Simulation of metal-supported metal-Nanoislands: A comparison of DFT methods
Graphical abstract
Introduction
Single-layer metal-supported metal clusters (nanoislands) are promising materials for many catalytic processes, including hydrogen oxidation/evolution reactions (HOR/HER), [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17] methanol and formic acid oxidation [18], [19], [20], CO oxidation [21], oxygen reduction reaction (ORR) [12,20,22], CO2 oxidation [23], and C-C bond splitting [24]. Many combination of metals have been explored as catalysts, including Pd and Pt supported on Au [2,4,6,7,9,[11], [12], [13], [14], [15], [16], [17],24,[19], [20], [21],25,26], Ni/Au [18,[27], [28], [29], [30], [31]], Cu/Au [23,[32], [33], [34], [35]], Rh/Au [3,8,22,[36], [37], [38]], Pd-Rh/Au [39], Ag/Au [40,41], Ir/Au [25], Au-Ag [1], Ir/Ni [25], Ag/Cu [42], Rh/Pd [43], Pd/Pt [44], Ir/Pt [25] and Pt/Cu [45]. In the case of Pt and Pd on Au(111), multiple reports indicate that the supported catalysts are two dimensional (2D) nanoislands with diameters of 2–30 nanometers [4,6,7,9,10,[13], [14], [15],17]. The properties of these metal-supported metal nanoparticles can depend on multiple factors, like the size and morphology of the nanoislands and lattice strain and ligand effects from the metal support. Thus, understanding how these factors and their coupling modulate surface catalytic properties is fundamental to customize metal-supported metal catalysts better.
The simulation of metal-supported metal nanoislands has been instrumental in understanding their properties [[46], [47], [48], [49], [50], [51], [52], [53], [54], [55], [56], [57],11,[58], [59], [60], [61], [62], [63]]. Density functional theory (DFT) methods [64] are at the center of most of these simulations [[46], [47], [48], [49], [50], [51], [52], [53], [54], [55], [56], [57],11,58,59,61]. For instance, DFT calculations have helped understand compressive finite-size effects [51,57] on metal-supported metal nanoislands and the role of low-coordinated sites on the catalytic properties of Pt and Pd nanoislands over Au(111) [46,47,55,59,61]. DFT calculations of metal-supported metal nanoislands have been performed either with the PBE [[46], [47], [48],52,53,[55], [56], [57],11,58], RPBE [51,54,57,59], PW91 [61] or PBE-D3 [49,50] functionals. Such standard functionals are widely used in the simulation of surface catalysis, and they generally yield reliable qualitative and semi-quantitative results [65], [66], [67], [68], [69], [70], [71], [72], [73], [74], [75]. However, this is not always the case, and there are many instances where these standard functionals are not even qualitatively reliable [76]. One of the key challenges is the energy scale of 10 kJ mol−1 of many surface processes. The adsorbed states of hydrogen [77,78] and CO [79] on metal surfaces are well-known examples, among others [80], of the difficulties of DFT methods to simulate surface processes on metal surfaces.
Taking this into consideration, the question of how consistent DFT methods are for the simulation of metal-supported metal nanoislands naturally arises. Answering such a question is important because multiple aspects of the simulation of metal-supported metal nanoislands involve small energy scales. For instance, understanding and predicting the atomic configuration of metal-supported metal nanoislands require resolving small energy differences, such as the energy difference for metal adatom on fcc and hcp sites on metal surfaces (of the order of 10 kJ mol−1 for Pt on Au) [56]. Reliable DFT calculations of the atomic structure of nanoislands are needed because the catalytic properties of metal nanoislands on metal surfaces can depend on their atomic configurations, as observed for Pt on Au [4]. Good energy resolution, below 10 kJ mol−1, is also needed to distinguish adsorption sites on metal-supported metal nanoislands, like hydrogen on Pt and Pd nanoislands on Au(111) [2,47]. Simulation of adsorption properties under high coverage conditions is another area where good energy resolution is needed. For instance, in hydrogen adsorption, identifying the hydrogen coverage where the free energy of adsorption is close to 0 is crucial for a better understanding of HOR/HER on metal catalysts [81], [82], [83]. However, in the case of hydrogen on Pt(111), DFT calculations yield values of 1.0 ML with PBE [83], 0.86 ML with RPBE [84], and 0.66 ML with the BEEF-vdW [85] method. Furthermore, studying the performance of DFT methods to simulate metal-supported metal nanoislands is of general interest because surface catalysts are often irregular mixed-metal surfaces with low-coordination sites, and it is not clear how reliable the DFT methods are for such systems. In the present work, we explore the performance of multiple DFT functionals to simulate Pt and Pd nanoislands supported on Au(111).
Section snippets
Computational details
All DFT calculations were performed with the Vienna Ab Initio Simulation Package (VASP) [86,87]. The projector augmented wave (PAW) method was used [88,89]. The calculations were performed without spin polarization. We performed calculations with the following DFT methods: PW91 [90], PBE [91], RPBE [92], revPBE [93] and PBESol [94], PBE-D3 [95], revPBE-vdW [96], [97], [98], SCAN [99,100], MS2 [101,102] and BEEF-vdW [103]. The PAW potentials employed for all calculations were the “PAW_PBE H
Results and discussion
We evaluated the performance of the DFT methods by comparing the energetic, geometric, and electronic properties of small Ptn and Pdn clusters on Au(111), with n = 1, 3, 4, and 7. In this section, we first discuss the reliability of the DFT methods for the energetics of the atomic conformations of Ptn and Pdn clusters on Au(111), with n = 1, 3, and 4. Afterward, we focus on the geometric and electronic properties of Pt7 and Pd7 clusters on Au(111). Finally, we end this section by comparing the
Summary
We have evaluated various DFT methods to study metal-supported metal nanoparticles, including GGA (PW91, PBE, RPBE, revPBE, and PBESol), GGA with van der Waals (vdW) corrected (PBE-D3), GGA with optimized vdW functionals (revPBE-vdW), meta-GGA (SCAN and MS2) and the machine learning-based method BEEF-vdW. We studied the geometric, energetic, electronic, and hydrogen adsorption properties for Au-supported Pt and Pd model nanoparticles. The results show that these DFT methods yield similar
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This project was supported by the “Fondo Institucional para el Desarrollo de la Investigación (FIDI 2019-2020)” of the University of Puerto Rico at Cayey. R.M.C. was supported in part by the National Institute of General Medical Sciences of the National Institutes of Health under Award Number R25GM059429-21. Calculations were performed on the computing facility at the University of Puerto Rico at Cayey, which is supported in part by the National Institute of General Medical Sciences of the
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