First-Principles Kinetic and Spectroscopic Insights into Single Atom

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First-Principles Kinetic and Spectroscopic Insights into Single Atom Catalysis Konstantinos Alexopoulos, Yifan Wang, and Dionisios G. Vlachos ACS Catal., Just Accepted Manuscript • Publication Date (Web): 24 Apr 2019 Downloaded from http://pubs.acs.org on April 24, 2019

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First-Principles Kinetic and Spectroscopic Insights into Single Atom Catalysis Konstantinos Alexopoulos, Yifan Wang, Dionisios G. Vlachos* Department of Chemical and Biomolecular Engineering and Catalysis Center for Energy Innovation, University of Delaware, 221 Academy St., Newark, DE 19716, USA * Corresponding author: [email protected]

Abstract Single atom catalysts receive extensive attention for reducing noble metal utilization and potential elimination of side reactions. Yet, their active sites remain highly debated and fundamental insights are limited due to experimental challenges. Here we introduce first-principles microkinetic modeling, with CO oxidation over Pd atoms on --alumina as a testcase, to provide insights into single atom catalysis. Contrary to widespread practice, we show that the state of the catalyst under working conditions is not described by ab initio thermodynamics without knowledge of the ratedetermining step. This is especially important for single atom catalysts whose reaction mechanism is less established and different from the one of extended surfaces. Kinetic Monte Carlo simulations indicate that the steady-state cationic view of single atoms on oxide supports is simplistic; metal atoms possess discrete, stochastic states during a catalytic cycle whose drastically different lifetimes dictate the observed, fractional, and strongly temperature-dependent catalyst oxidation state. We provide evidence that microkinetic simulations can discriminate mechanisms and sites and expose the oxidation state of a catalyst with high spatial and temporal resolution. Keywords: Density functional theory, single atom catalysis, --alumina, microkinetic model, kinetic Monte Carlo, reaction mechanism, CO oxidation, spectroscopy

Table of Contents (TOC) graphic

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1. Introduction Single atom catalysis (SAC) has received considerable interest due to both practical and fundamental reasons. Practically, SAC could maximize atom efficiency, which is important when precious metals are used, and minimize unwanted side reactions that require multiple neighboring active sites (ensemble effect).1 Fundamentally, it has been hypothesized that single atoms mimic homogeneous catalysts anchored on the support,2 and thus, they can provide a bridge between homogeneous and heterogeneous catalysis. Studies on SACs can also provide insights into metalsupport interactions at the atomic level. Currently there is significant debate as to the active site(s) on reactions over SACs,3,4 stemming in part from experimental challenges in observing single atoms operando. For example, aberration-corrected transmission electron microscopy is done ex situ and maybe altering the catalyst; X-Ray Absorption Spectroscopy (XAS) provides often ambiguous results due to low signal of ultra-low catalyst loading; and infrared (IR) spectroscopy is often done in situ, and IR spectra for SACs are not as established. First-principles simulations could overcome some of the challenges but have been under-employed for SAC. CO oxidation over noble metals has served as a testcase for understanding SAC. Since oxidation reactions invoke oxygen, the oxidation state of the catalyst is also crucial in understanding and predicting the catalytic performance. Ab initio thermodynamics is typically employed to predict the equilibrium phase of a catalyst,5,6 and the mechanism is subsequently studied via density functional theory (DFT) on this phase. This approach tacitly assumes that the catalyst is in thermodynamic equilibrium with the gas phase; yet, the relevance of this assumption has never been tested for single atom catalysis. Mechanistically, a Mars van Krevelen reaction scheme is typically invoked for CO oxidation on reducible metal oxides, with metal doping enhancing the formation of nearby oxygen vacancies.7-9 Although alumina is an irreducible oxide, recent studies have adopted the Mars van Krevelen mechanism for CO oxidation on a metal doped alumina.10,11 Unlike reducible metal oxides,12 metal doping on alumina surface is energetically unfavorable.13 Specifically, nuclear magnetic resonance (NMR) suggests that coordinatively unsaturated pentacoordinate Al centers, available on the (100) facet of --alumina, act as anchoring sites for atomically dispersed metal14 and structural models have been proposed.15-23 Spectroscopic and computational methods24,25 provide further evidence that CO adsorption can form isolated adsorbed metal atoms that oxidize CO. The aforementioned facts underscore the lack of mechanistic understanding of CO oxidation even on the most basic catalyst (Pd/--alumina) employed in catalytic converters.10 More broadly than understanding CO oxidation, identification of the active site, catalyst oxidation state, and the reaction mechanism under working conditions of SACs, by leveraging first principles calculations, can be invaluable. Here, we employ ab initio based microkinetic modeling (MKM) to study the reaction mechanism of CO oxidation over single Pd atoms adsorbed on and doped in alumina (Fig. 1) as a prototype of SACs. Unlike prior works using mainly DFT calculations,10,11,16-19 microkinetic simulations assess the effect of reaction conditions on turnover frequency, reaction orders, and surface coverages. We demonstrate that by confronting them directly with available experimental kinetic data,10 we can discriminate mechanisms and active sites and as such, MKM is a rather sensitive and complementary tool to spectroscopy. We introduce a simple and powerful method to estimate 2 ACS Paragon Plus Environment

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force convergence criterion of 0.05 eV Å–1 was used and each self-consistency loop was iterated until a convergence level of 10–6 eV was achieved. Atomic charges were calculated using Bader analysis36 as implemented by Henkelman et al.37 To obtain formal Pd charges, a calibration of Bader charges was first performed using bulk Pd references with known oxidation states (see SI for more information). Transition state search was performed using nudged elastic band and dimer calculations.38,39 The nudged elastic band method was used to find an initial guess for the minimal energy path, which was used as a starting point for the dimer calculations. Normal mode analysis was performed using a Partial Hessian Vibrational Analysis (PHVA),40,41 considering only the adsorbates on the alumina surface to be free for the numerical Hessian calculation. 2.3 Mean field microkinetic modeling (MKM) Reaction rate coefficients were computed using transition state theory and were incorporated into a mean-field MKM to investigate the effect of reaction conditions on turnover frequencies and surface coverages.42 Unlike CO oxidation on extended metal surfaces,43 for single atom catalysis the mean-field model is equivalent to kinetic Monte Carlo (kMC) simulations (e.g., see Fig. S9 of SI) since reactions occur on isolated single sites anchored on the support and elementary steps are essentially first order, where stochastic averaging is equivalent to deterministic mean field models.44 Lateral interactions are also irrelevant for SACs, while the interaction between multiple adsorbates on the isolated single site is explicitly considered in the energy calculation of each state. This equivalence between the two models holds of course only in the case when there is no diffusion or sintering of the single sites on the alumina surface. The single site MKM consists of alumina-supported Pd atoms and A*PdB complexes (see Fig. S3 for a complete list of complexes). Pd represents the site in its empty state, while A*PdB are occupied states. For example, CO*PdO2 represents co-adsorbed CO and O2 on the supported Pd atom. Based on site conservation, the coverage of free Pd atoms and A*PdB complexes equals 1. The rates of reactions involving a gas-phase species (e.g., A(g)+PdB A*PdB) are proportional to the partial pressure of the gaseous reactant and the coverage of the surface species. The rates of reactions involving a surface species only (e.g., A*PdB A*Pd+B(g)) are proportional to the surface coverage of that species. Steady-state coverages of the considered surface species were obtained by solving the following set of continuity equations analytically: (1)

=0

where 4ji is the stoichiometric coefficient of surface species i in reaction j, and rj is the rate of reaction j. 2.4 Kinetic Monte Carlo (kMC) modeling To map out the time scales of individual events and capture the fluctuations of the oxidation state of the single Pd atom, stochastic simulations were performed using the kMC software package ZACROS.45 This real time monitoring of the catalyst state produces information that can be compared to time-resolved operando experiments such as quick X-ray absorption spectroscopy. The input to ZACROS is taken from the same DFT calculations used in the mean-field modeling.


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The probability of finding the system in a particular state is estimated by solving the chemical master equation:46

[

=

( )]

()

(2)

where wi j denotes the propensity of the system going from state i to j. At each instant, one event is selected randomly to be executed with a probability proportional to its microscopic rate. The time clock and the state of the catalyst are updated continuously with the time increments given by an exponential distribution.47,48 The ensemble average of multiple (a large enough number of) Pd sites converges to the mean-field model results, so we do not duplicate presentations of these results. Instead, we use the kMC results to illustrate temporally resolved single atom spectroscopylike data.

3. Results & discussion 3.1 Reaction mechanisms and ab initio data Single atom structures and their stability and the detailed reaction network of CO oxidation over single Pd atoms adsorbed on alumina are available in SI, Fig. S1-S3. The reaction network consists of several catalytic cycles, as explained below. Activation energies and pre-exponential factors for each elementary step are provided in Table S1. Kinetic parameters for the Mars van Krevelen mechanism (Fig. S4), proposed by Peterson et al.,10 over a single Pd atom doped in alumina have also been calculated (Table S2). CO2(g)

(a)

-

Pd

CO(g)

O

O

(b)

C

C

Al

Al

1+

Pd

C

O

C

O

O

C

C 2+

2+

O O Al Al

O Al

CO(g)

O C

O Al

Al

O

2+

Pd O

CO2(g)

C

1+

Pd

O

O

O

Al

2+

Al

Al O

O C

C

CO(g)

0

Pd

Pd

CO2(g)

O

CO(g)

Al

Al

2+

Pd

Pd

Al

-

Pd

Pd Al

Al

O2(g)

CO2(g)

O

Al

1+

O

Al

Al

Al

Al

CO2(g)

O

0

Pd

Al

Pd

O

O

C

C

C

2+

Pd O O Al Al

Pd Al

Al

CO(g)

+

Al

O2(g)

O Al

Al

Fig. 2. Catalytic cycles for (a) carbonate-mediated and (b) self-promoted CO oxidation over Pd16+, Al2O3 (100). Formal Pd oxidation states are obtained from the calibrated Bader charge analysis (see Fig. S5).


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CO oxidation on the adsorbed single Pd atom is envisaged to proceed via carbonate-mediated and self-promoted catalytic cycles (Fig. 2). Two variants of the carbonate-mediated CO oxidation are considered depending on whether an Eley-Rideal (ER) step is included or not (inner and outer cycle of Fig. 2a, respectively). The carbonate-mediated CO oxidation without an ER step starts with CO adsorption on Pd followed by O2 adsorption at the interface between Pd and alumina (Fig. 2a). The first activated step entails insertion of O into CO, while the second activated step leads to the carbonate intermediate. The next steps involve CO2 desorption and a second CO adsorption on Pd. Like the first CO oxidation, O is inserted into CO with a similar activation barrier (ca. 80 kJ/mol, Table S1), while the second CO2 desorption regenerates the active site. Instead of performing the second CO oxidation event in a stepwise (Langmuir-Hinshelwood) manner, an alternative cycle considers an ER step where the leftover oxygen is picked up by a second CO molecule to form directly CO2 (Fig. 2a). Finally, instead of a single CO adsorption followed by O2 adsorption, the catalytic cycle of self-promoted CO oxidation49-52 considers two sequential CO adsorption steps on Pd followed by O2 adsorption at the interface (Fig. 2b). In the first activated step, one of the adsorbed CO molecules abstracts an O atom from O2 to form CO2. The second activated step involves a second O insertion into the leftover CO molecule, which then desorbs as CO2, regenerating the active site. The geometric flexibility in accommodating adsorbates on SACs results in different mechanistic paths and adsorbates from those on extended surfaces.

Pd+2CO2(g)

CO2*Pd+CO2(g)

TS6+CO2(g) TS10+CO2(g)

-500

PdO+CO(g)+CO2(g)

CO3*Pd+CO(g)

TS4+CO(g)

TS9

TS3+CO(g)

Carbonate-mediated w/o ER Carbonate-mediated with ER Self-promoted

CO*PdO+CO2(g)

-400

CO2*PdO+CO(g)

-300

2CO*PdO2

-200

CO*Pd+CO(g)+O2(g)

-100

Pd+2CO(g)+O2(g)

0

2CO*Pd+O2(g)

CO*PdO2+CO(g)

Standard Gibbs free energy diagrams for the different catalytic cycles are shown in Fig. 3. The carbonate-mediated CO oxidation without ER step is energetically most favorable. Nevertheless, since surface coverages and reaction rates are not governed by energetics alone, but also depend on reaction conditions, it is important to perform microkinetic simulations.

G0400K (kJ/mol)

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Fig. 3. Standard Gibbs free energy diagram for CO oxidation over Pd16+, 2O3 (100). Transition states are numbered according to the elementary step they belong to (see Table S1 for the complete list of elementary steps). 3.2 Active site discrimination using microkinetic modeling and experimental data The microkinetic model is first assessed against available experimental data.10 Table 1 shows that the predicted turnover frequencies on the adsorbed single Pd atoms are within an order of 6 ACS Paragon Plus Environment

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magnitude (or better at lower temperatures) of the experimental values, and the reaction orders with respect to CO and O2 fall within the observed range of experimental values. Given the typical uncertainty of DFT-based microkinetic models,53,54 the agreement is very good. In contrast, microkinetic modeling on Pd-doped alumina, with a Mars van Krevelen mechanism, fails to closely describe the experimental data. The differences from the experiments on Pd-doped alumina stem from the rather low reaction barrier for CO oxidation (ca. 20 kJ/mol) and the very weak CO adsorption on this active site (Table S2), respectively. The fact that the microkinetic model on adsorbed single Pd atoms is capable of reproducing the experimental observations provides strong evidence that adsorbed rather than doped Pd is the kinetically relevant site. As mentioned in the introduction, previous NMR and DFT studies have indicated respectively that isolated adatoms can exist at low loadings on alumina and are more stable than doped metal atoms.13,14 The exclusion of the doped Pd site based on our microkinetic analysis points basically to the fact that this site does not form on the alumina surface due to its much lower stability. On account of the aforementioned stability, it appears that the thermodynamic stability of the site dominates its presence and subsequently the kinetics. Interestingly enough, a recent study55 has suggested that doped sites can be effectively stabilized by adding Mg to the alumina support. Clearly, our simulations indicate that CO oxidation is site sensitive, in analogy to the well-known structure sensitivity on nanoparticles but now extended to single atoms. Table 1. Comparison between experimental (first two rows) and theoretical (last two rows) turnover frequencies (TOF) and reaction orders. TOF (s-1) b Reaction orders at 343 K c CO O2 343 K 398 K st a -4 -3 -0.20 0.18 1 experimental run 3.8 10 1.6 10 nd a -5 -4 -1.20 0.84 2 experimental run 9.7 10 2.4 10 ads -5 -4 Pd1 MKM (this work) 1.9 10 6.1 10 -0.87 0.16 doped d 2 2 Pd1 MKM (this work) 5.1 10 7.2 10 1.00 0.00 a Reproduced with permission from Reference 10. b p cp Q p Q 8 torr. CO O2 CO = 14-52 torr, pO2 = d 10 7-28 torr. Based on the proposed reaction mechanism of Peterson et al. Table 2. Catalyst characterization upon CO adsorption. Formal Pd oxidation state, adsorption energy (CO) for CO adsorption on alumina-supported single atom species. System CO site /Eads (kJ/mol) RCO (Å) RPdC (Å) 4CO (cm-1) Pd1ads/Al2O3 Pd0 -160 1.16 1.86 2055 3+ doped Pd1 /Al2O3 Pd -45 1.14 1.89 2131 As proposed recently,56 supported single atoms can also readily be discriminated using CO stretching frequencies and adsorption energies. The values are not only sensitive to the location of single atoms on the support but they, unlike those on large nanoparticles, depend on the support as well.56,57 Table 2 demonstrates this sensitivity that could eventually be used to probe and discriminate different single atom species on alumina. In the absence of experimental IR data, our study shows that microkinetic analysis of CO oxidation along the experimental kinetics can be an alternative, sensitive tool to complement spectroscopy for active site discrimination in SAC. The 7 ACS Paragon Plus Environment

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‘resolution’ of combined kinetics and IR data on inferring accurately active sites is yet to be determined, but looks promising. Finally, the site/structure sensitivity of CO oxidation can further be utilized to quantify the extent of Pd sintering after the 2nd experimental run on the alumina surface (see Table 2). Peterson et al.10 reports at 343 K an average turnover frequency ( ) and O2 reaction order ( ) of 9.7 10-5 s-1 and 0.84, respectively. Theoretically, the O2 reaction order on metal nanoparticles is assumed to be 1,10 while the present MKM gives a TOF of 1.9 10-5 s-1 and an O2 reaction order of 0.16 for adsorbed Pd atoms on alumina (Table 2). Taking into account the definition of the reaction order and that both nanoparticles (NP) and single atoms (SA) can contribute to the overall average turnover frequency for CO oxidation: (3)

= =

(4)

+

we can derive the following equations for the fraction of single atoms (wSA) and nanoparticles (wNP) present on the alumina surface: = =1

( (

) )

(5) (6)

Using the aforementioned input, equations 5 and 6 give respectively wSA = 0.97 and wNP = 0.03. Hence, the extent of Pd sintering seems to be minimal at these low reaction temperatures. 3.3 Microkinetic analysis on the kinetically relevant adsorbed single atom sites Fig. 4 shows the effect of temperature on turnover frequencies, surface coverages, normalized sensitivity coefficients, and average Pd oxidation state (see next section) using the entire reaction network (Fig. S3), by including simultaneously all cycles and no assumptions about the ratedetermining step. The carbonate-mediated mechanism without an ER step is dominant at all temperatures, while selfpromoted CO oxidation is only important at temperatures below 400 K (Fig. 4a). Sensitivity analysis shows (Fig. 4c) that the rate-determining reaction entails co-adsorbed CO and O2 (reaction 3: CO*PdO2 U CO2*PdO), while the reaction between CO and O2 in the presence of an additional CO on Pd (reaction 9: 1 + , +1U + , +M +2(g)) is somewhat significant at low temperatures only. Such low temperatures favor the co-adsorption of O2 with two CO molecules on the supported Pd atom (Fig. 4b), 2CO*PdO2, in contrast to larger Pd ensembles that are mainly covered by CO at these reaction conditions.58 Although the coverage of the 2CO*PdO2 intermediate is high at low temperatures, CO oxidation from this intermediate has a fairly large reaction barrier (reaction 9 in Table S1), limiting the contribution of the self-promoted mechanism. As temperature increases, the adsorbed Pd carbonyl species, CO*Pd, becomes most abundant due to the strong CO adsorption on the single Pd atom (ca. -160 kJ/mol). At intermediate temperatures, the 2CO*Pd state exists in small fraction. 8 ACS Paragon Plus Environment

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(b)

1.E-02 1.E-04 1.E-06 1.E-08 1.E-10 1.E-12 1.E-14 1.E-16 400

500 600 700 Temperature (K)

Coverage

Carbonate-mediated w/o ER Carbonate-mediated with ER Self-promoted CO2 formation 300

(c)

1 0.8 0.6

CO*Pd

0.4

2CO*Pd 2CO*PdO2

0.2 0 300

800

400


800

(d)

1 0.8 0.6

rxn3: CO*PdO2-->CO2*PdO

0.4

rxn9: 2CO*PdO2-->CO*PdO+CO2(g)

0.2 0

Average property

TOF (mol molPd -1 s -1)

(a) 1.E+00

NSC

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2.0 1.5 1.0 Pd-O (Å) Pd-O CN Pd ox.state

0.5 0.0

300

400


800

300

400


800

Fig. 4. Effect of temperature on catalyst performance and structure. (a) Turnover frequencies (TOF), (b) surface coverages, (c) normalized sensitivity coefficients (NSC) of most important reactions, (d) average Pd oxidation state, Pd-O coordination number (CN) and Pd-O bond distance; pCO = pO2 = 0.1 bar. Numbering of reactions corresponds to the list of elementary steps in Table S1. The reaction order analysis of the previous section has shown that at low temperatures (< 400 K) sintering of the supported Pd atoms is minimal. Interestingly, Pd carbonyl species are not present at these low temperatures but they do become more abundant as the reaction temperature increases. Their presence can result in a higher mobility of the metal atom on the alumina support. The higher mobility of the metal atom by adsorbed CO is actually known in literature as the ‘harpooning’ effect.59 As observed by the ab initio molecular dynamics simulation (AIMD) at 800 K (see SI), diffusion and sintering of the Pd carbonyl species on the alumina surface is expected to be rather facile at such high temperatures. Therefore, to avoid Pd sintering at high reaction temperatures, the single atom catalyst should be synthesized by placing a single metal atom per support nanoparticle.60


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(a)

(b)

CO*Pd

(c)

PdO

PdO2

2CO*Pd

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CO*PdO

(d)

CO reaction order

O2 reaction order

Fig. 5. Effect of reactant pressure on catalyst state and reaction orders. Dominant surface species based on (a) kinetics vs. (b) thermodynamics; (c) CO and (d) O2 reaction orders at 400 K. Reaction orders correlate strongly with coverages and provide a signature of the dominant surface species and oxidation state of the catalyst. Fig. 5a reveals the most abundant reaction intermediates at different reactant pressures. Unexpectedly, the thermodynamically determined most stable state of the catalyst (Fig. 5b) differs from the kinetically controlled one (Fig. 5a). This finding, reported here for the first time for single atom catalysis, underscores that ab initio thermodynamic phase diagrams may not capture the state of catalyst under kinetically relevant conditions. This is in agreement with what has been reported for larger catalytic ensembles,61,62 namely that the surface termination will depend on both thermodynamic conditions and reaction kinetics. This is because a thermodynamic analysis assumes that the gas phase is equilibrated with the surface. In reality, the system is usually driven far away from equilibrium. The dominant species, corresponding in general to the initial state of the rate-determining step or to a quasi-equilibrated state that is lower in energy than the initial state of the rate-determining reaction, control the oxidation state of the single atom catalyst. If the thermodynamic analysis was to include only the species that came before the rate-determining step, then the thermodynamic phase diagram would agree with the kinetic one. However, knowledge of the possible rate-determining steps requires a microkinetic analysis that cannot be obtained a priori from a mere thermodynamic standpoint.


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Importantly, the simulated kinetic phase diagram seems to be responsible for the changes in the reaction orders of both CO and O2. Depending on the reactant pressures, CO reaction orders vary from +1 to -1 (Fig. 5c), while O2 reaction orders vary from +1 to 0 (Fig. 5d). In addition, optimal partial pressures that maximize the reaction rate can easily be estimated (see SI). Our simulations indicate, as expected, a strong correlation of reaction orders with dominant species (Fig. 5) and also with the catalyst oxidation state, and delineate why macroscopic measurements of the former are an excellent signature of microscopic events providing implicit information on surface coverages and oxidation states of SACs. 3.4 Spectroscopic insights into the single atom catalyst structure and oxidation state The surface coverage of state i, Bi, is dictated from the state lifetime and reflects the probability of observing this state. Unlike traditional heterogeneous catalysts, the monodispersity of the single atoms allows for ‘clean’ observation of the various states of the catalyst. By computing the formal Pd oxidation state qi of the ith state (see Computational methods and SI), the average oxidation state of Pd is estimated as (Fig. 4d): "=

#"

(7)

Other properties, such as the Pd-O coordination number and the bond distances, are similarly calculated (Fig. 4d). Different from the typical, steady-state view of a time invariant oxidation state of a catalyst,57,63 a Pd atom undergoes a complete oxidation/reduction cycle during a catalytic cycle (Fig. 2). Changes in the oxidation state of the single metal as a result of the ongoing reactions have being reported on other supports as well,64-67 but these studies lack information regarding the lifetime of each catalyst state. The latter information is of paramount importance, since the longest living catalyst state dictates mainly the average oxidation state (and the other catalyst properties). Increasing the reaction temperature leads to reduction of Pd2+ to Pd0 (Fig. 4d). Although the Pd-O bond distance is rather insensitive to increasing the reaction temperature, the Pd-O CN decreases from 2 to 1 in agreement with the reduction of Pd. The fractional oxidation state values result precisely from the temperature dependent lifetimes of the states the Pd atom possesses. This finding departs from the intuitive and rather simplistic cationic view of single atoms. Interestingly, non-integer values of the oxidation state do not indicate catalyst heterogeneity but arise from time averaging of the states over a catalyst cycle. Due to the ergodicity of Markov processes, temporal averages coincide with the common spatial averages provided by spectroscopic methods, such as X-ray absorption near-edge structure (XANES) spectroscopy. By combining scanning tunneling microscopy and X-ray photoelectron spectroscopy (XPS), Zhou et al.68 observed a change in the charge state of single Au atoms on CuO(111) when the catalyst was exposed to CO. This observation was possible because CO oxidation proceeds via a Mars van Krevelen mechanism on that catalyst, allowing to isolate catalyst reduction, via observing vacancies, from reoxidation. This mechanism is inapplicable on alumina-supported Pd single atoms. Importantly, (short) temporal resolution of the catalytic cycle is experimentally inaccessible and most experimental methods provide ensemble averages, i.e., lack spatial resolution. 11 ACS Paragon Plus Environment

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Motivated by their work,68 we investigated the dynamics of the oxidation state of SACs using kinetic Monte Carlo (kMC) simulations to provide high temporal and spatial resolution (single cycle over a single atom) first-principles spectroscopy-like data. This provides a wealth of insights that are currently unattainable by experiments. Given that the carbonate-mediated cycle without an ER step is the dominant cycle (Fig. 4a), kMC simulations were run using the eight catalyst states of the outer loop in Fig. 2a. The full kMC simulation results of the frequency of each reaction event and the average lifetime of each state are given in Fig. S10-S12.

Fig. 6. Select kinetic Monte Carlo results. (a) Pd oxidation state vs. time at millisecond scale. (b) Average time spent in each oxidation state per CO oxidation cycle. (c) CO*Pd species count vs. time at millisecond scale. (d) CO*Pd lifetime distribution, for the carbonate-mediated cycle without an Eley-Rideal (ER) step. pCO = pO2 = 0.1 bar, T = 500 K. Fig. 6a shows the temporal evolution of the Pd oxidation state for a short period of time. The first three spiky transitions between PdW- and Pd0 indicate fluctuations due to CO adsorption/desorption events on the single Pd atom, while the next four between Pd0 and Pd2+ indicate O2 adsorption/desorption events on the CO*Pd. These fluctuations in site occupation and oxidation state are associated with partially equilibrated (adsorption/desorption) events being fired frequently. Once the rate-determining step, i.e., CO*PdO2 U CO2*PdO, is executed, subsequent reactions occur rapidly to complete the catalytic cycle (at ca. 35 ms). The Pd atom spends most of its time in its neutral oxidation state (Fig. 6b), consistent with the long lifetime of CO*Pd species during a single catalytic cycle (Fig. 6c). As a consequence of stochasticity, the lifetime of CO*Pd follows an exponential distribution (Fig. 6d). The rest of the species responsible for the non-zero Pd oxidation state have a very short lifetime (Fig. S10-S12), well outside the millisecond resolution of XANES.69 Our results demonstrate that kMC analysis can fill an important gap associated with the current lack of temporal and spatial resolution of existing spectroscopic methods and provide valuable kinetic information at picosecond or even femtosecond time scales. 12 ACS Paragon Plus Environment

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4. Conclusions First-principles mean field and stochastic microkinetic simulations were conducted for SACs with focus on CO oxidation on Pd/--alumina. Temporally (single event) and spatially (single atom) resolved spectroscopic insights obtained herein are revealing and unattainable by currently available experimental methods. Even though a single catalyst atom fluctuates stochastically among multiple discrete oxidation states, the spectroscopic signature of an ensemble (spatially average), observed via XANES and XPS, or of the long time average of a single catalyst atom, is continuous. The average oxidation state is generally fractional, despite the monodispersity of the catalyst, and is dictated by the disparate lifetimes of the various catalyst states. The implications of this behavior are remarkable. In contrast to the intuitive steady-state picture that single atoms are cationic and reduced metal nanoparticles are metallic, our simulations reveal that Pd converts gradually from cationic (expected for single atoms) to metallic (expected for nanoparticles) with increasing temperature even without sintering. Importantly, we show for the first time that the well-established ab initio thermodynamics approach fails to describe the coverages and the correct oxidation state of a catalyst, at least in the single atom or small cluster limit. Instead, a fully kinetic modeling approach is required to expose simultaneously kinetics, adsorbate coverages, and the catalyst oxidation state. These findings have important ramifications well beyond the specific system studied herein for closing the gap between models with kinetic and operando spectroscopic experimental studies.

Supplementary Information: Different locations of the adsorbed Pd single atom on alumina, the full microkinetic model for CO oxidation over adsorbed Pd single atoms, a Mars van Krevelen mechanism for CO oxidation over doped Pd single atoms, a calibration of Bader charges to obtain formal Pd oxidation states, AIMD simulations at 800 K, optimization of partial pressures, additional information regarding phase diagrams, and additional results from the kMC simulations. This material is available free of charge via the Internet at http://pubs.acs.org.

Acknowledgments: This work is performed in the framework of the PARTIAL-PGMs project – funded by the European Union’s Horizon 2020 research and innovation programme under grant agreement No 686086.

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