Density Functional Calculations of the Sequential Adsorption of Hydrogen on Single Atom and Small Clusters of Pd and Pt Supported on Au(111)

We have used density functional theory calculations to study the sequential adsorption of hydrogen on Pd and Pt atomic site catalysts such as single-atom alloy catalysts (SAAC), single-atom catalysts (SAC), and single cluster catalysts (SCC) on Au(111). The results show that Pd systems tend to have near-zero free energy of hydrogen adsorption (ΔGHads≈0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta {G}_{{\mathrm{H}}_{\mathrm{ads}}}\approx 0$$\end{document}) under various coverage conditions of adsorbed hydrogen. In the case of Pt systems, ΔGHads≈0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta {G}_{{\mathrm{H}}_{\mathrm{ads}}}\approx 0$$\end{document} only at high coverage conditions of adsorbed hydrogen. Such differences come from the preference of hydrogen for high-coordination and low-coordination sites on Pd and Pt, respectively. The low coordination of hydrogen results in multiple adsorption sites with ΔGHads≈0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta {G}_{{\mathrm{H}}_{\mathrm{ads}}}\approx 0$$\end{document} in SCC of Pt/Au. These results can help to understand the different catalytic properties of Pd/Au and Pt/Au.

In the case of metal-supported metal electrocatalysts, the experimental techniques for preparing well-defined systems and the instrumentations to identify differences in coordination have become available only recently [6,7]. The new methods and instrumentations have provided invaluable details on the role of site coordination in the catalysis of metal-supported metal electrocatalysts. The step-like sites in Pt/Au(111) were shown to contribute more to the overall catalytic activity in hydrogen evolution reaction (HER) than either the Pt or Au terrace sites [8]. In another study, the electrochemical scanning tunneling microscope (n-ECSTM) method was used to show that the catalytic activity for HER is different for Pd and Pt nanoislands on Au(111) [9]. It was found that the catalytic activity is maximal at the Pd/ Au boundary while relatively uniformly across the Pt/Au boundary and the inner region of the Pt nanoislands [9]. These differences between Pt/Au and Pd/Au were rationalized initially in terms of the interplay between ligand and strain effects. It was postulated that Au tensile strain effects dominate in the case of Pt/Au, but both ligand and strain effects played a role in Pd/Au [9].
However, we used density functional theory (DFT) calculations to show that Au tensile strain is 50% larger in Pd/Au than in Pt/Au [10]. We postulated that instead, the catalytic activity is different for Pd/Au and Pt/Au nanoislands because, for Pd, there are sites with the near-zero free energy of hydrogen adsorption ( ΔG H ads ≈ 0 ) only at the Pd/ Au boundary, while such sites are at the Pt/Au boundary and inner region of the Pt nanoislands [11]. Such differences come from the preference of hydrogen for low-coordination and high-coordination sites on Pt and Pd, respectively, which can be traced to relativistic contraction and stabilization of the valence s-orbital in Pt [12,13]. These computational results reveal multiple sites with a free energy of hydrogen adsorption near zero on Pd and Pt nanoislands on Au(111). Electrocatalyst sites with ΔG H ads ≈ 0 play an essential role in understanding many aspects of hydrogen oxidation reaction (HOR)/HER on metal electrocatalysts [14][15][16][17][18].
We identify the catalytic sites with ΔG H ads ≈ 0 on metalsupported metal nanoislands by simulating the high coverage conditions of adsorbed hydrogen [11] using model Pt and Pd nanoislands of 1-2 nm in diameter. The so-called atomic site catalysts are another class of systems where the preference of hydrogen for low-coordination and high-coordination sites should be clearly understood. Atomic site catalysts are usually single metal atoms or sub-nanosize clusters coordinated with non-metallic or metallic support matrices [19][20][21][22][23]. Atomic site catalysts are typically divided into three main groups: (i) single-atom catalyst (SAC), (ii) single clusters catalyst (SCC), and (iii) single-atom alloy catalyst (SAAC) [20-22, 24, 25]. Each one has the potential for reactions like C-C coupling for the formation of ethane [26], C-C cleavage for ethanol decomposition through steam reforming, formation of CH 4 and CO [27], dehydrogenation [28,29], and hydrogenation [30]. These catalysts work around common problems such as catalyst and ligands recovery, slow/fast release of adsorbate, selectivity between species, and overall yields. SAAC, SAC, and SCC of Pt and Pd are among the most studied of these systems [19][20][21][22][23]. Many studies of Pt and Pd catalysts have focused on hydrogen dissociation and binding because of the crucial role of hydrogenation reactions. Tierney et al. performed a combination of experimental and theoretical works to demonstrate the effectiveness in promoting the H 2 dissociation of an inert host metal when alloyed with Pd. On the computational side, calculations have mainly focused on the SAAC of PdAu(111) [31][32][33] and SCC of Pd/Au [34][35][36][37][38][39] and Pt/Au [34,35]. However, there are no systematic computational studies comparing hydrogen adsorption on metal-supported SAAC, SAC, and SCC under high coverage of adsorbed hydrogen. In the present work, we aim to close this gap by exploring high coverage conditions of adsorbed hydrogen on Au-supported atomic site Pt and Pd catalysts.

Methodology
We employed the Vienna Ab-initio Simulation Package (VASP) [40][41][42] for all DFT calculations. The Perdew-Burke-Ernzerhof (PBE) [43] variant of the generalized gradient approximation (GGA) was used to represent exchange-correlation effects. The ionic cores were described by the projector augmented-wave (PAW) [44,45] method. The electronic one-particle wave functions were expanded on a plane-wave basis to an energy cutoff of 350 eV. The technique of fractional occupation numbers with a level width of 0.05 eV was used. All total energies were extrapolated to k b T = 0 eV. The interaction between the repeated slabs was modified for a dipole correction implemented in VASP. We restricted our calculations to the spin-averaged strategy because adsorption energies of hydrogen evaluated from spin-polarized and spin-averaged calculations differ by only one kJ mol −1 .
For the Pd n /Au(111) and Pt n /Au(111) (n = 1 and 3) systems, calculations were performed with a (4 × 4) surface model of four atomic layers, separated by a vacuum region over 10 Å. Our model systems are limited to the near-ideal Au(111) surface, where herring-bone reconstruction is not considered, even though they have been experimentally observed [46,47]. Such reconstructions are outside the focus of the present work. Our computational results are still relevant because, in experimental measurements of Au(111), patches without herring-bone reconstruction are also observed. During geometry optimization, the two "bottom" atomic layers of the surface models were fixed at the calculated lattice constants [48], while the remaining atoms were allowed to relax until all residual forces were less than 0.02 eV/Å. Brillouin zone integrations were carried out with (5 × 5 × 1) and (7 × 7 × 1) k-point sampling [49] for geometrical optimization and the final results, respectively.
Hydrogen adsorption on Au-supported SAAC, SAC, and SCC was studied by calculating the free energy of adsorption ΔG H ads as follows: where ΔE H ads is the differential hydrogen adsorption energy, and 23 kJ mol −1 is the difference in zero-point energy and entropy per H ads at 300 K [50,51]. The differential hydrogen adsorption energy was calculated following Skúlason et al. [52,53]: where E int H ads is the integral hydrogen adsorption energy calculated as: In Eq. 3, E tot (nH@M) , E tot H 2 , and E tot (M) are the total DFT energy energies of the combined hydrogen/ metal system, the hydrogen molecule, and the metal slab, respectively. The number of adsorbed hydrogen atoms is n H . The number of active surface metal atoms M is N , and H ads = n H ∕N is the coverage of adsorbed hydrogen [10,11,33,36]. The calculated bond energy of H 2 is − 436 kJ mol −1 and − 408 kJ mol −1 after zero-point energy correction.

Results and Discussion
We studied the effects of adsorbed hydrogen coverage on the adsorption of hydrogen on Au(111)-supported SAC (Pd 1 /Au and Pt 1 /Au), SAAC (Pd 1 Au and Pt 1 Au), and SCC (Pd 3 /Au and Pt 3 /Au). There are multiple atomic configurations for n H hydrogen atoms adsorbed on Pd n (or Pt n ) on Au(111). We search for low-energy configurations employing standard optimization methods. We also used molecular dynamics (MD) to corroborate the stability of the low-energy atomic structures. In the following, we first discuss our DFT result for adsorbed hydrogen energetic and geometric properties on SAC and SAAC of Pd and Pt. We later discuss the DFT results for hydrogen adsorbed on triangular Pd 3 , along with triangular and linear Pt 3 SCC on the Au(111). In discussing the calculated properties of these systems, we focus on three main aspects: (i) trend of the free energy of adsorption ΔG H ads , (ii) the oxidation state of adsorbed hydrogen atoms, and (iii) finally, the effects of H ads on the spillover of hydrogen from Pd and Pt SAC, SAAC, and SCC onto the Au(111) surface. Please note that we focus on the trend of free energy of adsorption as its numerical values depend on the employed functionals [54]; numerical values are provided in the Supplementary Information (SI) section.  (111) Figure 2i shows the corresponding ΔG( H ads ) for the dissociative adsorption of hydrogen. Contrariry to the SAAC, Pt 1 /Au (111)

Hydrogen on SCC
We turn now to the hydrogen adsorption on Pd 3 and Pt 3 clusters on Au(111). Figure 3 shows the low-energy geometrical structures of hydrogen atoms adsorbed on linear Pt 3 and triangular Pt 3 and Pd 3 on Au(111). Other H ads configurations were explored and are included in Fig./Table S3 and S4, of the SI. We include the linear (wired) structure only for Pt 3 since wired Pd 3 is not the preferred structure on Au(111). The stability of wired Pt 3 on Au(111) was first pointed out in the work of Schulte et al. [34]. We recently showed that the relative stability of this linear structure might come from steric repulsion in the triangular conformation of Pt 3 because linear structures are not the preferred conformations for larger Pt clusters on Au(111) [54].
For the linear Pt cluster (Pt 3 -L), hydrogen with H ads ≤ 4∕3ML is located on bridge sites. For H ads = 2ML , hydrogen atoms are on-top position with an average-nearest neighbor distance of 2.7 Å between H atoms; see Table S4. For triangular-arranged systems, the adsorption configurations for hydrogen atoms are different on Pd 3 and Pt 3 for H ads ≤ 1ML . On Pd 3 , one hydrogen is located on the hollow site, and the other hydrogen atoms are at the Pd 3 /Au boundary (the rim sites), where hydrogen is coordinated to both Pd and Au. In the case of Pt 3 , all hydrogen atoms are at Pt/ Au boundary, where hydrogen atoms are single-coordinated to Pt, lying parallel to the Au(111) surface with Au-H distances over 2.7 Å. These results at low coverage of adsorbed hydrogen agree with previous calculations on Pd [34][35][36][37][38][39] and Pt [34,35] nanoislands on Au(111). At hydrogen coverage H ads ≥ 5∕3ML , the adsorption configurations are also different for Pd 3 and Pt 3 ; the hydrogen atoms are on the hollow, rim, and bridge sites on Pd 3 and on bridge, rim and on-top sites on Pt 3 . Figure 4 a shows ΔG H ads for the dissociative adsorption of hydrogen on Pd 3 and Pt 3 on Au(111). At very low H ads , ΔG is below −30kJ∕mol for all SCC systems. Increasing hydrogen coverage starts showing different ΔG H ads behavior between Pd 3 and Pt 3 . For H ads = 2∕3 − 4∕3ML in Pd 3 , ΔG H ads ≈ 0kJ∕mol suggesting that the active sites will be at the Pd/Au boundary. For H ads ≥ 5∕3ML , ΔG H ads > 0 suggesting that no other sites are active on Pd 3 /Au. Such findings align with the work of Liang et al. [9], showing that the catalytic activity for HER is maximal at the Pd/Au boundary in Pd nanoislands on Au(111). For linear and triangular Pt 3 clusters, the situation is different, and there are multiple sites with ΔG H ads ≈ 0 . At hydrogen coverages of H ads of 6∕3ML , 9∕3ML , and 12∕3ML on Pt 3 /Au, adsortion on the bridge, ontop, and Pt/Au boundary sites have ΔG H ads ≈ 0 . These results indicate that there could be various active sites for Pt 3 /Au as we recently reported [11] for nanoislands of Pt/Au. Figure 4b and c shows the Bader charge for hydrogen, Pt (Pd), and Au atoms in the systems comprised of Pt 3 -L and triangular Pt 3 and Pd 3 supported on Au(111). The Bader charge analysis indicates that the charge transfer processes differ on Pd 3 /Au and Pt 3 /Au, but they can also vary through geometrical configurations. On triangular Pd 3 /Au, the charge is transferred from both Pd and Au to the hydrogen atoms. In triangular and linear Pt 3 /Au, the charge is mainly transferred from the Au surface to the hydrogen atoms.

Hydrogen Spillover from SAAC, SAC, and SCC
The effects of H ads on the spillover of hydrogen from Pd (or Pt) to the Au(111) surface was studied by calculating the diffusion energy E dif f ; the energy change due to hydrogen migration from the Pd (or Pt) metal to the Au(111) surface [31,35]. E dif f is the so-called thermodynamic barrier. The kinetic barrier or activation energy ( E act ) is expected to be 10-15 kJ/mol higher that E dif f , based on our previous calculations for hydrogen spillover on Pd 3 and Pt 3 on Au(111) under low coverage conditions of adsorbed hydrogen [35]. The hollow site on the Au-substrate directly accessible from diffusion was chosen as the final location. The E dif f for SAAC and SAC of Pt and Pd are included in Table S5 and S6 of the Supporting Information sections. In both SAAC and SAC, E dif f is generally over 20 kJ/mol. Note that the spillover of hydrogen atoms from Pd-SAAC to Au sites can be enhanced by coadsorption of CO [32]. Figure 5 shows E dif f as a function of the hydrogen coverage H ads for Pt 3 /Au and Pd 3 /Au. For every hydrogen coverage studied for Pt 3 /Au and Pd 3 /Au, the least stable adsorbed hydrogen atom was simulated to migrate from Pt (or Pd) to Au(111). In the case of Pt 3 /Au, such a direct diffusion pathway is unlikely, but it provided a lower-bound estimate of the diffusion energy. Up to H ads = 1ML , E dif f is close to 40 kJ mol −1 and 80 on Pd 3 and Pt 3 , respectively. At hydrogen coverage of H ads ≥ 2ML , the diffusion energy is reduced to ∼ 20kJ∕mol −1 in the case of Pd 3 . In the case of Pt 3 , the lowest value of E dif f is around 40 kJ mol −1 . These calculated energies show that hydrogen spillover from supported Pd 3 or Pt 3 to well-defined Au(111) is not thermodynamically favorable [31] even under high hydrogen coverage conditions. This result reflects the low reactivity of well-defined Au surfaces toward the hydrogen dissociate adsorption, ΔG ≈ 30kJ∕mol for hydrogen adsortion on Au(111). However, hydrogen diffusion could be thermodynamically feasible from SCC to an Au surface with adatoms, surface alloys,  Table S3 and S4 of the Supplementary Information section.