liquid-phase catalysis in the future. Moreover, although gas-phase reactions are not expected to be significant for the trial application below, the core gas-phase chemistry of RMG is still present in RMG-Cat, so it is possible to build homogeneous/heterogeneously coupled systems, such as oxidative coupling of methane or catalytic combustion.

Results and discussion Proof of Concept: Methane dry reforming on nickel To demonstrate the capabilities of automatic mechanism generation, we apply RMG-Cat to the problem of methane dry reforming on nickel. Our goal is to see if the code can produce a microkinetic mechanism that is consistent with a mechanism that was developed “by hand” by experts – in this case, the mechanism developed by Olaf Deutschmann and coworkers. 77 The original mechanism in Delgado et al. consists of 26 reversible reactions, with the forward and reverse rate coefficient expressed explicitly. For this study three sets of modifications were made to the original mechanism. First, for each of the 26 reversible reactions, the rate coefficient was imported in only one direction; the reverse direction was computed directly from the thermochemistry, so as to maintain thermodynamic consistency. 97 The second modification was to neglect coverage effects in the activation energy. These effects are important, and they will be incorporated into RMG-Cat in a systematic fashion in the near future. For demonstration purposes, however, they are not essential. The third modification was for the adsorption of three species. In the Deutschmann mechanism, the adsorption of CH4 , CO2 , and H2 O proceed through pre-adsorbed complexes – CH4 *, CO2 *, and H2 O*,



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

respectively – which then dissociate on the surface. Because the van der Waals functionality has not yet been fully implemented, RMG-Cat cannot represent these three species, and so these three reactions were removed. Instead, any reaction that forms CH4 *, CO2 *, or H2 O* as a product was modified to produce the gas-phase species instead. For example, the reaction OH* + H* * ) H2 O* + * becomes OH* + H* * ) H2 O + 2*. The rate parameters in the associative desorption direction were included in the mechanism. Once the physisorption reactions for CH4 , CO2 , and H2 O were removed, 23 reactions remained. These reactions were then analyzed and used to populate the kinetics library. Three reactions were used to populate the Surface Abstraction tree: CH2 * + OH* → CH3 * + O*, CH* + OH* → CH2 * + O*, and C* + OH* → CH* + O*. Six reactions were used to populate the Surface Dissociation tree: CH2 * + H* → CH3 * + *, CH* + H* → CH2 * + *, C* + H* → CH* + *, OH* + * → H* + O*, HCO* + * → CO* + H*, and COOH* + * → CO* + OH*. The remaining 14 reversible elementary reactions were treated as a reaction library. These reactions include the necessary adsorption/desorption reactions, as well as elementary reactions that do not fit within the three reaction families described above (e.g. O-atom insertion reactions, such as HCO* + HO* * ) COOH* + H*). If RMG-Cat proposes a reaction that is in the Deutschmann mechanism, then RMGCat will use the specified kinetic parameters for that reaction (either by finding it within the kinetics database or within the reaction library); if, on the other hand, RMG-Cat proposes a reaction that is not in the Deutschmann mechanism, then it will estimate it from the rate libraries, as predicted by Equations (4)-(8). For the sample runs, RMG-Cat was initialized with a molar composition of 10% CH4 , 10% O2 , and 80% of N2 at 1000 K and 1 bar. Additionally, the nickel surface was completely vacant, with a surface site density of 2.9 × 10−9 mole/cm2 , and the reactor was assumed to have a surface-to-volume ratio of 105 m−1 . The termination criterion was set to a CH4 conversion of 50% or 0.1 seconds, whichever comes first. The error tolerance was decreased gradually from = 1 × 100 to = 1 × 10−8 .


Page 20 of 43

Page 21 of 43

no. of species

10 3

no. of reactions

10 4

(a)

no. of core reactions

400

(b)

(c)

350

Abstraction Dissociation Adsorption Deutcschmann

300 10 3 ge

250

10 2

ed

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


g ed

10 2

co

e cor

200

e

150 100

re

50

10 1

10 1 10

0

10

-4

10

-8

0 10

error tolerance, ε

0

10

-4

10

-8

error tolerance, ε

10 0

10 -4

10 -8

error tolerance, ε

Figure 6: Results for adjusting the error tolerance. (a) and (b) demonstrate how the number of species and reactions, respectively, in the core and edge grows exponentially with increasing the tolerance tightness. (c) the total number of instances from each reaction family in the core, as a function of error tolerance. 98

Figure 6 demonstrates how the size of the mechanism increases as the error tolerance is tightened. At = 1, the core contained 17 species and 30 reactions, and the edge contained 42 species and 61 reactions. By = 1 × 10−8 , the core contained 68 species and 366 reactions, and the edge 740 species and 1505 reactions. An important aspect of the graph theory methodology is its computational efficiency. The total mechanism generation process was ∼1 minute for = 1 × 10−1 and ∼5 minutes for = 1 × 10−8 , on a single core of a 3.2 GHz Intel Core i5 (circa 2013 iMac).



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 43

Table 2: List of reactions in the RMG-Cat mechanism for an initial composition of 10% CH4 , 10% O2 , and 80% N2 at 1000 K and 1 bar. Units of A are [m2 /mol-s] (or dimensionless - see note b) and Ea are [kJ/mol]. Rxn

reaction

A

n

Ea

notes

a

1

CH3 * + H* * ) CH4 + 2*

1.44×1018

−0.087

63.4

c,g,h

10−2

2

CH2 * + H* * ) CH3 * + *

3.09×1019

−0.087

57.2

e, h

10−2

3

CH* + H* * ) CH2 * + *

9.77×1020

−0.087

81.0

e, h

10−2

4

CH2 * + CH2 * * ) CH* + CH3 *

2.00×1017

0.0

40.0

f

10−2

b,c,h

10−2

e,h

10−2

5

H2 + 2* * ) 2H*

3.00×10−2

0.0

5.0

6

H* + C* * ) CH* + *

1.70×1020

−0.5

157.9

7

CH3 * + C* * ) CH2 * + CH*

3.00×1017

0.0

40.0

f

10−2

8

CH2 * + C* * ) CH* + CH*

2.00×1017

0.0

40.0

f

10−2

COOH* + * * ) CO2 + H* + *

3.73×1016

0.475

33.6

c,g,h

10−2

2CO* * ) CO2 + * + C*

1.62×1010

0.5

241.7

c,g,h

10−2

9 10 11

C* + OH* * ) CO* + H*

3.88×1021

0.188

62.5

c,h

10−2

12

COOH* + * * ) CO* + OH*

1.46×1020

−0.213

54.3

e,h

10−2

2.98×1018

0.101

25.8

c, h

10−2

1.75×109

0.0

116.2

c,h

10−2

123.6

c,g,h

10−2

13

CH3 * + OH* * ) CH4 + O* + *

14

CO* + * * ) C* + O*

15

O* + CO* * ) CO2 + *

2.15×1015

0.0

16

OH* + * * ) H* + O*

2.25×1016

0.188

29.6

e,h

10−2

17

CH2 * + OH* * ) CH3 * + O*

1.39×1017

0.101

19.0

f,h

10−2

18

CH* + OH* * ) CH2 + O*

4.40×1018

0.101

42.4

f,h

10−2

19

C* + OH* * ) CH* + O*

2.43×1017

−0.312

118.9

f,h

10−2

5.00×10−1

0.0

0.0

b,c,h

10−2

109.9

c,h

10−2

15.9

c,h

10−2

e,h

10−2

f

10−2

20

CO + * * ) CO*

21

CH* + O* * ) HCO* + *

4.59×1016

0.0

22

HCO* + OH* * ) COOH* + H*

2.28×1016

0.263

23

HCO* + * * ) CO* + H*

3.71×1017

0.0

0.0

1.00×1017

0.0

40.0

24

HCO* + CH2 * * ) CO* + CH3 *

Continued on Next Page. . .


Page 23 of 43

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 2 – Continued Rxn

reaction

A

n

Ea

notes

a

25

HCO* + CH* * ) CO* + CH2 *

1.00×1017

0.0

40.0

f

10−2

26

HCO* + C* * ) CO* + CH*

1.00×1017

0.0

40.0

f

10−2

27

HCO* + O* * ) CO* + OH*

1.00×1017

0.0

40.0

f

10−2

28

CH3 CH2 * + * * ) CH2 * + CH3 *

1.00×1017

0.0

117.7

e

10−2

29

C2 H6 + 2* * ) 2 CH3 *

2.00×10−2

0.0

41.8

b,d

10−2

30

C2 H6 + 2* * ) CH3 CH2 * + H*

1.20×10−1

0.0

41.8

b,d

10−2

31

CH3 CH2 * + * * ) CH3 CH* + H*

2.00×1017

0.0

180.2

e

10−3

32

CH3 CH* + * * ) CH3 * + CH*

1.00×1017

0.0

148.7

e

10−3

33

CH3 CH* + OH* * ) CH3 CH2 * + O*

1.00×1017

0.0

40.0

f

10−3

34

CH3 CH* + HCO* * ) CH3 CH2 * + CO*

1.00×1017

0.0

40.0

f

10−3

35

CH2 * + CH3 CH2 * * ) CH3 * + CH3 CH*

2.00×1017

0.0

40.0

f

10−3

36

CH2 * +CH3 CH* * ) CH* + CH3 CH2 *

2.00×1017

0.0

40.0

f

10−3

37

C* + CH3 CH2 * * ) CH* + CH3 CH*

2.00×1017

0.0

40.0

f

10−3

38

C* + CH3 CH2 * * ) CH2 * + CH3 C*

1.00×1015

0.0

80.0

f

10−3

39

CH3 C* + * * ) CH3 * + C*

1.00×1017

0.0

604.3

e

10−3

40

CH3 CH* + * * ) CH3 C* + H*

1.00×1017

0.0

0.0

e

10−3

41

O* +CH3 CH* * ) OH* + CH3 C*

1.00×1017

0.0

40.0

f

10−3

42

CO* +CH3 CH* * ) HCO* + CH3 C*

1.00×1017

0.0

40.0

f

10−3

43

CH2 * +CH3 CH* * ) CH3 * + CH3 C*

1.00×1017

0.0

40.0

f

10−3

44

CH* +CH3 CH* * ) CH2 * + CH3 C*

1.00×1017

0.0

40.0

f

10−3

45

CH* +CH3 C* * ) C* + CH3 CH*

1.00×1017

0.0

40.0

f

10−3

1.00×1017

0.0

40.0

f

10−3

1.00×10−2

0.0

16.0

b,d

10−3

46 47

CH3 CH* + CH3 CH* * ) CH3 CH2 * + CH3 C* CH3 • + * * ) CH3 *

48

CH3 C*O + * * ) CH3 * + CO*

1.00×1017

0.0

316.8

e

10−3

49

CO* + CH3 CH2 * * ) CH3 C*O + CH2 *

1.00×1015

0.0

80.0

f

10−3

50

CO* + CH3 CH* * ) CH3 C*O + CH*

1.00×1015

0.0

80.0

f

10−3

Continued on Next Page. . .



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 43

Table 2 – Continued Rxn

reaction

A

n

Ea

notes

a

51

CH3 C*O + C* * ) CO* + CH3 C*

1.00×1015

0.0

80.0

f

10−3

52

H* + OH* * ) H2 O + 2*

1.85×1016

0.086

41.5

c,g,h

10−3

2.34×1016

0.274

92.3

c,g,h

10−3

b,d

10−4

OH* + OH* * ) H2 O + O* + *

53 54

C3 H8 + 2* * ) CH3 * + CH3 CH2 *

4.00×10−2

0.0

71.1

55

CH3 CH2 CH2 * + * * ) CH2 * + CH3 CH2 *

1.00×1017

0.0

215.7

e

10−4

1.20×10−1

0.0

41.8

d

10−4

56b

C3 H8 + 2* * ) H* + CH3 CH2 CH2 *

57

CH3 CH*CH3 + * * ) CH3 * + CH3 CH*

2.00×1017

0.0

220.8

e

10−4

58

CH3 CH2 * + CH3 CH* * ) CH2 * + CH3 CH*CH3

1.00×1015

0.0

80.0

f

10−4

59

CH3 CH* + CH3 CH* * ) CH* + CH3 CH*CH3

1.00×1015

0.0

80.0

f

10−4

60

C* + CH3 CH*CH3 * ) CH3 C* + CH3 CH*

2.00×1015

0.0

80.0

f

10−4

61

C3 H8 + 2* * ) H* + CH3 CH*CH3

4.00×10−2

0.0

41.8

b,d

10−4

62

CO* + CH3 CH2 * * ) CH3 C*O + CH2 *

1.00×1015

0.0

80.0

f

10−4

63

CO* + CH3 CH* * ) CH3 C*O + CH*

1.00×1015

0.0

80.0

f

10−4

64

C* + CH3 C*O * ) CH3 C* + CO*

1.00×1015

0.0

80.0

f

10−4

2.00×1015

0.0

80.0

f

10−4

65

CO* + CH3 CH*CH3 * ) CH3 C*O + CH3 CH* +

a

minimum value of the error tolerance for RMG-Cat to find this reaction.

b

rate coefficient is a sticking coefficient; pre-exponential factor A is unitless.

c

reaction directly from Deutschmann library

d

adsorption

e

dissociation

f

abstraction

g

associative desorption (see discussion in text)

h

kinetic parameters from Deutschmann [77]

i

kinetic parameters estimated by RMG-Cat


Page 25 of 43

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In order to illustrate the rate-based algorithm in practice, Table 2 lists the reactions found by RMG-Cat for three values of error tolerance: = 1×10−2 , 1×10−3 , and 1×10−4 . For ≥ 1 × 10−2 , RMG-Cat returned 30 elementary reactions. 20 of those 30 reactions were direct hits from the Deutschmann mechanism, including the main pathways for adsorption of CH4 and CO2 and desorption of H2 and CO. When the tolerance was decreased to = 1 × 10−3 , RMG-Cat found 23 additional reactions, including the 2 Deutschmann pathways that lead to small concentrations of H2 O. By = 1 × 10−4 , the mechanism contains 65 reactions. Tightening the tolerance beyond 1 × 10−4 further increases the size and complexity of the mechanism, including the formation of trace gas-phase products not listed in Table 2, such as CH2 O. The only reaction in the original Deutschmann mechanism that RMG-Cat did not include under these conditions was the associative desorption of 2O* to O2 . Inspection of the edge confirms that RMG-Cat did propose this reaction, but it determined that the flux was insufficient to move it from the edge to the core. Under these conditions, O2 is not predicted to be formed at a significant rate; integration of the original literature mechanism yielded a peak mole fraction of y2 ≤ 1 × 10−20 , so the rate-based algorithm behaved properly. It is important to emphasize that 43 of the 65 rate coefficients in Table 2 were created by RMG-Cat based upon the rate rules, and as such have higher uncertainty than the 22 rate coefficients that were taken from Delgado et al.. Nonetheless, including these new proposed reactions in a mechanism is a useful starting point for subsequent sensitivity analysis. In time, we expect the accuracy of these predictions to improve considerably, as the database becomes populated with more values. Additionally, as illustrated in Figure 6c, the largest single percentage of the proposed reactions are abstraction reactions. This result is in contrast to many mechanisms in the literature, which assume that bond-fission pathways dominate. The higher-than-expected prevalance of abstraction reactions is due in part, no doubt, to the simplicity of the rate rule; with a more densely populated database, we could develop more accurate BEP-style rules for this family, and these better rules may end up predicting fewer reactions to be signifi-



cant. However, it is also worth emphasizing that these reactions could play an increasingly important role under high-pressure conditions for which there are fewer vacant sites. As detailed above, the RMG-Cat mechanism is larger than the original mechanism of Delgado et al.. To illustrate the impact of the new reactions, a new simulation was performed. To simplify the comparison, the same initial conditions were chosen as in Figure 6, but the termination criterion was set to 1 second, and the constant T,V batch reactor was integrated to 1 second. These results are illustrated in Figures 7 - 9. 0.10

0.20

0.006

0.05

moles

0.15

moles

moles

CH 4

0.10 0.05

0.00 0.5

1.0

0.002

H2 O 0.000

0.0

time (s)

0.5

1.0

time (s)

0.10

0.004

CO

0.00 0.0

0.0

0.5

1.0

time (s)

0.20

CO 2

RMG-Cat Delgado et al.

0.15

moles

moles

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 43

0.05

0.10 0.05

0.00

H2

0.00 0.0

0.5

time (s)

1.0

0.0

0.5

1.0

time (s)

Figure 7: Simulation results for methane dry reforming at 1000 K and 1 bar (see text for initial conditions). A comparison of major gas-phase species. Black dashes are the results from the Deutschmann mechanism, and the red lines are from the RMG-Cat mechanism. 98 Figure 7 presents the gas-phase species that were in the Deutschmann mechanism. The agreement among the reacants, CH4 + CO2 , and major products, CO + H2 , is excellent. The profiles for H2 O differ slightly, with the original mechanism predicting a peak H2 O that is 13% higher than that of the new mechanism.


Page 27 of 43

10 -3 10 -4 10 -5

moles

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


10 -6

C2 H6 10

-7

C3 H8

CH 2 O

10 -8

CH 3

10 -9 0.0

0.5

1.0

time (s)

Figure 8: Simulation results for methane dry reforming at 1000 K and 1 bar. Some gas-phase species predicted by RMG-Cat that were not in the Deutschmann mechanism. 98 Additionally, RMG-Cat found several gas-phase species there were absent from the Deutschmann mechanism. The most abundant of these new products are shown in Figure 8, and even these species are mostly present in sub-ppm levels. The concentration of methyl radicals, CH3 , peaks around 1 ms. Effectively, the adsorption/desorption reaction equilibrates, and the radical concentration decreases as the surface CH3 * is consumed by surface oxidation reactions.



10 0

vacant

10 -1

H*

CH* 10

site fraction

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 28 of 43

CO*

-2

C* CH 3 C*O

10 -3

CH 3 C* 10 -4

O*

10 -5

C 2 HO*

CH 2 *

O*

CHO 2 *

10 -6 10 -6

10 -5

10 -4

10 -3

10 -2

10 -1

10 0

time (s)

Figure 9: Simulation results for methane dry reforming at 1000 K and 1 bar. Surface site fractions. Solid lines are the RMG-Cat predictions, black dashes are predicted by the Deutschmann mechanism. 98

Figure 9 compares the main adsorbate site fractions. As with Figure 7, the agreement is excellent, with minor deviations for C* and O* in the µs region, and new adsorbates – such as CH3 C* and CH3 C*O – becoming significant in the ms region.

Future Directions RMG-Cat is open source, and it is intended to be a community–driven project. Our immediate goals are to populate the thermodynamic and kinetic databases with more data (including metals beyond nickel) and to refine the rate rules within the reaction families (e.g. further distinguish the bond fission rule based upon both the bond type and nearest neighbors, or refine the abstraction family to distinguish between abstracting a hydrogen atom versus some other moeity). In principle, reactor models other than a constant-T,V batch reaction could be used 28 ACS Paragon Plus Environment

Page 29 of 43

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within the integration routine, such as plug flow reactors (PFR). The main challenge with a PFR is that the governing equations are differential algebraic equations (DAE) and thus are somewhat more difficult to implement numerically. Furthermore, there is nothing to prevent RMG-Cat from moving beyond mean-field models and apply the rate-based screening to stochastic methods, such as kinetic Monte Carlo (kMC), which may give a physically more realistic portrayal of the heterogeneous chemistry. 99,100

Conclusions A novel software was presented that can automatically generate microkinetic mechanisms for heterogeneous catalysis. The software iteratively proposes new reactions according to reactions templates, but it includes only the reactions that are kinetically significant. It combines a precompiled database of thermodynamic properties and rate coefficients for known species and reactions with the ability to estimate these parameters for new species and reactions. The software was tested on methane dry reforming on nickel. It successfully “discovered” the many of the same reactions as a previously compiled mechanism that was developed over many years by experts.

Acknowledgement The project was made possible by collaborative tools GitHub, Slack, FaceTime, Screen Sharing, and Blue Bottle. CFG gratefully acknowledges support from Brown University, and RHW the same from Northeastern University.



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Supporting Information Available The following files are available free of charge. • Instructions, input files, output files, and post-processing scripts to generate figures 6–9, and the figures themselves, are at http://doi.org/10.6084/m9.figshare.4640098.v1 (ref. 98). • The source code for the version of RMG-Cat described here is archived at https://doi.org/10.5281/zenodo.290119 (ref. 54). • The database for the version of RMG-Cat described here is archived at https://doi.org/10.5281/zenodo.290120 (ref. 55). This material is available free of charge via the Internet at http://pubs.acs.org/.

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Graphical TOC Entry 10 0

CH4 CO2

CO H2

vacant

10 -1

H*

CH*

CO*

10 -2

site fraction

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C* CH 3 C*O

10 -3

CH 3 C* 10 -4

O*

10 -5

C 2 HO*

CH 2 *

O*

CHO 2 *

10 -6 10 -6

10 -5

10 -4

10 -3

10 -2

time (s)

XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX


10 -1

10 0

Automatic Generation of Microkinetic Mechanisms for Heterogeneous

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