First Principles Determination of CO Adsorption and Desorption on Pt

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C: Surfaces, Interfaces, Porous Materials, and Catalysis

First Principles Determination of CO Adsorption and Desorption on Pt(111) in the Free Energy Landscape Chenxi Guo, Ziyun Wang, Dong Wang, Haifeng Wang, and Peijun Hu J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b06782 • Publication Date (Web): 30 Aug 2018 Downloaded from http://pubs.acs.org on August 30, 2018

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The Journal of Physical Chemistry

First Principles Determination of CO Adsorption and Desorption on Pt(111) in the Free Energy Landscape Chenxi Guo,† Ziyun Wang,† Dong Wang,‡ Hai-Feng Wang*‡ and P. Hu*†‡ †

School of Chemistry and Chemical Engineering, The Queen’s University of Belfast, Belfast, BT9

5AG, the United Kingdom ‡

Key Laboratory for Advanced Materials, Research Institute of Industrial Catalysis and Centre for

Computational Chemistry, East China University of Science and Technology, Shanghai, 200237, China

ABSTRACT: Traditionally, catalytic processes are calculated using the total energy approach from density functional theory (DFT) and the method to determine the barriers of the adsorption/desorption from DFT calculations is thus still not available. In this work, we choose CO adsorption/desorption on Pt(111) as a model for two reasons. Firstly, it is often a rate-limiting step in many catalytic reactions and secondly, the disagreement between the experiment and DFT calculations on the CO adsorption sites of Pt(111) has been known as “the CO puzzle” in the literature, and to further understand the puzzle is desirable. We introduce a molecular dynamics method within the framework of DFT, allowing us to calculate the free energy barriers of

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adsorption/desorption without experimental inputs. Our results show that the top site is more preferred for CO adsorption in terms of free energy, which agree with experimental work, but in contrast to the traditional DFT total-energy calculations. A delocalized nature of CO chemisorption on the hollow site is found and the key reason of the discrepancy between the free energy simulations and the total energy calculations is identified, which may have some profound implications in total energy calculations in general.

INTRODUCTION Heterogeneous catalysis plays a tremendous role in our society, and has become increasingly important. In the past 20 years or so1, numerous properties including chemisorption energies2-4, surface reactions5-9 and reaction mechanisms10-12 in heterogeneous catalysis were well described by first principles calculations. However, the barriers of the most basic processes, i.e. adsorption/desorption of molecules, which are vital, often being rate-determining steps in reaction kinetics13-15, could not be directly calculated from first principles due to the following reason: The barriers are mainly contributed to the changes of entropies in the processes of adsorption/desorption, while the traditional first principles simulations were carried out to give rise to the total energies. In other words, the traditional total energy calculations could not determine the transition state of adsorption/desorption and thus would not yield the barriers.

Moreover, in previous work, all the free energy barriers of surface reactions were estimated by total energy calculations with thermodynamic corrections16,17. However, thermodynamic corrections were built upon some approximations, especially for adsorbates on surfaces, where


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zero-point energy and entropies were calculated based on vibrational frequencies, and all the translational motions were ignored on the surfaces. These approximations may lead to considerable errors. How significant are the errors associated with this approach? Can a reliable method be developed to calculate the barriers of adsorption and desorption in free energy directly? In this work, we address these fundamental questions.

Previously, some approximate methods were used to estimate the adsorption and desorption barriers in catalytic systems. In the Fischer-Tropsch reaction18,19, either the sticking coefficient from experimental work with Hertz-Knudsen equation20,21 was used to calculate the adsorption rate22,23, or the adsorption barrier was ignored, and the process was considered as an equilibrium2426

. The desorption barrier was usually approximated as the chemisorption energy which was then

used in the micro-kinetic modelling. These approximate methods can be problematic because (i) the sticking coefficients are not only reactant-dependent but also surface-dependent; and (ii) they are affected by temperature. Thus, a very limited number of the sticking coefficients are available. The errors from these approaches are unpredictable or could be fatal for analyses. Hence, computing adsorption and desorption barriers has become imperative in catalysis.

CO/Pt(111) is arguably the most studied catalytic system in surface science and heterogeneous catalysis as CO is not only one of the simplest diatomic molecules, but also one of the most important species in many industrial catalytic processes27, such as CO oxidation and FischerTropsch reaction. In the last several decades, the adsorption of CO on Pt(111) has extensively investigated by various methods28-31. Experimentally, CO has been observed to be mainly adsorbed


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on the top site of Pt(111) with a low surface coverage (coverage < 0.33 ML)32, and the bridge site was partly occupied when the coverage reached 0.5 ML29. However, the computational calculations indicated that the CO adsorption energy on the hollow site30 is stronger than that on the top site and the bridge site is a meta-stable site with negative vibrational frequency33. In other words, “the CO puzzle’’32 has been found: Experimental work showed that CO prefers to adsorb on the top site of Pt(111)32,33, but the conventional DFT results showed that the hollow site was more stable for CO adsorption. The chemisorption energy of CO on Pt(111) was calculated early to be 0.07 eV stronger on the hollow site31 with the Perdew-Burke-Ernzerhof (PBE) functional34. Then, it was reported that using the PBE functional causes the error in describing the molecular orbitals of CO. Thus, some studies focused on the effect of singlet-triplet excitation energy of CO on metal surfaces using correction value U35. The GGA+U approach generated more reasonable results compared to the experimental work35. Furthermore, a hybrid functional, the PBE0 functional36, corrected the favoured site of CO on Pt(111). Finally, “the CO puzzle” appeared to be solved when the random phase approximation (RPA) was used37, which showed that the chemisorption of CO is 0.07 eV more stable on the top site of Pt(111) than the hollow site with a reasonable chemisorption energy compared with experimental result. It has appeared that “the CO puzzle” has been solved in the terms of total energy. However, is the functional the only problem causing the “puzzle”? Is there any further understanding for CO adsorption and desorption?

COMPUTATIONAL METHOD In this work, density functional theory (DFT) calculations with Perdew-Burke-Ernzerhof (PBE) functional34 were performed using the Vienna Ab-initio Simulation Package (VASP)38,39. A 4-


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layer Pt(111) slab (two layers fixed) with the periodicity of p(2×2) was used including 20 Å vacuum slab. The cut-off energy was set to 450 eV for the optimization calculations with the convergence of force 0.01 eV·Å-1 and the K-point 6×6×1 (see Supporting Information). ab-initio molecular dynamics (AIMD) was used in this work using VASP code, including constrained MD and umbrella sampling40. The cut-off energy was set to 450 eV with the K-point 2×2×1 and the time step is 0.5 femtoseconds. The temperature of MD simulation was oscillating controlled using algorithm of Nosé and the average of temperature was set to 300 K (see Supporting Information).

RESULTS AND DISCUSSION In this work, the adsorption/desorption processes of CO on Pt(111) were investigated using advanced molecular dynamics (MD)40 and the free energy barriers of adsorption/desorption were calculated. Furthermore, “the CO puzzle”32 is addressed in terms of free energy in contrast to previous DFT total energy calculations and a weakness of the traditional total energy calculations is revealed. A concept of surface delocalised state is demonstrated.


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Figure 1. Free energies of CO adsorption and desorption from Pt surface at the temperature of 300 K. (a) Free energy desorption (1.14 eV) and adsorption (0.08 eV) barrier on top site. (b) Free energy desorption (1.00 eV) and adsorption (0.05 eV) barrier on hollow site.

An umbrella sampling with the weighted histogram analysis method (WHAM)41,42 was developed to calculate the processes of CO adsorption/desorption on Pt(111) in this work. All the MD simulations were conducted with the temperature of 300 K and one CO per unit cell. The 2dWHAM code of Grossfield43 was utilised in conjunction with VASP code and the Gaussian peak model was used for constraints44. After a series of MD simulations based on the umbrella sampling, the free energy changes of CO adsorption/desorption on the top and hcp hollow sites were obtained, shown in Figures 1a and 1b, respectively. The zero points in the two curves represent the adsorbed states of CO on the top site and hollow site, respectively, and the maximum points are the transition states in the processes. The final states are at the points where the free energies reach plateaus. It is interesting that a small barrier can be found between the transition state and final state in Figure 1a. It is worth noting that the free energy barriers of adsorption and desorption processes were, for the first time, calculated rigorously from first principles simulations. Furthermore, the chemisorption energies of CO on Pt(111) in terms of free energy on both the top site and hollow site were determined to be -1.06 eV and -0.95 eV, respectively, which shows surprisingly that the adsorption of CO on the top site is more stable than that on the hollow site. This free energy result obtained from PBE functional is in contrast to all the total energy calculations using the same functional, but consistent with experimental work33.


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To confirm the free energy results of the umbrella sampling simulations, another free energy calculation technique, the constrained MD, was used (details of constrained MD simulations and the weakness of the technique for surface reactions can be found in Supporting Information). The free energy barrier of desorption was calculated by integrating the force through the distance between the C atom and a Pt atom. It is found that the free energy barriers and the positions of the transition states from the constrained MD results are indeed consistent with the umbrella sampling simulations.

It is worth comparing the free energies from this work with those from the traditional approach. The estimated free energy of chemisorption was conventionally computed from the total energy calculations with the thermodynamic corrections16,17 (the zero point energy, thermal energy and entropy from the conventional total energy calculation, see Supporting Information). It is found that the estimated free energy of CO chemisorption on the top site of Pt(111) from the total energy calculations with the thermodynamic corrections is -1.04 eV which is very close to -1.06 eV from the umbrella sampling simulations. However, the estimated free energy of CO chemisorption on the hollow site from the total energy calculations with the thermodynamic corrections is -1.14 eV that is substantially lower than -0.95 eV from the umbrella sampling simulations. Perhaps more importantly, it displays an opposite trend for CO adsorption from the umbrella sampling simulations: CO is more stable on the hollow site from the estimated free energies from the total energy calculation with the thermodynamic corrections, suggesting that the calculations of free energies from the total energy calculation with the thermodynamic corrections may not be accurate. The thermodynamic corrections with a consideration of translational and rotational motion of adsorbates, which was proposed and named as the hindered translator and hindered rotor


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models by Sprowl et al.45, was also tried in this case. However, it still shows that CO adsorption on the hollow site is stronger (details see Supporting Information)45. This raises some questions: Why is the result of CO on the top site from the umbrella sampling simulations consistent with that from the total energy calculations with the thermodynamic corrections while it is not for CO on the hollow site? Why does the top site show higher stability in terms of free energy, but the hollow site is more stable from the total energy calculations? How can we understand these results?

Figure 2. (a) Length of C-Pt bond in long standard MD simulation on top site and hollow site. (b) The trajectory of CO in the long standard MD simulation on top site and hollow site. The position of CO was calculated using the position of C. The blue line represents the trajectory on top site, while red line stands for hollow site.

To address these questions, two standard MD simulations at 300 K were performed with the initial structures of CO on the top site and hollow site, respectively. Figure 2 shows the characteristics of CO motion in the systems, which are measured by the bond distances of C-Pt.


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The figure reveals the following interesting features. Firstly, the simulations show that CO on the top site has a regular single vibrational motion (blue line) while a variety of motions can be found on the hollow site (red line). Compared with the bond distances of C-Pt30, the average distance on the top site from the MD simulations is 1.85 Å while the optimized C-Pt distance for CO on the top site is 1.86 Å from the total energy calculations. It is reasonable that the average distance in the MD simulations is a little longer than that in the optimized structure, considering the temperature effect in the MD simulations. However, the average distance on the hollow site is substantially longer from the MD simulations (2.26 Å) than that from the optimized structure (2.09 Å). This obviously longer bonding distance of CO on the hollow site from the MD simulations results in a weaker chemical bond between CO and the surface compared to that from the total energy calculations, indicating that the real structure of CO adsorption on the hollow site is considerably different from the traditional total energy calculations even though it is the room temperature. This considerable C-Pt bond weakening on the hollow site may be a key reason for the difference between our free energy simulations and the traditional total energy calculations for CO adsorption site preferences. In other words, the traditional total energy calculations might considerably over-estimate the bonding between CO and the surface for the hollow site compared to the free energy simulations with the same calculation settings; the thermo-motions of surface atoms may result in the CO adsorption on the hollow site significantly differing from the energy minimum structure from the total energy calculations.

The results of the two standard MD calculations above are consistent with the free energy profiles shown in Figure 1, in which the minimum position of the free energy profile from the top site is at 1.86 Å, corresponding to the distance between the C and the averaged Pt atoms on the top


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layer of the Pt surface (1.85 Å from the total energy calculation) but 1.51 Å for the hollow site from the MD simulations (1.42 Å from the total energy calculations). Furthermore, the centre of the distance oscillation is almost constant on the top site but varied on the hollow site with multifrequencies. In order to identify the difference of motions on the different adsorption sites, the trajectory of CO on Pt(111) was obtained from the MD simulations (Figure 2 (b)). It shows clearly that, during the same period, the motion of CO on the top site is restricted in a limited area and the vibrational motion is the common one. On the hollow site, on the other hand, a more complex movement area is found.

It is also interesting to note that the translational motion can be seen on the hollow site from the MD simulations: CO is observed not only being on one specific hollow site, but crossing one bridge site and reaching another hollow site several times within the period (this diffusion motion was seen in all the MD simulations and it is general). Therefore, CO adsorption on the hollow site is not at a single site even at room temperature; instead, it is rather dynamic, changing constantly adsorption sites on the surface. A classical chemical bond is well defined, where a well-defined local minimum and well-defined vibrational frequency can be found; surely CO adsorption on the top site belongs to this class. However, CO adsorption on the hollow site at 300 K cannot be described well by this class; CO on the hollow site is not limited on a specific site according to our calculations, being clearly evident of a delocalised chemisorption state.

Towards further understanding of the delocalized chemisorption state and the difference between two different adsorption sites, the standard MD sampling was used in this work to estimate


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CO adsorption site probabilities: The higher the probability of CO adsorption on a specific site, the lower the free energy is. To this end, some adsorption positions were uniformly spread in p(2×2) unit cell of Pt(111) to catch the random nature of adsorption process. Initial structural optimizations with all the slab atoms fixed and the C position of CO in the surface plane fixed for each adsorption position were carried out first as the initial structures, followed by long-time standard MD simulations for each of the initial structures. Figure 3 shows the distribution of CO adsorption site probabilities (calculated on C) in one p(2×2) supercell.

Figure 3. Distribution map of CO on Pt(111) surface by standard molecular dynamics. X and Y axis represent the distance in one p(2×2) unit cell in Å. The whole p(2×2) unit cell was separated into 20×20 parts and the number of CO emerged in every part was counted and described by the colours showed on the right. 2.5×105 points were calculated in map with the time step 0.5 femtosecond, which is 125 picoseconds.


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The following features can be seen in Figure 3: Firstly, the distribution of CO adsorption probabilities on the top site is localized, while the adsorption area on the hollow site and bridge site seems to be combined. Namely, the top site areas on the surface are independent with each other while the hollow site areas are interconnected. Secondly, the CO adsorption state on the top site is in a limited area with a high probability in the centre (i.e. low free energy), whereas the probability of CO adsorption on the hollow site is averaged out, spreading in a larger area leading to a low probability of CO adsorption on the specific hollow site. These results confirm that the hollow site is not a well-defined single site and the CO adsorption appears to be delocalized in contrast to the top site. Moreover, the direct relationship between probability and free energy displayed in Figure 3 demonstrates that the higher probability on the top site is indeed a lower free energy site compared with the hollow site. This is consistent with the result obtained from the umbrella sampling simulations. Perhaps more interestingly, they provide a different perspective on why the hollow site is less favoured for CO adsorption.

In order to understand the delocalized nature of adsorption state for CO on Pt(111), a total energy potential surface was calculated (see Figure 4). It can be seen that there is a small barrier between the hollow site and bridge site, which is 0.01 eV from the bridge site to hollow site and 0.03 eV from the hollow site to bridge site. A larger barrier exists between the hollow site and top site, which costs 0.22 eV from the hollow site to top site and 0.10 eV from the top site to hollow site (0.18 eV from the bridge site to top site and 0.08 eV from the top site to bridge site). It is possible for CO to cross the barrier between the hollow site and bridge site at 300 K but is difficult to move between the top site and hollow site. The trajectory map of CO adsorption (Figure 2 (b)) is consistent with the potential surface, where the probability for CO to move between the top site


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and the hollow (bridge) site is small, which means that the CO moving areas are separated into two parts; (i) the top site area and (ii) the hollow-bridge combining area. The hollow-bridge combining area is quite even, demonstrating a delocalized adsorption state.

Figure 4. Potential surface of CO on Pt(111). The distance on surface shows the track described as inner figure.

Having presented the CO adsorption/desorption results in terms of free energy, we are in a position to discuss some implications of our work. Firstly, the method developed in this work to obtain the free energies of adsorption/desorption processes including the free energy barriers is very robust: It can be used not only to calculate the free energy barriers of adsorption/desorption


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for any molecules on any surfaces, but also to simulate surface catalytic reactions, directly giving rise to the free energy changes along a reaction coordinate. Secondly, our method is a MD simulation-based approach, which means that the temperature effect is naturedly incorporated. As demonstrated above, the structures from the traditional total energy calculations might be substantially different from those from the free energy-based simulations even at room temperature. One can envisage that to simulate catalytic reactions at high temperatures the structures from the traditional total energy calculations may significantly differ from the correct ones, let along the energies. This may be of paramount importance to obtain reliable results for catalytic systems from first principles calculations. Thus, the usage of our approach in heterogeneous catalysis may be highly desirable. Thirdly, the discovery of the delocalized adsorption state may be conceptually of significance in the understanding of surface catalytic reactions: The traditional picture of CO adsorption on the hollow site is far away from the real one even at room temperature, which may be of general importance in heterogeneous catalysis.

CONCLUSION In summary, advanced molecular dynamics calculations within the framework of DFT were used to study CO adsorption/desorption on Pt(111) and the free energies of the processes were obtained. Total energy calculations with thermodynamic corrections were also carried out for comparison. Standard molecular dynamics simulations were further performed to obtain a deep understanding of CO on Pt(111). The main conclusions are summarized as follows: (i) The free energy barriers of CO adsorption on Pt(111) on the top and hollow sites were found to be similar at ~0.1 eV, while the free energy barriers of desorption from the top and hollow sites


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are 1.14 eV and 1.00 eV, respectively. This is the first time that the free energy barriers of adsorption/desorption, arguably the most basic process in heterogeneous catalysis, were rigorously computed from first principles calculations. (ii) The free energy results reveal that CO prefers to adsorb on the top site rather than on the hollow, which is consistent with experimental observations but in contrast with the traditional total energy calculation results as well as the free energy results obtained from total energy calculations with thermodynamic corrections. (iii) The reason for the discrepancy between our free energy simulations and the traditional total energy calculations is identified; the total energy calculations over-estimated the bonding between CO and the surface hollow site compared to the top site. (iv) It is found that the motion of CO is localized on the top site, while CO on the hollow site is a delocalised chemisorption state at 300 K. The diffusion barriers are determined.

Our method is general and the results reported may possess some profound implications in obtaining correct structures and energies not only in catalysis but also in other areas. The finding that the structures from the traditional total energy calculations might be substantially different from those from the free energy-based simulations even at room temperature may have profound implications in first principles calculations in catalysis in the future.

ASSOCIATED CONTENT


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Supporting Information. Computational details including chemisorption energy calculations, free energy corrections, constrained MD simulations and bootstrapping error analysis are available in supporting information. Supporting Information is available free of charge via the Internet at http://pubs.acs.org. Additional details of the calculations as described in the text (PDF).

AUTHOR INFORMATION Corresponding Author * Email for P.H.: [email protected] * Email for H.-F.W.: [email protected] Author Contributions †‡ ‡ † † P. H.* and H.-F.W.* conceived the project. C.X.G. carried out all the calculations. Z.Y.W. and

D.W.‡ contributed to the discussions of the project. C.X.G.† wrote the first draft of the manuscript and prepared figures and all the authors contributed to the revision of the manuscript.

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENT UK Archer provides supercomputing service. C.X.G. thanks the Queen’s University of Belfast and China Scholarship Council for finance support. This project was supported by the National Natural


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Science Foundation of China (21333003, 21622305), Young Elite Scientist Sponsorship Program by CAST (YESS20150131), “Shu Guang” project supported by Shanghai Municipal Education Commission and Shanghai Education Development Foundation (17SG30), and the Fundamental Research Funds for the Central Universities (WJ616007).

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First Principles Determination of CO Adsorption and Desorption on Pt

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