Microkinetic Modeling

Any process involving the reactions of gases at surfaces, and specifically a heterogeneous catalytic process or a vapor-based deposition/etch process, is the result of the repeated occurrence of competing elementary steps whereby the product of one step becomes a reactant in subsequent steps. For example, reactants must first adsorb onto the surface, then diffuse towards each other, then react forming the product, and finally desorb. Some or all of the elementary processes may be thermally activated and so take place over various timescales.

For a single reaction, there are several possible reaction channelsThe possible pathways of elementary reactions that can link a product and reactant (pathways) connecting reactants and products (see the below graphic). Each reaction channel (usually) constitutes multiple elementary steps. A collection of reaction channelsThe possible pathways of elementary reactions that can link a product and reactant form a reaction networkA collection of reaction channels. There is often a minimum energy pathway (blue arrows on the figure), but most reactions take place through several channels simultaneously.

Microkineticsan approach to determining the properties of a reaction network by studying the elementary reactions that compose it is an approach that determines the outcome of the coupled kinetics of a reaction network. As input, microkinetics requires:

the initial concentrations (coverages) of surface species
partial pressures of gasses
temperature
a reaction network where the kinetics of each elementary step is defined by reactants, products, activation energies and pre-exponential factors for the forward and reverse elementary reactions

Microkinetics then solves the set of coupled kinetic equations for the rates and surface coverages of the reactants, intermediates and products. Analyzing the results reveals the effectiveness of the overall chemical process - perhaps in terms of the turn-over frequency (TOF) for each elementary step and the factors that control it, such as rate determining steps or optimal reactor conditions. In the case of thin film deposition, typical output would be the growth rate over a period of time. Microkinetic modeling (MKM) thus provides a powerful tool for optimization of reactor conditions, catalysts, and gaseous reactants or precursors. Such modeling is useful for studying reactivity relevant to heterogeneous catalysis and atomic layer deposition or etching.

The forward and reverse free energy barriers for elementary reaction steps necessary for microkinetics, can be obtained from experiment, empirical estimates, or directly calculated using a quantum mechanical approach.

In this tutorial, we will learn to use the Microkinetic Modeling and Microkinetic Viewer panels to investigate the process kinetics of a CO oxidation catalyst. As inputs, we provide a reaction network and corresponding forward and reverse activation free energies that were previously determined from periodic quantum mechanics calculations with the Schrödinger implementation of Quantum ESPRESSO.

On overview of the workflow is shown below:

For additional practice in solid-state modeling with Schrödinger, see the Electronic Structure Calculations of Bulk Crystals Using Quantum ESPRESSO, Modeling Surfaces and Activation Energies for Reactivity in Solids and on Surfaces tutorials.

2. Creating and Saving Projects

At the start of the session, change the file path to your chosen Working Directorythe location where files are saved in MS Maestro to make file navigation easier. Each session in MS Maestro begins with a default Scratch Projecta temporary project in which work is not saved, closing a scratch project removes all current work and begins a new scratch project, which is not saved. A MS Maestro project stores all your data and has a .prj extension. A project may contain numerous entries corresponding to imported structures, as well as the output of modeling-related tasks. Once a project is saved, the project is automatically saved each time a change is made.

Structures can be built in MS Maestro or can be imported using File > Import Structures (or drag-and-dropped), and are added to the Entry Lista simplified view of the Project Table that allows you to perform basic operations such as selection and inclusion and Project Tabledisplays the contents of a project and is also an interface for performing operations on selected entries, viewing properties, and organizing structures and data. The Entry Lista simplified view of the Project Table that allows you to perform basic operations such as selection and inclusion is located to the left of the Workspacethe 3D display area in the center of the main window, where molecular structures are displayed. The Project Tabledisplays the contents of a project and is also an interface for performing operations on selected entries, viewing properties, and organizing structures and data can be accessed by Ctrl+T (Cmd+T) or Window > Project Table if you would like to see an expanded view of your project data.

Double-click the Materials Science icon
- (No icon? See Starting Maestro)

Figure 2-1. Change Working Directory option.

Go to File > Change Working Directory
Find your directory, and click Choose
Pre-generated files are included for running jobs or examining output. Download the zip file here: schrodinger.com/sites/default/files/s3/release/current/Tutorials/zip/microkinetic_modeling.zip
After downloading the zip file, unzip the contents in your Working Directorythe location where files are saved for ease of access throughout the tutorial

Figure 2-2. Save Project panel.

Go to File > Save Project As
Change the File name to MKM_tutorial, click Save
- The project is now named MKM_tutorial.prj

3. Summary of Input Reaction Energetics

Microkinetic modeling requires the specification of all elementary reactions in terms of all reactants, products, and forward and reverse free energy barriers for each elementary step. In this section, we summarize the data that will be used in the subsequent sections of the tutorial.

In this tutorial, we consider the CO oxidation (COO) reaction catalyzed by a metallic surface:

CO + ½ O₂ → CO₂

The overall oxidation reaction is believed to consist of the following elementary steps (see References). Here, and in what follows, the asterisk (*) indicates the active site of the catalyst and/or the molecule adsorbed on this site. Molecular symbols without an asterisk refer to the gas phase species.

1.	* + CO → CO*	CO adsorption on the catalyst
2.	* + O₂ → O₂*	O₂ molecular adsorption on the catalyst
3.	* + O₂* → 2 O*	O₂ dissociation at the surface
4.	CO* + O* → CO₂* + *	CO oxidation (COO)
5.	CO₂* → CO₂ + *	CO₂ desorption

In this specific example, we shall examine an Au terminated (111) surface on an AuPd alloy catalyst, and so we label the active sites as *:AuPd. It can be verified by DFT calculations that the CO₂ adsorption energy to this surface is positive (i.e. energetically unfavorable at zero Kelvin), and furthermore that the CO₂ molecule desorbs from the surface without barrier. Therefore, the CO₂* intermediate in the reaction network is unstable (no minimum on the potential energy surface), and Reactions 4 and 5 (above) can be merged into a single elementary step:

4+5.

CO* + O* → CO₂ + 2*

Oxidation and CO₂ desorption

Note that the catalyst is defined in this MKM scheme as providing surface sites (denoted with the asterisk) that can be bare or occupied by intermediates, but that the catalyst itself does not undergo any chemical change. All atoms that take part in surface reactions must feature explicitly in the reaction network. The chemical equation for each elementary step must be balanced, including balancing the number of catalyst sites (*).

The forward and reverse free energy barriers for elementary reaction steps can be obtained from experiment, empirical estimates, or directly calculated using a quantum mechanical approach.

For this example, we have performed quantum mechanical calculations for CO oxidation on the AuPd alloy, modeled on a literature study (Rationally Tailoring Catalysts for the CO Oxidation Reaction by Using DFT Calculations, DOI:10.1021/acscatal.1c04331). This involves optimizing the structures of reactants and products, as well as finding the transition states that link them with a technique such as the nudged elastic band approach. Optimizations and nudged elastic band calculations were performed at the GGA-PBE level of theory with the DFT-D3 dispersion correction.

The current MKM model assumes the lack of adsorbate-adsorbate interactions. As we will see, this assumption is justified in this case due to the very weak-binding nature of the catalyst, which results in very low coverages. At these low coverages, repulsive adsorbate-adsorbate interactions are minimized. But in other cases, such as when coverages are very high or when there are strongly attractive adsorbate-adsorbate interactions, it may be more accurate to model the effect of these interactions on the standard free energies of the adsorbates (see, Achieving Theory–Experiment Parity for Activity and Selectivity in Heterogeneous Catalysis Using Microkinetic Modeling. DOI:10.1021/acs.accounts.2c00058).

Following steps similar to those introduced in the tutorials Electronic Structure Calculations of Bulk Crystals Using Quantum ESPRESSO, Modeling Surfaces and Activation Energies for Reactivity in Solids and on Surfaces, the below structures and their corresponding electronic energies were generated.

Summary of Structures

Name	Description	Image
CO	Gaseous CO
_O₂	_{Gaseous O₂}
_CO₂	_{Gaseous CO₂}
*:AuPd	Bare slab
CO:AuPd	Slab with CO bound in an atop position
O2:AuPd	Slab with O₂ interacting with the surface
O:AuPd	Slab with O atom bound in a hollow position
TS-COO	Transition state associated with OC-O bond formation (CO oxidation)

The calculated electronic energies for the gas species were converted into free energies at 623 K with p(CO) = p(O₂) = p(CO₂) = 1 bar, via a vibrational analysis calculation performed with Quantum ESPRESSO, assuming the ideal gas model. The free energies of the solid catalyst and of the adsorbed intermediates were calculated using a quasiharmonic approximation, whereby the zero point energy (ZPE) corrections, vibrational free energy and vibrational entropy contributions were calculated from phonon frequencies. From these free energy values, the reaction network to be used in the MKM calculation was generated and is summarized in the table below.

Reaction Network

	Reaction	∆G_rxn Forward (eV)	∆G_TSForward (eV)	Forward Barrier (eV)	Reverse Barrier (eV)
1.	*:AuPd + CO → CO:AuPd	0.446	assumed same as ∆G_rxn	0.446	0.000
2.	*:AuPd + O₂ → O2:AuPd	1.045	assumed same as ∆G_rxn	1.045	0.000
3.	*:AuPd + O2:AuPd → 2 O:AuPd	0.713	assumed same as ∆G_rxn	0.713	0.000
4+5.	CO:AuPd + O:AuPd → CO₂ + 2 *:AuPd	-4.056	0.250	0.250	4.306

The kinetics of the forward and reverse reactions depend on the forward and reverse barriers (i.e. activation free energies). The forward barrier is the free energy difference from reactants to the transition state, and the reverse barrier is the free energy difference from the products to the transition state. The table above shows how these are derived arithmetically from ∆G_rxn(forward) and ∆G_TS(forward). Specifically, in the cases of reactions 1-3, we assume that the reverse reaction is barrierless and therefore that the reaction energy ∆G_rxn(forward) is the forward barrier. For reaction 4+5, we located a transition state for CO oxidation and computed its barrier with quantum mechanics, ∆G_TS(forward), which is the forward barrier, meaning that the reverse barrier is given by ∆G_TS(forward) - ∆G_rxn(forward).

Note that it is important that both atoms and surface sites (:AuPd) are balanced in each elementary step.

As an alternative view of the energy landscape, the reaction profile is summarized (both electronic energies and free energies) in the plots below, with a black dot indicating the transition state. Note that to account for stoichiometry, the energy profiles are shown for the reaction: 2 CO + O₂ → 2 CO₂.

Reaction Profile

4. Performing a Microkinetic Modeling Calculation

In this section, we will set up a calculation using the Microkinetic Modeling panel.

Figure 4-1. Opening the Microkinetic Modeling panel.

Go to Tasks > Materials > Quantum Mechanics > Surface Science > Microkinetic Modeling
- The Microkinetic Modeling panel opens

Figure 4-2. The Reactor Settings tab.

The Reactor Settings tab is used to specify the Physical conditions to model, as well as the Catalyst(s).

Change the Temperature to 623 K
- For this example, we will explore the kinetics at this specific temperature

In this example, we have a single catalyst.

Under Catalysts, click Add…
- A window appears to name the catalyst

Figure 4-3. Defining the catalyst name.

For Name input AuPd
Click OK

Figure 4-4. The catalysts table after adding AuPd.

A row is added to the Catalysts table with the catalyst, now named AuPd. The Loading, Specific Surface Area and Site Density can be modified. Note that in this example with constant pressure and no explicit model reactor, these quantities will not matter. See the help documentation for summaries of these parameters.

^{Note: In some chemical processes, surface species may be exchanged with the bulk solid, as well as with the gas phase. For example, atoms may diffuse into the solid catalyst or onto a support, or layers of a solid product may be deposited or etched away. To account for such situations, the notion of Bulks is introduced as a source or a sink of absorbed species. Bulks will not be used in this tutorial. See the help documentation for more on Bulks.}

Figure 4-5. The Reaction Network tab.

Go to the Reaction Network tab

The Reaction Network tab is used to specify the relevant Species (Adsorbed intermediates, Absorbed intermediates and Gas/solute species), and their corresponding Reactions.

Note: The reactants that appear or disappear from/into the bulks (see the Note above) are defined as Absorbed intermediates. These will not be used in this tutorial - they should only be defined when Bulks are used. See the help documentation for more on Absorbed intermediates.

Figure 4-6. Adding the CO adsorbate.

First we will define the Adsorbed intermediates, which will be bound CO, O₂, and O.

Click Add Adsorbate
- A panel appears to define the adsorbate
For Chemical formula input CO
Skip the Description and click OK
- The Description can be useful for additional labeling that is not a chemical formula, which, if used, will be added to the name of the adsorbed intermediate

Note: In this case, there is only one catalyst (AuPd). In cases with multiple catalysts or multiple active sites per catalyst (defined as unique catalysts on the Reactor Settings tab), be sure to also select the corresponding Catalyst from the dropdown.

Figure 4-7. The CO adsorbate added to the panel.

The Adsorbed intermediates table is updated to include CO:AuPd.

Note: In this case of a single catalyst, the nomenclature (CO:AuPd) is equivalent to the commonly used CO* nomenclature.

Figure 4-8. Adding the O2 and O adsorbates.

Following the same procedure, add O2 and O as additional Adsorbed intermediates
- The Figure depicts the panel after completing this process

Figure 4-9. Adding the CO gas molecule.

In this example, there are no Absorbed intermediates. Accordingly, we will proceed to enter the Gas/solute species.

Click Add Gas/Solute
- A panel appears to define the gas/solute
For Chemical formula input CO
Skip the Description and click OK
- An additional label can be specified in the Description and, if used, will be added to the name of the species

Figure 4-10. The CO adsorbate added to the panel.

The Gas/solute species table is updated to include CO.

Figure 4-11. Adding the O2 and CO2 gas molecules.

Following the same procedure, add O2 and CO2 as additional Gas/solute species
- The Figure depicts the panel after completing this process

Figure 4-12. Adjusting the Partial Pressures and Molecular Weights.

In this example, we will take the Partial Pressure in Inlet Stream to be 1 bar, 1 bar and 0 bar for CO, O₂ and CO₂, respectively.

Change the Partial Pressure for CO and O2 to 1 bar

Figure 4-13. The panel before adding the Reactions.

We have now accounted for all of the relevant species which will be used in the Reactions section of the panel. Notice that the species are now listed across the top of the Reactions table.

Figure 4-14. Adding the CO_adsoprtion reaction.

Let’s proceed to add the relevant Reactions.

Click Add Reaction
- A panel appears to define the reaction name
For Name input CO_adsorption
Click OK

Figure 4-15. The CO_adsoprtion reaction added to the panel.

The Reactions table is updated to include CO_adsorption.

Figure 4-16. Adding the additional Reactions.

Following the same procedure, specify O2_adsorption, O2_dissociation, and CO_oxidation as additional Reactions
- The Figure depicts the panel after completing this process

Each elementary step is defined by the stoichiometric coefficients of the balanced reaction and the forward and reverse free energy barriers (i.e. activation free energies).

Negative integers are used for the stoichiometric coefficients of reactants and positive integers are used for those of products.

The forward and reverse barriers are taken from the discussion in Section 3.

Figure 4-17. Defining stoichiometry and barriers for the CO_adsorption reaction.

For the CO_adsorption reaction, input -1, 1, 0, 0, -1, 0, 0 for the coefficients
- These coefficients represent the reaction of one CO molecule adsorbing on the AuPd surface
For the CO_adsorption reaction, input 0.446 for the Forward Barrier and 0.000 for the Reverse Barrier

Figure 4-18. Defining stoichiometry and barriers for the remaining reactions.

For the remaining three reactions, use the following coefficients and barriers (consult the Figure to be sure you are inputting the values correctly):
- O2_adsorption: -1, 0, 1, 0, 0, -1, 0; 1.045, 0.000
- O2_dissociation: -1, 0, -1, 2, 0, 0, 0; 0.713, 0.000
- CO_oxidation: 2, -1, 0, -1, 0, 0, 1; 0.250, 4.306

Figure 4-19. Viewing the reaction network.

Click View Reactions
- A window depicting the reaction network opens. Compare this with the reaction network shown earlier. The 4th and 5th step are merged into a single step.
Close the window.

Figure 4-20. Finalizing the settings, naming, and running the job.

Go to the Steady State tab
Check Calculate degree of rate control
- The degree of rate control is an important feature in analyzing the rate-limiting step(s) in the overall reaction. However, in cases of more complex reaction networks, note that it can also substantially slow down the calculation
Check Calculate reaction order
Change the Job name to microkinetic_modeling_AuPd_COO
Adjust the job settings () as needed. The job can be completed in 5 minutes on a CPU host
If you would like to run the job yourself, click Run. Otherwise, we will proceed with imported results files in the next section

Figure 4-21. The Solver Settings tab.

In this example, we maintain the defaults available on the Solver Settings tab. Feel free to visit the tab to see the available parameters, and view the help documentation for more information.

We also will not adjust the settings in the Multistage tab, though this tab is useful when looking at reaction steps that may be occurring under different reaction conditions. See the help documentation for more information.

Close the Microkinetic Modeling panel

Given the reaction network, reactor conditions, and activation barriers, the microkinetic solver searches for the steady state concentrations (coverages) of all species, equilibrium reaction rates, and (optionally) reaction orders, as well as turnover frequencies and (optionally) degrees of rate control of relevant reactions. The current numerical implementation solves for time dependent surface coverages and reaction rates and can optionally search for a time independent steady state solution, where all coverages are constant. In the next section, we discuss how to analyze these complex data.

5. Analyzing a Microkinetic Modeling Calculation

In this section, we will use the Microkinetic Viewer panel to analyze the output of the previous calculation.

Figure 5-1. Loading the output file.

We will proceed to import the results (in this case from the provided files).

Go to File > Import Structures
Navigate to the provided files and choose microkinetic_modeling_AuPd_COO.mae via Section_05 > microkinetic_modeling_AuPd_COO
Click Open

Note: When running the job yourself, after successful completion, it will be incorporated into the entry lista simplified view of the Project Table that allows you to perform basic operations such as selection and inclusion. The entry will have a WAM (workflow action menu) button () for loading the results. If the calculation fails, you can still manually import the .mae output into MS Maestro and then manually into the panel. All results for failed jobs are reported to enable analysis of the failure.

Figure 5-2. Opening the Microkinetic Viewer panel.

An entry group containing a dummy structure is added to the entry lista simplified view of the Project Table that allows you to perform basic operations such as selection and inclusion. This contains all of the data for loading the Microkinetic Viewer panel.

Use the WAM (workflow action menu) button () to access the Microkinetic Viewer panel
- Alternatively, go to Tasks > Materials > Quantum Mechanics > Surface Science > Microkinetic Modeling and use the Import from Workspace button to load the panel
- The Microkinetic Viewer panel opens

The output data is organized into two main tabs, Time Profile and Steady State, each with various subtabs. The Time Profile tab includes data across the various integration steps, whereas the Steady State tab provides the data at the last step of the simulation. Complete descriptions of each tab are available in the help documentation.

Feel free to explore all of the tabs of interest. For this example, we will only highlight the outputs most relevant to this specific case.

Figure 5-3. The Coverage plot in the Time Profile tab.

Go to the Time Profile tab
Go to the Coverage subtab
Check Plot log10, increasing small values to this power -20
- In this case with very small coverage values, log conversion helps visualize the data

The plot shows the log₁₀(Coverage) versus integration step. The plot indicates that a steady state solution is achieved (constant coverages, evidenced by plateaus on the plot).

Figure 5-4. The Coverage plot in the Steady State tab.

Go to the Final State tab
Go to the Coverage subtabCheck Plot log10

This plot illustrates the surface fractions (coverages) occupied by reactants, intermediates as well as of vacant active sites.

Note that the sum of all coverages equals 1.

Minding the log scale on the vertical axis, we conclude that at the given conditions, most of the active sites are empty, and the surface coverages of CO* and O* are very low.

Figure 5-5. The Reaction Rate plot in the Steady State tab.

Go to the Reaction Rate (1/s) subtab
Check Plot log10

In this plot, we can observe the difference between forward and reverse rates for all reactions.

There is often only one (or very few) reaction(s) where the forward rate is much greater than the reverse rate (proportionally). In this case, it is CO₂ formation (CO_oxidation). All other steps are observed to be "quasi-equilibrated," where the forward and reverse rates are approximately equal, and therefore much greater than the small net rate. The dominant forward rate of CO_oxidation is an indication that the CO₂ formation step is irreversible. Oftentimes, irreversible steps are rate-limiting steps, but not always. Indeed, as we will see in the next plot, this irreversible step is not the rate-limiting step in this example.

Figure 5-6. The Degree of Rate Control plot in the Steady State tab.

Go to the Degree of Rate Control subtab
Uncheck Plot log10, increasing small values to this power -20

The plot shows that the overall rate of the reaction is essentially controlled by the O₂ dissociation step. Therefore, decreasing the reaction barrier for the O₂ dissociation elementary step could directly speed up the net reaction, whereas decreasing the barriers for other steps will have less effect on the overall reaction rate.

Figure 5-7. The reactions_data.csv.

Finally, note that in the output job directory, all the raw data is recorded in a series of .csv files. This is the data that has been used for the visualization in this section.

For example, in the Figure, the reactions_data.csv output is shown.

Figure 5-8. The rxn_order.csv.

In this Figure, the rxn_order.csv output is shown.

As expected based on the above analysis, the reaction orders are ~0, 0 and ~1 for CO, CO₂ and O₂, respectively.

The calculations indicate that at the tried conditions, CO₂ production over the (111) Au:AuPd catalyst is very slow. The prime deficiency of this catalyst is that it is not efficient in O₂ adsorption and dissociation which becomes the rate limiting step for this system. An optimal catalyst would exhibit a much lower barrier for oxygen dissociation and higher atomic O binding, such that the steady state O coverage would stay in the region of 30% and would be comparable with CO coverage. Such conditions and materials would lead to the ‘CO oxidation’ step becoming rate limiting and would deliver a more effective catalytic reaction overall.

The presented modeling demonstrates the power of microkinetic modeling, especially in combination with studying mechanism and quantifying free energies with density functional theory. It also demonstrates that the rate limiting step for a given catalyst and reaction conditions can be determined automatically. Notably, simple analysis of the free energy profile (see Section 3) alone may lead to incorrect conclusions.

It must be noted that in the current implementation, MKM implicitly assumes that standard state activation energies are independent of surface coverage (which is true for small and moderate coverages), and also assumes fast surface diffusion, assuring that diffusion of the species is not a rate limiting step. These assumptions, referred to as the mean field model, must be critically assessed in each individual case.

6. Modeling Adsorbate-Adsorbate Interactions in a Microkinetic Modeling Calculation

In the case study above, we observe that the steady state coverages of the reactants, intermediates, and the products are very low (Fig. 4.5). However, in some catalytic systems, the reagent coverages could reach the values of order of 1 (complete coverage). In practice, at high coverages the adsorbates interact with each other (mostly repulsively). Therefore, the adsorption energies and the activation barriers at high coverages become coverage-dependent. Such coverage dependence in principle can be explicitly calculated using ab initio calculations by varying the concentration of the adsorbates in the unit cell. In the MKM model adsorbate-adsorbate interaction is introduced via the quadratic repulsive term

_{f(θ)=(a_ia_j)^1/2 θ_iθ_j}

_{where θ represents the coverage of the species i and j, and ai,j are the constants for the quadratic terms of the species i and j respectively. The other term reflecting the adsorbate-adsorbate interaction at the transition state is the lateness parameter. The TS lateness parameter takes the values between 0 and 1 and reflects whether the transition state is similar to the initial state (TS lateness = 0) or to the final state of the reaction (TS lateness = 1). In the example below we shall learn how to set up these parameters and how they are used for more accurate modelling.}

In this section, we will set up a calculation using the Microkinetic Modeling panel to study adsorbate-adsorbate interactions of CO oxidation on Pd (111) surface as illustrated below

The key elementary reactions involved in the catalytic oxidation of CO on a Pd(111) surface are (* denotes a free surface site):

CO Adsorption: CO(g) + * → CO*

O₂ Dissociative Adsorption: O₂(g) + 2* → 2O*

CO Oxidation: CO* + O* → CO₂(g) + 2*

It's worth noting that while the catalyst has been changed from AuPd to Pd, we are still examining the same CO oxidation reaction as before. Additionally, the four elementary steps previously outlined have now been streamlined into three.

Figure 6-1. Opening the Microkinetic Modeling panel.

Go to Tasks > Materials > Quantum Mechanics > Surface Science > Microkinetic Modeling
- The Microkinetic Modeling panel opens

Figure 6-2. The Reactor Settings tab.

The Reactor Settings tab is used to specify the Physical conditions to model, as well as the Catalyst(s).

Change the Temperature to 623 K
- For this example, we will explore the kinetics at this specific temperature

In this example, we have a single catalyst.

Under Catalysts, click Add…
- A window appears to name the catalyst

Figure 6-3. Defining the catalyst name.

For Name input Pd111
Click OK

Figure 6-4. The catalysts table after adding Pd111.

A row is added to the Catalysts table with the catalyst, now named Pd111.

Set Loading to 1
Set Specific Surface Area to 3.82e-09
Set Site Density to 7.7e+14

Figure 6-5. The Reaction Network tab.

Go to the Reaction Network tab

The Reaction Network tab is used to specify the relevant Species (Adsorbed intermediates, Absorbed intermediates and Gas/solute species), and their corresponding Reactions.

Figure 6-6. Adding the CO adsorbate.

First we will define the Adsorbed intermediates, which will be bound CO and O.

Click Add Adsorbate
- A panel appears to define the adsorbate
For Chemical formula input CO
Skip the Description and click OK

Figure 6-7. The CO adsorbate added to the panel.

The Adsorbed intermediates table is updated to include CO:Pd111.

Note: In this case of a single catalyst, the nomenclature (CO:Pd111) is equivalent to the commonly used CO* nomenclature.

Figure 6-8. Adding the O adsorbate.

Following the same procedure, add O as additional Adsorbed intermediates
- The Figure depicts the panel after completing this process

Figure 6-9. Adding the CO gas molecule.

In this example, there are no Absorbed intermediates. Accordingly, we will proceed to enter the Gas/solute species.

Click Add Gas/Solute
- A panel appears to define the gas/solute
For Chemical formula input CO
Skip the Description and click OK
- An additional label can be specified in the Description and, if used, will be added to the name of the species

Figure 6-10. The CO adsorbate added to the panel.

The Gas/solute species table is updated to include CO.

Figure 6-11. Adding the O2 and CO2 gas molecules.

Following the same procedure, add O2 and CO2 as additional Gas/solute species
- The Figure depicts the panel after completing this process

Figure 6-12. Adjusting the Partial Pressures and Molecular Weights.

Change the Partial Pressure for CO to 0.02 bar
Change the Partial Pressure for O2 to 0.08 bar

Figure 6-13. The panel before adding the Reactions.

We have now accounted for all of the relevant species which will be used in the Reactions section of the panel. Notice that the species are now listed across the top of the Reactions table.

Figure 6-14. Adding the CO_adsoprtion reaction.

Let’s proceed to add the relevant Reactions.

Set Adsorbate-adsorbate interactions to Simple quadratic
Click Add Reaction
- A panel appears to define the reaction name
For Name input CO_adsorption
Click OK

Figure 6-15. The CO_adsoprtion reaction added to the panel.

The Reactions table is updated to include CO_adsorption.

Note: A Lateral Scaling Parameter option has been added to the adsorbed intermediates section when adsorbate-adsorbate interactions are set to simple quadratics; this will be discussed later in the setup.

Figure 6-16. Adding the additional Reactions.

Following the same procedure, specify O2_dissociation and CO_oxidation as additional Reactions
- The Figure depicts the panel after completing this process

Figure 6-17. Defining stoichiometry and barriers for the CO_adsorption reaction.

For the CO_adsorption reaction, input -1, 1, 0, -1, 0, 0 for the coefficients
- These coefficients represent the reaction of one CO molecule adsorbing on the Pd111 surface
For the CO_adsorption reaction, keep 0.000 for the Forward Barrier and input 0.137 for the Reverse Barrier
Set the Collision Factor to Hertz-Knudsen
For now, keep the TS Lateness Parameter as the default value
- A TS lateness parameter is used to partition the lateral interaction correction to the reaction energy into corrections for the forward and reverse barriers

Figure 6-18. Defining stoichiometry and barriers for the remaining reactions.

For the remaining reactions, use the following coefficients and barriers (consult the Figure to be sure you are inputting the values correctly):
- O2_dissociation: -2, 0, 2, 0, -1, 0; 0.000, 1.151, Hertz-Knudsen
- CO_oxidation: 2, -1, -1, 0, 0, 1; 0.717, 999, Auto

Figure 6-19. Viewing the reaction network.

Click View Reactions
- A window depicting the reaction network opens.
Close the window

Figure 6-20. Finalizing the naming and running the job.

All other tabs will retain their default settings for this calculation.

Change the Job name to microkinetic_modeling_Pd111
Adjust the job settings () as needed. The job can be completed in 5 minutes on a CPU host
If you would like to run the job yourself, click Run. Otherwise, we will proceed with imported results files

Figure 6-21. Varying the Lateral Scaling Parameter.

We will conduct four additional calculations. In the first two, we will vary the lateral scaling parameter to 0 and 2 eV, keeping the TS Lateness Parameter constant at 0.5. For the next two calculations, the TS Lateness Parameter will be adjusted to 0 and 1, while the Lateral Scaling Parameter remains at its default value of 1.0. This will allow for a comparison of results across lateral scaling parameters of 0, 1, and 2 eV, and TS Lateness Parameters of 0, 0.5, and 1.

Set the Lateral Scaling Parameter to 0
Change the Job name to microkinetic_modeling_Pd111_scaling_0
Adjust the job settings () as needed. The job can be completed in 5 minutes on a CPU host
If you would like to run the job yourself, click Run. Otherwise, we will proceed with imported results files
Repeat for a Lateral Scaling Parameter of 2 and change the Job name to microkinetic_modeling_Pd111_scaling_2

Figure 6-22.Varying the TS Lateness Parameter.

Reset the Lateral Scaling Parameter to the default value of 1.0
Set the TS Lateness Parameter to 0.0
Change the Job name to microkinetic_modeling_Pd111_lateness_0
Adjust the job settings () as needed. The job can be completed in 5 minutes on a CPU host
If you would like to run the job yourself, click Run. Otherwise, we will proceed with imported results files
Repeat for a TS Lateness Parameter of 1 and change the Job name to microkinetic_modeling_Pd111_lateness_1
Close the Microkinetic Modeling panel

Figure 6-23. Importing and viewing the results

Go to File > Import Structures
Navigate to the provided files and choose Section_06 > microkinetic_modeling_Pd111 > microkinetic_modeling_Pd111.mae
Click Open
Import in the other 4 output structures, microkinetic_modeling_Pd111_scaling_0.mae, microkinetic_modeling_Pd111_scaling_2.mae, microkinetic_modeling_Pd111_lateness_0.mae, microkinetic_modeling_Pd111_lateness_1.mae
Use the WAM (workflow action menu) button () to access the Microkinetic Viewer panel
- Alternatively, go to Tasks > Materials > Quantum Mechanics > Surface Science > Microkinetic Modeling and use the Import from Workspace button to load the panel
- The Microkinetic Viewer panel opens
Go to the Final State tab
Repeat this viewing process for the remaining 4 results

Note: To conceal the lateral scaling parameter, click the orange box within the legend.

The graphs below display the coverage results and TOF values, demonstrating the impact of varying the lateral scaling and TS lateness parameters. The central graph represents the default settings.

7. Conclusion and References

In this tutorial, we learned how to use the Microkinetic Modeling panel to predict the overall reaction kinetics of a gas-surface chemical process and the factors controlling it.

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For further learning:

For introductory content, focused on navigating the Schrödinger Materials Science interface, an Introduction to Materials Science Maestro tutorial is available. Please visit the materials science training website for access to 70+ tutorials. For scientific inquiries or technical troubleshooting, submit a ticket to our Technical Support Scientists at help@schrodinger.com.

For self-paced, asynchronous, online courses in Materials Science modeling, including access to Schrödinger software, please visit the Schrödinger Online Learning portal on our website.

For related practice, proceed to explore other relevant tutorials:

Catalytic Selectivity Through Microkinetic Modeling
Introductory and advanced topics in solid-state modeling:

Introductory and advanced topics in homogeneous catalysis and reactivity:

Click to Expand

For further reading:

Help documentation on Microkinetic Modeling and Microkinetic Viewer panels
Rationally Tailoring Catalysts for the CO Oxidation Reaction by Using DFT Calculations. DOI:10.1021/acscatal.1c04331.
Introduction to microkinetic modeling. 20.500.12657/53253.
Microkinetic Modeling: A Tool for Rational Catalyst Design. DOI:10.1021/acs.chemrev.0c00394
Fundamental Concepts in Heterogeneous Catalysis. DOI:10.1002/9781118892114.
Chapter X: The Oxidation of Carbon Monoxide. DOI:10.1016/S0167-2991(08)64835-1
Achieving Theory–Experiment Parity for Activity and Selectivity in Heterogeneous Catalysis Using Microkinetic Modeling. DOI:10.1021/acs.accounts.2c00058
Influence of Coverage Dependence on the Thermophysical Properties of Adsorbates and Its Impact on Microkinetic Models. DOI:10.1021/acs.jcim.4c02167

8. Glossary of Terms

Entry List - a simplified view of the Project Table that allows you to perform basic operations such as selection and inclusion

Microkinetics - an approach to determining the properties of a reaction network by studying the elementary reactions that compose it

Project Table - displays the contents of a project and is also an interface for performing operations on selected entries, viewing properties, and organizing structures and data

Reaction Channels - The possible pathways of elementary reactions that can link a product and reactant

Reaction Network - A collection of reaction channels

Scratch Project - a temporary project in which work is not saved, closing a scratch project removes all current work and begins a new scratch project

Working Directory - the location where files are saved

Workspace - the 3D display area in the center of the main window, where molecular structures are displayed