Kinetic Monte Carlo Simulations of Methanol Synthesis from Carbon

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Kinetic Monte Carlo Simulations of Methanol Synthesis from Carbon Dioxide and Hydrogen on Cu(111) Catalysts: Statistical Uncertainty Study Drejc Kopa#, Matej Hus, Mitja Ogrizek, and Blaž Likozar J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b04985 • Publication Date (Web): 08 Aug 2017 Downloaded from http://pubs.acs.org on August 10, 2017

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The Journal of Physical Chemistry

Kinetic Monte Carlo Simulations of Methanol Synthesis from Carbon Dioxide and Hydrogen on Cu(111) Catalysts: Statistical Uncertainty Study Drejc Kopa£,

∗

Matej Hu², Mitja Ogrizek, and Blaº Likozar

Department of Catalysis and Chemical Reaction Engineering, National Institute of Chemistry, Hajdrihova 19, SI-1001 Ljubljana, Slovenia

E-mail: [email protected]

1

ACS Paragon Plus Environment


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Abstract An optimal multi-scale linking and integration of atom-scale density functional theory (DFT) computations with mesoscopic kinetic Monte Carlo (KMC) is gaining in importance, particularly upon considering the engineering and intensication of unconventional feedstock processing, as well as the design of emerging catalysis routes. Carbon dioxide activation for methanol synthesis reactions on Cu(111) catalysts was studied using rst principles calculations and KMC modeling simulations. CO2 hydrogenation pathway model was applied, consisting of the formate and the reverse water gas shift (RWGS) mechanistic steps. The dependence of conversion, selectivity and the rate of desorbed bulk CH3 OH production upon operating process conditions, primarily temperature and pressure, was examined. Catalytic performance results are qualitatively well comparable with the available literature data for heterogeneous copper-based materials. Furthermore, the numerical stability analysis of KMC simulations was statistically assessed with respect to random seed parameters and activation energy barriers. Surface product distribution was found to be particularly sensitive to the smallest perturbations of the activation standard Gibbs energy. The eects of binding site size, crystal lattice dimensions, packed-bed inux composition (gaseous phase reactant partial pressures) and input randomized numbers were, however, less pronounced. This demonstrates that an accurate evaluation of ab initio theoretical research is crucial, especially upon paralleling them to experimental reactor concentrations.

1 Introduction Methanol is an important industrial resource used either as fuel (e.g. in methanol fuel cells) or as feedstock for the production of other chemicals. 1 Methanol synthesis via hydrogenation of the captured CO2 using surplus electricity for hydrogen production represents an innovative way to decrease CO 2 emissions and increase renewable energy usage, as well as to mitigate the problem of CO2 storage.1 In this scenario, methanol can be produced at thermal power 1 European

Commission, MefCO2 accessed 2017, http://www.mefco2.eu/ , duration 2014-2018.

2


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stations running on fossil fuels, where CO 2 concentration in streams is high and surplus electricity can be used for water electrolysis to produce hydrogen. 2 The key ingredient for successful synthesis is the use of an eective catalyst, which should be robust, yet cost- and production-friendly. The catalysts of choice for methanol synthesis are various copper (Cu) alloys, especially Cu/transition metal/oxide dopants. 3,4 Most industrial processes nowadays use catalysts composed of copper, zinc oxide, and aluminum oxide, which oer good activity and selectivity for methanol production. However, such alloys often engage complex geometries, making active sites unaccessible for CO 2 adsorption. To alleviate this problem, high pressure conditions are required to facilitate stronger bonds with CO 2 , but compressing gas into high-pressure mixture is highly energy consuming. 5 Additionally, high pressures is favored from the stoichiometry point of view. A long term goal is to synthesize catalysts which would require lower pressure and less energy to produce the same amount of methanol. 5 By doing so, we could overcome obstacles such as instability and short-term durability of the catalyst, which are problematic at high pressures. In this paper, we concentrate on pure Cu(111) catalyst and perform the methanol synthesis study using graph-theoretical KMC simulations. We use the methanol synthesis pathway as proposed by Yang et al. (2012). 6 We simulate the system at various pressures and temperatures, to study the selectivity, conversion, and rate (via turn-over frequency, TOF) dependence at dierent conditions. Our results show similar qualitative trends as obtained from experiments. 7,8 The methanol production is favored at low temperatures and high pressures, which is also expected from the thermodynamic point of view. 1 Selectivity is reasonably high (∼ 90%) at high pressures (P = 40 bar), but drops with increasing temperature and decreasing pressure, and is highly dependent on pressure. Conversion and TOF are low, as expected for pure Cu(111) catalyst without additional dopants, which are commonly used to stabilize certain species and/or promote certain reactions. 9,10 Cu(111) was chosen for this study as we are interested in the investigated eects and trend dependence, not the exact reproduction of

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experimental data. Cu(111) allows for an intuitive easy-to-grasp representation, while still maintaining the eects we wish to study. Although rst-principle calculations, such as DFT, allow us to quickly map the reaction pathway and for example discover which elementary reaction represents the bottleneck, the KMC capabilities allow us to:

• Analyze the reaction pathway more precisely (in a stochastic manner), • Study long-term eects, catalyst saturation and deactivation, • Understand how changes of the conditions, especially pressure and temperature, aect the catalytic performance,

• Estimate valuable kinetic results for further use in computational uid dynamics (CFD) simulations. 11,12 The main goal of this paper is to study the sensitivity of KMC simulations. We evaluate DFT results in a statistical manner, as this is an important as well as necessary approach when comparing theory and experiment. 1315 The method employed here to study the distribution of KMC results is to alter the random seed parameter and perturb the activation energy of each individual elementary step. The latter is equivalent to assigning each activation energy some amount of uncertainty. Based on the literature, we used up to ±5% uncertainty. 16,17 We examine how such inaccuracies in activation energies aect KMC results for a wellknown and studied system of methanol synthesis on pure Cu(111) catalyst. We show that the overall results for selectivity, conversion, and TOF are statistically well described when using dierent random seed parameters, but are extremely sensitive to even slight changes in the activation energies, leading to bimodal selectivity distribution and a span of many orders of magnitude for conversion and TOF. The paper is organized as follows. In Section 2 we present the methods and tools used in our simulations, in Section 3 we analyze and discuss the results, and conclude in Section 4. 4


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2 Methods KMC simulations provide a tool for studying the dynamical evolution of systems. Firstprinciple methods, such as DFT, are nowadays widely employed at the molecular scale to understand the elementary events and the reaction mechanisms. Using transition state theory (TST), DFT results are converted into kinetic parameters. 18 However, to estimate activity, selectivity, and performance of the catalyst, and to examine various aspects of catalytic behavior under operating conditions, kinetic modeling studies are required. 19 KMC simulations integrate an accurate description of the involved elementary events (adsorption and desorption processes of reactants and intermediates, as well as surface diusion and reactions) with an account for their statistical interplay, in order to properly evaluate the surface chemical kinetics. 20 The main advantage of KMC, compared to conceptually more intuitive approaches such as rst-principles molecular dynamics (MD) simulations, is its statistical treatment of reactions. Instead of explicitly simulating each potential energy surface barrier crossing, the KMC employs TST arguments, where probabilities of elementary steps are obtained from the rate constants, kTST . These constants, calculated using DFT results and statistical thermodynamics approximations, provide a statistical description of the reaction occurrence; they do not provide exact time when the reaction will take place in the system, but rather imply that within a time interval [tinitial , tfinal ], on average kTST × (tfinal − tinitial ) reaction events will take place. The process is Markovian, i.e. the rates and the current state of the system are independent of the entire system history. 19

2.1

Graph theoretical KMC Zacros

We used the graph-theoretical KMC software package Zacros 2 for simulating catalytic processes. 21 We used the default hexagonal periodic lattice with the lattice constant of 3.6 Å and the size of 40 × 40 cells (3200 lattice sites, as the unit cell for this lattice type is not the 2 http://zacros.org/

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primitive unit cell but it contains 2 sites). For simplicity, we used the single site type lattice. Gas and surface species list, as well as energetics for each of the species, was obtained from Yang

et al.

(2012). 6 The energetics was mapped into Zacros as follows 3 : the reference

set of species is chosen (reference species must have linearly independent compositions), with ascribed relative energy 0 eV. The formation energies for other species is calculated from the reaction energies of elementary reactions steps. The model consists of 11 lattice (single-dentate) and 5 gas species. For the complete list of used species and their energies, the reader is referred to the Supporting Information (Table S1). Elementary reaction steps were also obtained from Yang

et al.

(2012). 6 Each step is

represented in Zacros using its initial and nal state, gas species participating in the reaction, activation energy and the pre-exponential factors for forward and reverse reaction. The methanol synthesis model consists of overall 25 reaction steps (both forward and reverse steps), in formate and RWGS pathway. We updated certain parameters using more thorough analyses, 22,23 as indicated in the Supporting Information section, where the list of all elementary reactions and corresponding parameters is available (Table S2). We note that Yang

et al.

(2012) 6 use constant pre-exponential factor of 1013 s−1 , while we recalculate

pre-exponential factors when changing the initial conditions (temperature and pressure). Following Stamatakis & Vlachos (2011), 21 for Langmuir-Hinshelwood type surface reactions (X∗ + Y∗ → Z∗ + ∗ ) we calculated the pre-exponential factors using

Afwd,rev Surface (T ) =

kB T h

(1)

for both forward and reverse surface reactions, where T is the system temperature, kB is the Boltzmann constant, and h is the Planck constant. For Eley-Riedel type reactions ( X(gas) +

Y∗ → Z∗ ) and for an activated adsorption elementary step (in our case, H 2 dissociative adsorption in the form of H2,(gas) + 2 ∗ → H∗ + H∗ ), we calculated the pre-exponential factors 3 http://zacros.org/index.php/tutorials/10-tutorial-4-mapping-dft-energies-to-zacros-input

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using

Afwd E−R (P, T ) =

1 P ×S √ qrot qtrans 2π m kB T

(2)

and

Arev E−R (T ) =

kB T , h

(3)

where P is the system pressure, S is the eective area of the site where the reaction takes place, and m is the mass of the gas species. The rotational ( qrot ) and translational ( qtrans ) partition functions were calculated using

lin qrot (T ) =

8π 2 I kB T σ h2

(4)

for H2 , CO2 , and CO (linear molecules), and

non−lin qrot (T )

√ 3/2 πIa Ib Ic 8π 2 kB T = σ h2

(5)

for H2 O and CH3 OH (non-linear molecules), while

qtrans (T ) = A

2π m kB T , h2

(6)

where I (Ia , Ib , Ic ) are principal moments of intertia of the molecule in vacuum, and σ is the symmetry number of the molecule. Furthermore, for non-activated adsorption, the pre-exponential factors are

Afwd non−A (P, T ) = √

P ×S 2π m kB T

(7)

kB T . h

(8)

and

Arev non−A (T ) = qrot qtrans

Note that in the above equations, we neglected the contribution of vibrational partition Q −hνi /kB T functions (qvib = 3N )), as well as their temperature dependence. To take i 1/(1 − e 7



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this into account, all vibrational frequencies νi of transition states and educts/products are required. However, in the temperature range that we used, the ratio between transition state and species' vibrational partition functions, which should be included in Equations (1), (2), (3), and (8), is within the same order of magnitude for all elementary reactions and does not change signicantly with the temperature 4 . Using Equations (1)(8), we implemented the change of temperature and pressure into our study and investigated the system behavior at various conditions. We used xed H 2 :CO2 =

8 : 2 molar fraction of species in the gas phase. We also investigated if the change of parameters, such as gas molar fractions, lattice size, and the eective area of the site where the reaction takes place, have any eect on the overall results (see Section 3.4).

3 Results and discussion We simulated methanol synthesis at 7 dierent temperatures (480, 500, 520, 540, 560, 580, 600 K) and at 4 dierent pressures (1, 10, 20, 40 bar). We ran a single simulation at every temperature and pressure, but we discuss in Section 3.5 how to obtain statistics by running multiple simulations at the same conditions, varying the initial random seed. We study how the overall methanol selectivity, conversion and TOF depend on temperature and pressure. The simulations ran for one week (elapsed wall time of 604800 s), each on a single core, reaching the simulation time from 108 s (for pressures of 40 bar) to up to 1012 s (for pressures of 1 bar). On average, 2.5 × 108 KMC steps (events) have occurred during the simulation. The energy of the lattice conguration reached the minimum of E ≈ −4.4 × 102 eV relatively early, typically at simulation times between ∼ 10−4 s (for pressures of 40 bar) and ∼ 10−1 s (for pressures of 1 bar), slightly dependent on the temperature. 4 This

has been tested and conrmed on our more detailed DFT+KMC study of methanol synthesis.

8


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3.1

CH 3 OH and CO production and selectivity

Figure 1 shows the selectivity ( CH3 OH/(CO + CH3 OH)) towards methanol at various temperatures and pressures. The selectivity peaks at ∼ 90% for high pressure and low temperature, but drops with decreasing pressure and increasing temperature. At P = 1 bar, the selectivity towards methanol is essentially zero, i.e. no methanol is produced at low pressures on pure Cu(111) catalyst. Additionally, we observe how CH 3 OH production is especially sensitive to pressure and not so much to temperature more methanol is produced at higher pressures. The opposite is seen for the CO production, which is not so sensitive to pressure, but to temperature more CO is produced at higher temperatures. Such behavior is in good agreement with experimental data. 7,8,24 Higher selectivities ( ∼ 99%) can be achieved at further increased pressures and by using Cu-oxide catalysts. 25,26

3.2

Conversion

Figure 2 shows the conversion ( 1−CO2 (out)/CO2 (in)) of CO2 . The conversions are relatively low, not higher than 10−3 even for the highest pressure. Conversion is highly dependent on pressure, with higher conversion achieved at higher pressures. The temperature dependence is not obvious a slight trend of decreasing conversions with higher temperatures is seen, but the tendency is statistically insignicant.

3.3

Production rate

Production rate or, rather, TOF (number of molecules produced per active site per unit time) for methanol can be obtained from the temporal evolution of methanol production, by tting the number of methanol molecules produced over the runtime of the simulation. Figure 3 shows the TOF versus temperature, for P = 20 bar and P = 40 bar (for lower pressures the TOF is essentially zero). The TOF is very low, but becomes higher at higher pressures and temperatures. Low TOF for pure Cu(111) catalyst was also reported in the literature, 27

9



1.0

P = 1 bar P = 10 bar P = 20 bar P = 40 bar

CH 3 OH ´ CH 3 OH + CO

0.8

0.4 0.2 0.0 120 100 80 60 40 20 0

480

500

520

540 560 580 600 Temperature [K] 120 100 80 60 40 20 0 480 500 520 540 560 580 600 480 500 520 540 560 580 600 Temperature [K] Temperature [K] Total CO

Selectivity

³

0.6

Total CH3 OH

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Figure 1: Top: Selectivity towards methanol versus temperature at various pressures, showing best selectivity at high pressures and low temperatures. Bottom: the total number of CH3 OH and CO molecules produced at the common time of ∼ 108 s, showing that the CH3 OH increase depends more on the pressure, while CO increase depends more on the temperature. Dashed line connects points to guide the eye. based on DFT and mean-eld microkinetic analyses. This is expected since a pure Cu(111) surface lacks defects, steps, interfacial and inter-metallic sites which are especially active for methanol production. The latter are created if support materials such as metal oxides are added. 7 As shown in the literature, 7 partial oxidation of the Cu surface doubles the activity with respect to the oxygen-free Cu surface, but is nevertheless still signicantly lower than the activity for the metal supported Cu-based catalysts. Similarly, polycrystalline Cu surfaces and 10


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10-3

´

P = 1 bar P = 10 bar P = 20 bar P = 40 bar

10-4

³

2 (out) Conversion 1 − CO CO 2 (in)

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10-5

10-6

480

500

520

540 560 Temperature [K]

580

600

Figure 2: Conversion of CO 2 versus temperature at various pressures. The conversion is mostly sensitive to pressure (mind the logarithmic scale), showing higher values at higher pressures. Dashed line connects points to guide the eye. Cu(110) single-crystal surfaces may have a higher inherent activity due to structural eects, resulting in many orders of magnitude higher TOF than obtained from our simulations. 28,29 In addition, adsorbates tend to bind more strongly to defects than to perfect facets, while the reactivity of the step defects is much larger than that of the terrace sites due to a combination of electronic and geometrical eects. 30 The particle-size eect also plays a signicant role, as Cu nanoparticles possess signicantly higher activity than Cu(111) surface. 8 Understanding the eects of structural sensitivity and geometry of active sites from the theoretical point of view is the key step towards designing improved multifaceted catalysts. 31 Alloying Cu with various dopants eectively makes certain steps in the reaction pathway kinetically more accessible and leads to higher activity and selectivity. One of the most commonly used metals is Zn, 9 which promotes the hydrogenation of the formate to the methoxy species. 32 Furthermore, Cu-ZnO interactions boost CO 2 hydrogenation, inhibit 11



10-8

CH 3 OH TOF per site [s −1 ]

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P = 20 bar P = 40 bar

10-9

10-10

10-11

10-12

480

500

520

540 560 Temperature [K]

580

600

Figure 3: TOF for methanol versus temperature at high pressures (20 and 40 bar). Higher temperatures and especially higher pressures (mind the logarithmic scale) favor higher TOF. Dashed line connects points to guide the eye. reactions producing unwanted CO, and stabilize the Cu sites against re-oxidation by CO 2 or H2 O. 10 Dierent types of catalysts, such as Pd/oxide, can provide higher TOF, 33 but can be problematic in terms of cost and production.

3.4

Initial conditions

For all simulations, we kept the gas molar fractions xed to H 2 :CO2 = 8 : 2. We nevertheless checked for a chosen example ( T = 500 K and P = 20 bar) the eect of changing gas molar fractions. We ran 3 additional simulations at H 2 :CO2 = 9 : 1, H2 :CO2 = 2 : 8, and H2 :CO2 :CH3 OH=8 : 1 : 1, and noticed that results do not change considerably compared to H2 :CO2 = 8 : 2 gas molar fraction. The uctuations of the results were interpreted as a consequence of the stochastic nature of the simulations. The only noticeable but not very

12


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signicant dierence was the rate (TOF) of methanol production, which was the highest for H2 :CO2 = 9 : 1 (TOF ≈ 1.6 × 10−11 s−1 ), and the lowest for H 2 :CO2 = 2 : 8 (TOF

≈ 3.7 × 10−12 s−1 ). This indicates that surplus H 2 in the gas composition boosts methanol production, which is expected given that the gas molar fraction is directly related to gas partial pressure. Moreover, the inclusion of 10% CH3 OH in the gas phase makes the adsorption of CH 3 OH very favorable (since it has Ea = 0, i.e. non-activated adsorption). Consequently, throughout the simulation only the loop steps of adsorption and desorption of CH 3 OH occur, and simulation does not proceed to further reaction steps. Such problems, commonly occurring when considering also diusion, are usually solved by articially slowing down the reaction using a scaling factor in the rate equation, 34,35 which reduces the computational costs without aecting the results. Furthermore, in Zacros, the gas molar fraction is treated as constant, so if the simulation is initialized with H 2 :CO2 = 8 : 2 fraction, CH3 OH is not present in the gas phase, and consequently no CH 3 OH can be re-adsorbed. This shows that the re-adsorption of methanol is an important reaction that needs to be taken care of in a more in-depth simulations. Another important parameter that we kept xed is the eective area of the site where reactions take place ( S in Equations 2 and 7). There is no strict denition of the area over which reactions take place, and we used the eective area of a single Cu atom, S ≈

6 × 10−20 m2 . As this number is relatively small compared to the number of active sites for typical Cu catalysts, which is around 1017 − 1018 per m2 , 36 we ran the simulations again for a few chosen examples at T = 500 K, changing the area S to 100× of the initial value. We noticed that the selectivity and conversion do not change considerably and stay consistent with the values reported for the original area size S . Similarly, the methanol production rate (TOF) using larger eective area does not show any signicant dierences between smaller and larger area size, independent of pressure (Figure 4).

13


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Total CH3 OH(g) produced per site


10-1

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P = 40 bar, S=1x P = 40 bar, S=100x P = 20 bar, S=1x P = 20 bar, S=100x

10-2

10-3 103

104

105

107 106 Time [s]

108

109

1010

Figure 4: Total methanol (gas phase) produced per active site versus time, at T = 500 K, for the cases of P = 20 bar and P = 40 bar, using dierent sizes of eective area where the reaction takes place (solid line for S = 6 × 10−20 m2 , and dashed line for S = 6 × 10−18 m2 ). The changes are not statistically signicant.

3.5

Stability of KMC simulations

The main objective of this work is to use a statistical approach to examine the DFT-derived values and test how uncertainties in rst-principle results aect KMC output. This has recently been brought into attention by various authors, 13,1517,37 suggesting that the accuracy of theoretical modeling is an important issue, especially in the upcoming era of multi-scale simulations (combining DFT, KMC, and CFD). In our simulations, we rst studied how the selectivity, conversion, and TOF depend on the random seed parameter. We ran 100 instances of the same simulation (at T = 500 K and P = 40 bar) on our HPC cluster, while randomly changing random seed parameter. We obtained a statistically signicant sample of results, which enabled us to estimate the accuracy of our KMC simulations. We conrmed that the distributions of parameters can be well described by the normal distributions, as indicated in Figure 5. The values obtained from the t are 0.82±0.03 for selectivity, (8.2±1.2)×10−4 for conversion, and (1.32±0.18)×

10−10 s−1 for TOF (uncertainties are 1σ ). Compared to results reported in Figures 1, 2, and

14


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3 for T = 500 K and P = 40 bar, these analyses give us an indication for the size of typical parameter uncertainty, which is approximately 4% for selectivity and 15% for conversion and TOF. 0.7

Number

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


0.8

0.9

5 × 10−4

1.0

60

60

50

50 0.82 ± 0.03

40

10−3

2 × 10−3 5 × 10−11

(8.2 ± 1.2) × 10

−4

50 (1.3 ± 0.2) × 10

−10

3 × 10−10

40

40

30

10−10

30

30 20

20

20

10

10

10

0

0.7

0.8

Selectivity

0.9

CH3 OH CH3 OH+CO

1.0

0

0 −3 −3 5 × 10−4 5 × 10−11 10−10 3 × 10−10 10 2 × 10 in CO2 Conversion 1 − COout CH3OH TOF per site [s−1] 2

Figure 5: Distributions of selectivity, conversion, and TOF obtained by changing random seed parameter, at T = 500 K and P = 40 bar. All parameters are well described by the normal distribution, as indicated by the black line. Red line indicates the results reported in Figures 1, 2, and 3 for each parameter at the same pressure and temperature. Another advantage of KMC simulations is that we can test the sensitivity of results to various parameters, especially activation energies of each elementary step. Kinetic parameters of reactions can be obtained using DFT, but DFT methods are notorious for their approximations and not 100% accurate. 13,15,38 The activation energies used in this paper were obtained via DFT. 6 By assuming that the activation energies have some intrinsic degree of uncertainty, we study how KMC results change if we alter the activation energies of elementary steps for ±1% and ±5%, drawn randomly from the normal distribution. For the typical activation energy of Ea = 1 eV, this amounts to ∆Ea = 10 meV and ∆Ea = 50 meV uncertainties (1σ ), respectively. Such, or in some cases even larger uncertainty range obtained from DFT, has been reported by various studies in the literature. 14,16,17 15



Once again, we ran 100 instances of the same simulation (at T = 500 K and P = 40 bar), this time perturbing the activation energies randomly, while keeping the random seed parameter xed. The results are presented in Figure 6. Green distributions (stars) represent

±1% perturbations, while blue distributions (lines) represent ±5% perturbation.

10-6

0.0 0.2 0.4 0.6 0.8 1.0 20

4±

0. 8

10-4

0 0. 1

10-2 (1. 2

10

100

.7

±0

10

10-8

15

10-6 10

± (1. 8

) 0. 7

0− ×1

10 5 5

5 0 0.0 0.2 0.4 0.6 0.8 1.0 ³ ´ 3 OH Selectivity CHCH 3 OH + CO

10-10

3

0−

1 )×

15 Number

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 16 of 28

0

10-6 10-4 µ 10-2 ¶ 100 0 10-10 10-8 10-6 −1 CO in2 CH OH TOF per site [s ] 3 Conversion 1 − COout2

Figure 6: Distributions of selectivity, conversion, and TOF for the case of T = 500 K and P = 40 bar, obtained by altering randomly the activation energy Ea of each elementary step for up to ±1% (green, stars) and ±5% (blue, lines) of the reported value. Only the green (stars) distributions (altering Ea for up to ±1%) can be well described by the normal distribution (black lines indicate the normal distributions t), while the blue (lines) distributions clearly show dispersed results. Red line indicates the results reported in Figures 1, 2, and 3 for each parameter at the same pressure and temperature. It is evident that when altering the activation energies for up to ±1%, the distributions are wider than in the case where we changed only the random seed parameter (Figure 5), but can be still described with the normal distribution. The values obtained from the t are

0.84 ± 0.10 for selectivity, (1.2 ± 0.7) × 10−3 for conversion, and (1.8 ± 0.7) × 10−10 s−1 for TOF, showing that the reported 1σ uncertainties are larger than in the case when changing random seed parameter. On the other hand, when altering the activation energies for up to ±5% of their initial values, the distributions are not normally shaped, but instead rep16


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resent a wide range of values; in case of selectivity, the distribution shows two discernible peaks (one around 0 and other around 1). This can be explained with one reaction step achieving favorable activation energy to lead to the state where only CO and no methanol was produced, and vice versa. Besides, for conversion and TOF, the distributions span over many orders of magnitude. If we assume that DFT derived activation energies used in our paper are uncertain by ±5%, which is a reasonable assumption due to approximations and trade-os occurring in practical implementation of DFT, we can expect much higher or lower conversions and TOF on pure Cu(111) catalyst (i.e., conversions up to 10%, TOF up to 10−7 s−1 , see Figure 6). Similar results have been recently reported in the literature. 39 Obviously, KMC simulations are extremely sensitive to the activation energies. To study the behavior of perturbing the activation energies further, we show on Figure 7 the frequency of elementary steps during the simulation. This is dened as the total number of step occurrence per site, divided by the total simulation time. We rst plot the step frequency histogram for the case of T = 500 K and P = 40 bar in which we kept the activation energies xed (left histogram), and then we do the same for both cases of

±1% (middle histogram) and ±5% (right histogram) perturbation of activation energies. The results show that the error bars in the case of ±5% perturbation are considerable and basically for all reaction steps the frequency can drop to 0, thus changing the overall catalysis pathway and results signicantly. Furthermore, in the case of ±5% perturbation, the most obvious dierence in the frequency histogram is seen for the HOCO ↔ CO + OH step, as the frequency of this reaction can be much higher and consequently much more unwanted CO can be produced, aecting the reaction pathway. Figure 7 also demonstrates that the formate pathway dominates the methanol production. The rate-determining step for methanol is the formaldehyde production, H 2 COO + H ↔ H2 CO + OH. Besides having the largest activation energy, this step represents the bottleneck in the formate pathway. The selectivity controlling step is the hydrogenation of CO2 . Should CO2 hydrogenate to HOCO, CO is ultimately formed via RWGS pathway,

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while hydrogenation to HCOO favors the formate pathway and methanol production. As such, selectivity in catalyst design can be achieved by tailoring the potential catalysts to favor CO2 hydrogenation to HCOO in the rst step.

-12 -10 H2, gas → H + H 2034 0 H + CO2, gas ↔ HOCO 7141 7095 HOCO ↔ CO + OH 6620 CO → COgas 460 H + CO ↔ HCO 00 H + HCO → H2 CO 00 H + CO2, gas ↔ HCOO 579045 578914 H + HCOO ↔ H2 COO 226506609 226506479 H + H2 COO ↔ H2 CO + OH 130 0 H + H2 CO → H3 CO 130 0 H + H3 CO ↔ CH3 OH 130 0 CH3 OH → CH3 OHgas 130 0 H + OH ↔ H2 O 176 0 H2 O → H2 Ogas 176 0 -12 -10

-8

-8

-6

-12 -10

-8

-6

-12 -10 -8 -6 -4

Forward Reverse

-6

-12 -10 -8 -6 -12 -10 -8 -6 -4 Log event frequency per site [s−1 ]

Figure 7: Elementary steps frequency for the case of T = 500 K and P = 40 bar. On the left histogram the activation energies were kept xed, while on the middle/right histograms they have been altered randomly for ±1% and ±5%, respectively. Red bars indicate forward reactions, while blue indicate reverse reaction (where the reaction step is reversible). The numbers in the left histogram show the total number of each reaction taking place over the course of simulation. The error bars on the middle/right plot are 1 standard deviation. Finally, we want to stress out that DFT and KMC studies often lack the proper statistical evaluation of results, which we showed to be an important aspect of research. This is crucial especially when comparing theoretical predictions and experimental results, as emphasized recently in the literature. 14,15 The choice of relevant DFT and KMC methods, and the proper analysis and interpretation of the computational results could provide much more accurate kinetic models. For example, when using current plane-wave DFT techniques, vanilla GGA pseudopotentials are inadequate for the required precisions. However, modern metaGGA and hybrid functionals (rPBE, HS06, SCAN) are performing much better. Most importantly, one should use pseudopotentials that have been tested on the similar systems as the investigated 18


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one.

4 Conclusion In this paper, we examine the properties of methanol synthesis on Cu(111) catalyst, using DFT derived results 6 and KMC simulations. By implementing statistical thermodynamics principles into the simulation, we study the eect of changing the operating conditions (temperature, pressure, eective area size) on the overall results. We study in particular how selectivity, conversion, and rate (TOF) change with temperature and pressure. The trends observed from our simulations, namely higher selectivity at higher pressure and lower temperature, higher conversion at higher pressure, and higher TOF at higher pressure and temperature, are commonly observed in methanol synthesis experiments using various Cutype catalysts, justifying our approach. Next, we turn our attention to the uncertainty of KMC simulations. We test how stable are the results against changes of the random seed parameter and perturbation of activation energies. We expect and conrm that by changing the random seed parameter, we probe the stochastic nature of KMC simulations. By obtaining statistically signicant sample of results, we perform statistical analysis in order to obtain the parameter uncertainties. For the case of T = 500 K and P = 40 bar, we show that the uncertainty for selectivity is not so signicant (4%), while conversion and TOF is determined less accurately (uncertainty around 15%). On the other hand, we demonstrate that simulations are highly dependent to the activation energies of elementary steps. Reaction rates, which are calculated from Equations (1)-(8) multiplied by the factor exp (−Ea /kB T ), are very sensitive to the activation energy, which enters in the exponential factor. Furthermore, most of the activation energies for elementary steps (Table S2) are of the same order of magnitude, around ∼ 1 eV. So even slight perturbation in the activation energy of a certain elementary step, due to its strong

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dependence in the rate equation, can result in a signicantly dierent outcome. Assuming that DFT derived parameters used in our paper have some intrinsic degree of uncertainty, we obtain highly dispersed results for selectivity, conversion, and TOF (see Figure 6, blue distributions). This indicates that a thorough analysis of results obtained from theoretical modeling is extremely important when comparing theory and experiments. Although in this paper we concentrate on a rather simple and in the literature very well studied methanol synthesis pathway on pure Cu(111) catalyst, the results are broadly applicable. We point out that combined DFT and KMC studies allow us to perform analyses of various catalytic processes at dierent conditions, which can not be done using solely DFT and microkinetic modeling. The KMC methods are capable of modeling complex surfaces (e.g., including defects, initialized states, multi-type sites), dierent reactants mixture composition, changing conditions (temperature, pressure) throughout the course of simulation, etc. Such studies provide deeper insights into catalysis, and will be used in designing more ecient catalysts.

Acknowledgement The authors gratefully acknowledge the European Commission, as the herein-presented research work was partially established within the MefCO2 project. This project has received funding through a Sustainable Process Industry through Resources and Energy Eciency (SPIRE) call under the European Union's Framework Programme for Research and Innovation Horizon 2020 (grant agreement No. 637016). The authors also gratefully acknowledge the Slovenian Research Agency (ARRS) for funding the program P2-0152 and project J27319.

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Supporting Information Available Gas and surface species energetics, elementary reaction steps activation energies and preexponential factors. This material is available free of charge via the Internet at http://pubs.acs.org/ .

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References (1) Wang, W.; Wang, S.; Ma, X.; Gong, J. Recent advances in catalytic hydrogenation of carbon dioxide.

Chem. Soc. Rev.

2011, 40, 37033727.

(2) Kauw, M.; Benders, R. M.; Visser, C. Green methanol from hydrogen and carbon dioxide using geothermal energy and/or hydropower in Iceland or excess renewable electricity in Germany.

Energy

2015, 90,

Part 1

, 208217.

(3) Tang, Q.-L.; Hong, Q.-J.; Liu, Z.-P. CO2 xation into methanol at Cu/ZrO2 interface from rst principles kinetic Monte Carlo.

2009, 263, 114122.

J. Catal.

(4) Grabow, L. C.; Mavrikakis, M. Mechanism of Methanol Synthesis on Cu through CO2 and CO Hydrogenation.

ACS Catal.

2011, 1, 365384.

(5) Liu, C.; Yang, B.; Tyo, E.; Seifert, S.; DeBartolo, J.; von Issendor, B.; Zapol, P.; Vajda, S.; Curtiss, L. A. Carbon Dioxide Conversion to Methanol over Size-Selected Cu4 Clusters at Low Pressures.

J. Am. Chem. Soc.

2015, 137, 86768679.

(6) Yang, Y.; White, M. G.; Liu, P. Theoretical Study of Methanol Synthesis from CO2 Hydrogenation on Metal-Doped Cu(111) Surfaces.

J. Phys. Chem. C

2012, 116, 248

256. (7) Szanyi, J.; Goodman, D. W. Methanol synthesis on a Cu(100) catalyst.

Catal. Lett.

1991, 10, 383390. (8) Yang, Y.; Evans, J.; Rodriguez, J. A.; White, M. G.; Liu, P. Fundamental studies of methanol synthesis from CO2 hydrogenation on Cu(111), Cu clusters, and Cu/ZnO(000[1 with combining macron]).

Phys. Chem. Chem. Phys.

2010,

12

, 9909

9917. (9) Jiang, X.; Koizumi, N.; Guo, X.; Song, C. Bimetallic Pd-Cu catalysts for selective CO2 hydrogenation to methanol.

Appl. Catal., B

22

2015, 170-171, 173185.


Page 23 of 28

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) Martin, O.; Mondelli, C.; Curulla-Ferré, D.; Drouilly, C.; Hauert, R.; Pérez-Ramírez, J. Zinc-Rich Copper Catalysts Promoted by Gold for Methanol Synthesis.

ACS Catal.

2015, 5, 56075616. (11) Maestri, M.; Cuoci, A. Coupling CFD with detailed microkinetic modeling in heterogeneous catalysis.

Chem. Eng. Sci.

2013, 96, 106117.

(12) Matera, S.; Maestri, M.; Cuoci, A.; Reuter, K. Predictive-Quality Surface Reaction Chemistry in Real Reactor Models: Integrating First-Principles Kinetic Monte Carlo Simulations into Computational Fluid Dynamics.

ACS Catal.

2014, 4, 40814092.

(13) Hess, F.; Farkas, A.; Seitsonen, A. P.; Over, H. "First-Principles" kinetic monte carlo simulations revisited: CO oxidation over RuO2(110).

J. Comput. Chem.

2012,

33

,

757766. (14) Exner, K. S.; Hess, F.; Over, H.; Seitsonen, A. P. Combined experiment and theory approach in surface chemistry: Stairway to heaven?

Surf. Sci.

2015, 640, 165180.

(15) Sutton, J. E.; Guo, W.; Katsoulakis, M. A.; Vlachos, D. G. Eects of correlated parameters and uncertainty in electronic-structure-based chemical kinetic modelling. Chem.

Nat.

2016, 8, 331337.

(16) Medford, A. J.; Wellendor, J.; Vojvodic, A.; Studt, F.; Abild-Pedersen, F.; Jacobsen, K. W.; Bligaard, T.; Nørskov, J. K. Assessing the reliability of calculated catalytic ammonia synthesis rates.

Science

2014, 345, 197200.

(17) Nørskov, J. K.; Bligaard, T.; Rossmeisl, J.; Christensen, C. H. Towards the computational design of solid catalysts.

Nat. Chem.

2009, 1, 3746.

(18) Stamatakis, M.; Vlachos, D. G. Unraveling the Complexity of Catalytic Reactions via Kinetic Monte Carlo Simulation: Current Status and Frontiers. 26482663. 23


ACS Catal.

2012, 2,


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 28

(19) Stamatakis, M. Kinetic modelling of heterogeneous catalytic systems. dens. Matter

(20) Reuter, K.

J. Phys.: Con-

2015, 27, 013001.

Modeling and Simulation of Heterogeneous Catalytic Reactions

; Wiley-VCH

Verlag GmbH & Co. KGaA, 2011; pp 71111. (21) Stamatakis, M.; Vlachos, D. G. A graph-theoretical kinetic Monte Carlo framework for on-lattice chemical kinetics.

J. Chem. Phys.

2011, 134, 214115.

(22) Gokhale, A. A.; Dumesic, J. A.; Mavrikakis, M. On the Mechanism of Low-Temperature Water Gas Shift Reaction on Copper.

J. Am. Chem. Soc.

2008, 130, 14021414.

(23) Zhao, Y.-F.; Yang, Y.; Mims, C.; Peden, C. H.; Li, J.; Mei, D. Insight into methanol synthesis from CO2 hydrogenation on Cu(111): Complex reaction network and the eects of H2O.

J. Catal.

2011, 281, 199211.

(24) Yang, Y.; Mims, C.; Mei, D.; Peden, C.; Campbell, C. Mechanistic studies of methanol synthesis over Cu from CO/CO2/H2/H2O mixtures: The source of C in methanol and the role of water.

J. Catal.

2013, 298, 1017.

(25) Saito, M.; Takeuchi, M.; Fujitani, T.; Toyir, J.; Luo, S.; Wu, J.; Mabuse, H.; Ushikoshi, K.; Mori, K.; Watanabe, T. Advances in joint research between NIRE and RITE for developing a novel technology for methanol synthesis from CO2 and H2. Organomet. Chem.

Appl.

2000, 14, 763772.

(26) Hirano, M.; Imai, T.; Yasutake, T.; Kuroda, K. Methanol Synthesis by Catalytic Hydrogenation of Carbon Dioxide on CuO-ZnO-Al2O3 and CuO-ZnO-Al2O3 Ga2O3 MgO Catalysts.

Kagaku Kogaku Ronbunshu

2001, 27, 1520.

(27) Janse van Rensburg, W.; Petersen, M. A.; Datt, M. S.; van den Berg, J.-A.; van Helden, P. On the Kinetic Interpretation of DFT-Derived Energy Proles: Catalyzed Methanol Synthesis.

Catal. Lett.

24

2015, 145, 559568.


Cu-

Page 25 of 28

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


(28) Yoshihara, J.; Parker, S. C.; Schafer, A.; Campbell, C. T. Methanol synthesis and reverse water-gas shift kinetics over clean polycrystalline copper.

Catal. Lett.

1995, 31,

313324. (29) Yoshihara, J.; Campbell, C. T. Methanol Synthesis and Reverse Water-Gas Shift Kinetics over Cu(110) Model Catalysts: Structural Sensitivity.

J. Catal.

1996, 161, 776782.

(30) Dahl, S.; Logadottir, A.; Egeberg, R. C.; Larsen, J. H.; Chorkendor, I.; Törnqvist, E.; Nørskov, J. K. Role of Steps in N2 Activation on Ru(0001).

Phys. Rev. Lett.

1999, 83,

18141817. (31) Calle-Vallejo, F.; Loreda, D.; Koper, M. T. M.; Sautet, P. Introducing structural sensitivity into adsorption-energy scaling relations by means of coordination numbers. Nat. Chem.

2015, 7, 403410.

(32) Fujitani, T.; Nakamura, J. The chemical modication seen in the Cu/ZnO methanol synthesis catalysts.

Appl. Catal., A

2000, 191, 111129.

(33) Ye, J.; jun Liu, C.; Mei, D.; Ge, Q. Methanol synthesis from CO2 hydrogenation over a Pd4/In2O3 model catalyst: A combined DFT and kinetic study.

J. Catal.

2014,

317

,

4453. (34) Yang, L.; Karim, A.; Muckerman, J. T. Density Functional Kinetic Monte Carlo Simulation of Water-Gas Shift Reaction on Cu/ZnO.

J. Phys. Chem. C

2013, 117, 34143425.

(35) Prats, H.; Álvarez, L.; Illas, F.; Sayós, R. Kinetic Monte Carlo simulations of the water gas shift reaction on Cu(111) from density functional theory based calculations. Catal.

J.

2016, 333, 217226.

(36) Behrens, M.; Studt, F.; Kasatkin, I.; Kühl, S.; Hävecker, M.; Abild-Pedersen, F.; Zander, S.; Girgsdies, F.; Kurr, P.; Kniep, B.-L. et al. The Active Site of Methanol Synthesis over Cu/ZnO/Al2O3 Industrial Catalysts. 25

Science

2012, 336, 893897.



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 28

(37) Zuo, Z.-J.; Gao, X.-Y.; Han, P.-D.; Liu, S.-Z.; Huang, W. Density Functional Theory (DFT) and Kinetic Monte Carlo (KMC) Study of the Reaction Mechanism of Hydrogen Production from Methanol on ZnCu(111).

J. Phys. Chem. C

2016, 120, 2750027508.

(38) Hammer, B.; Hansen, L. B.; Nørskov, J. K. Improved adsorption energetics within density-functional theory using revised Perdew-Burke-Ernzerhof functionals. B

Phys. Rev.

1999, 59, 74137421.

(39) Döpking, S.; Matera, S. Error propagation in rst-principles kinetic Monte Carlo simulation.

Chem. Phys. Lett.

2017, 674, 2832.

26


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Graphical TOC Entry KMC results: perturbing activation energies Ea Number (arb. unit)

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


1

0

no perturbation 1% perturbation 5% perturbation

0

0.5 Selectivity

1

-10 -8 log TOF [s−1 ]

27


-6

Number (arb. unit)

KMC results: perturbing activation energies Ea 1

1 2 3 4 50 6 7

The Journal of Physical Chemistry Page 28 of 28

no perturbation 1% perturbation 5% perturbation


0

0.5 Selectivity

1

-10 -8 log TOF [s−1 ]

-6

Kinetic Monte Carlo Simulations of Methanol Synthesis from Carbon

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