Strain and Low-Coordination Effects on Monolayer Nanoislands of Pd and Pt on Au(111): A Comparative Analysis Based on Density Functional Results

Abstract

Recent experiments demonstrated that the catalytic centers for the hydrogen evolution reaction (HER) are different on Pd and Pt nanoislands on Au(111). Inspired by these experiments, we examined the geometric, energetic, electronic and hydrogen adsorption properties of monolayer model nanoislands of Pd and Pt supported on Au(111) with density functional theory calculations. Accordingly, Au-tensile strain effects can be nearly 50% larger on the geometric structure of nanoislands of Pd on Au(111) than their Pt analogs, resulting on different electronic properties for these nanoislands. Despite these differences between Pd and Pt nanoisland on Au(111), our computational modelling of the hydrogen adsorption suggests that the unique catalytic centers for the HER on Pd and Pt nanoislands supported on Au(111) derive from the existence of low-coordinated adsorption sites and the intrinsic properties of Pd and Pt, but not from Au-tensile strain effects.

Graphical Abstract

1. Introduction

The nature of the catalytic centers for the hydrogen evolution reaction (HER) in acidic media on Au(111)-supported Pt and Pd monolayer nanoislands was recently revealed¹ by analyzing the noise of the tunneling current during electrochemical scanning tunneling microscopy experiments (n-ECSTM). It was concluded that for Pd nanoislands on Au(111), the catalytic activity is maximal in the edge region, i.e., at the Pd/Au boundary. In contrast, for Au(111)-supported Pt nanoislands, the catalytic activity is rather similar for Pt atoms at the edge and in the inner regions.¹ These results were rationalized¹ in terms of the d-band model,² and the interplay between ligand and strain effects. The authors postulated that Au-tensile strain effects dominate in the case of Pt, but both effects were assumed to play a role in the case of Pd on Au.¹ These arguments are able to rationalize the difference in the catalytic properties of pseudomorphic overlayers of Pd and Pt on Au. However, it is unclear how only ligand and strain effects account for the differences found¹ in experiments on monolayer nanoislands of Pd and Pt on Au(111).

Compact 2D metal-supported metal nanoislands experience size-dependent compressive stress because of strain caused by finite-size effects.^3–7 For Pt nanoislands on Au(111), such finite-size compressive stress competes with the tensile strain due to the Au(111) substrate,^3,5 resulting in the formation of Pt nanoislands where Pt atoms are not aligned with the substrate, occupying different sites on the Au substrate.⁸ At variance, little or nothing is understood about the local structure of Pd nanoislands on Au(111) as computational works are limited to sub-nanometer-size models of Pd on Au.^4,9–12 Pd and Pt differ in their cohesive energies,¹³ measured at 377 kJ mol⁻¹ and 564 kJ mol⁻¹, respectively, which gives rise to a different interplay between the lateral and vertical bonding of Pd and Pt nanoislands on Au(111), as will be shown in this work.

Previously, we studied computationally the geometric, energetic, and electronic properties of monolayer Pt nanoislands supported on Au(111) and Cu(111).⁵ We determined that the properties of monolayer Pt nanoislands do not scale to reach those of the corresponding pseudomorphic overlayers. Instead, the Pt nanoislands adopt a similar structure on both Au and Cu surfaces. Another noteworthy outcome of that study was our suggestion to quantify the difference in the binding of atoms at the edge and the inner region of the nanoislands.⁵ This energy difference, related to the step formation energy, is useful for understanding the thermal stability of nanoislands.¹⁴ An analysis of the computed energetics of monolayer nanoislands also revealed a subtle competition between lateral and vertical bonding that ultimately determines the geometric and electronic properties of metal-supported metal nanoislands.⁵

In the present work, we compare monolayer model nanoislands of Pd and Pt on Au(111) to reveal similarities and differences between these two catalytic systems, aiming at a better understanding of the catalytic centers identified¹ in nanoislands of Pd and Pt on Au. Pd nanoislands have been studied extensively in experiments because of their high activity toward HER/HOR (hydrogen oxidation reaction).^15–19 Furthermore, Pd nano-catalysts are used in a plethora of chemical processes, among others in carbon-carbon and carbon-heteroatom cross-coupling reactions, carbon-carbon homocoupling reactions, C-H activation, hydrogenation, and esterification.²⁰ Therefore, theoretical studies of metal-supported Pd nanoislands are also relevant to many applications in heterogeneous catalysis.

2. Methods

To study and compare monolayer nanoislands of Pd and Pt on Au(111), we employed a hexagonal planar model cluster with 61 atoms supported on an Au(111) surface. Such islands comprise four hexagonal rings of increasing edge length, around a central atom, Figures 1a, 1b. The Au(111) surface was simulated by (10×10) slab models of four atomic layers, separated by a vacuum region of more than 1 nm. [Fractional atomic coordinates of all optimized structures are provided as supplementary information (SI).] In this way, the closest lateral distances between images of the nanoislands were at least 400 pm. These models of nanostructured Au(111) surfaces are not intended as a complete representation of the complex experimental systems of Au(111), where surface reconstruction and defects often are present. Instead, our computational models are a limited representation of Pd and Pt nanoislands on well-defined Au(111) surfaces, which, nevertheless, have been observed under experimental conditions.⁸ For geometry optimization, Brillouin zone integration was carried out with a (1×1×1) k-grid.²¹ Pd and Pt atoms were initially placed above the fcc (octahedral) hollow sites of Au(111). During the geometry optimizations, the two “bottom” atomic layers of the surface models were held fixed at the optimized bulk lattice structure,¹⁰ while the remaining atoms were allowed to relax until residual forces were less than 2×10⁻⁴ eV/pm on each atomic center. The energetics and electronic structure were analyzed for calculations obtained with a finer k-point mesh of (2×2×1).

Figure 1.

Optimized structures of a) Pd₆₁ and b) Pt₆₁ supported on Au(111). Panels c) and d) display the corresponding distributions of M-M nearest-neighbor distances, M = Pd or Pt. Panels e) and f) show the distributions of the atom-projected d-band centers (relative to the Fermi energy of each system) in Pd₆₁ and Pt₆₁ supported on Au(111), respectively.

Our calculations are based on Density Functional Theory (DFT) within the Generalized Gradient Approximation (GGA) as implemented in the Vienna Ab-initio Simulation Package (VASP).^22–24 We used the Perdew–Burke–Ernzerhof (PBE)²⁵ parameterization of the exchange-correlation energy functional, and the projector augmented wave (PAW)^26,27 method to represent ionic cores. We employed an energy-cut-off of 350 eV for the plane-wave basis set. Calculations were carried out in spin-averaged fashion, with a level broadening of 0.05 eV. The employed energy-cut-off, k-point meshes, and surface models provide converged results at a reasonable computational cost.⁵

The monolayer nanoislands Pd₆₁ and Pt₆₁ on Au(111) show significantly different geometric and electronic properties, as quantified below by lateral Pd-Pd and Pt-Pt nearest-neighbor distances and the atom-projected d-band center of Au-supported Pd₆₁ and Pt₆₁, Table 1. To reveal the source of such differences, and better understand the energetics of the subtle competition between lateral and vertical bonding, we also carried out calculations for Pd employing hexagonal planar clusters of 19, 37, 61 and 91 atoms, of 2–5 hexagonal rings of atoms, supported on Au(111) following the same computational approach⁵ as previously used; see the SI.

Table 1.

Calculated properties of the nanoisland M₆₁ (M = Pd, Pt) supported on Au(111).^a

Property	Pd61/Au	Pt61/Au
⟨M-M⟩	282 (3)	269 (5)
⟨M-M⟩s0-s1	287 (0)	271 (0)
⟨M-M⟩s1-s2	286 (1)	272 (2)
⟨M-M⟩s2-s3	281 (1)	267 (2)
⟨M-M⟩s3-s4	277 (1)	266 (2)
⟨M-M⟩s1,t	287 (0)	271 (2)
⟨M-M⟩s2,t	286 (2)	272 (4)
⟨M-M⟩s3,t	284 (2)	270 (4)
⟨M-M⟩s4,t	282 (2)	269 (2)
ɛd(M)	−1.35 (0.06)	−1.83 (0.11)
ɛd(Ms0)	−1.37	−1.87
ɛd(Ms1)	−1.36 (0.04)	−1.85 (0.07)
ɛd(Ms2)	−1.40 (0.05)	−1.89 (0.10)
ɛd(Ms3)	−1.41 (0.04)	−1.96 (0.06)
ɛd(Ms4)	−1.27 (0.07)	−1.69 (0.13)

^aAverage distance ⟨M-M⟩ between nearest-neighbor M atoms, M = Pd, Pt, average nearest-neighbor distance ⟨M-M⟩_si-s(i+1) between consecutive shells s_i and s_i+1 (radial), average nearest-neighbor distance ⟨M-M⟩_si,twithin a shell s_i (tangential), average d-band center ɛ_d(M) of M₆₁ relative to the Fermi energy ɛ_F of the system, average d-band centers ɛ_d(M_si) of individual M atoms in the shell s_i of the nanoislands. The label s_i designates the atoms in shell i (i = 0 – 4) of the nanoislands; i = 0 refers to the central atom, see Figure S1 in the SI. Distances are given in pm and one-electron energies in eV. Values in parenthesis correspond to the mean absolute deviation (MAD) of the averaged property.

3. Results and Discussion

Our discussion will be focused on the properties of the model systems M₆₁ (M = Pd, Pt) supported on Au(111). We will compare the geometric properties of these two systems in terms of their M-M and M-Au nearest-neighbor distances and their electronic properties via the atom-projected d-band center of M₆₁. We focus on these parameters because the d-band center has been shown to correlate with the catalytic activity of metal surfaces.²

First, we studied the geometry of planar M₆₁ model clusters as well as infinite monolayers of M, without the Au(111) support, because such “freestanding” models provide useful reference systems for examining substrate effects. The calculated average nearest-neighbor distances 〈M-M〉 of Pd₆₁ and Pt₆₁ are 261 pm and 259 pm, respectively. The values 〈M-M〉 of atoms at the edges of these planar M₆₁ clusters are shorter (by 1 pm for Pd₆₁ and 2 pm for Pt₆₁) than for atoms in the inner region because of the lower coordination number (CN) of edge atoms: CN = 6 for atoms in the inner region and CN ≈ 3.8 for atoms at the edges of the planar M₆₁ clusters. M-M nearest-neighbor distances in the freestanding infinite layers of Pd and Pt were calculated at 262 pm and 261 pm, respectively. The rather comparable values of the Pd-Pd and Pt-Pt nearest-neighbor distances in these unsupported models are expected since the lattice constants of bulk Pd and Pt are rather similar,¹⁰ corresponding to nearest-neighbor distances of 279 pm in Pd and 281 pm in Pt. Note the well-known substantial compressive stress on the free-standing clusters as a consequence of their finite size.^28–30

Turning to the computational results for the nanoislands, we show in Figures 1a and 1b the optimized structure of Pd₆₁ and Pt₆₁ on Au (111), respectively. Figures 1c and 1d show the distributions of the Pd-Pd and Pt-Pt nearest-neighbor distances, respectively, for the optimized structures. The nearest-neighbor distance distributions differ significantly between Pd and Pt. This is a first important computational result for the supported nanoislands on Au(111). The majority of Pd-Pd bond distances are above 280 pm, Figure 1c, i.e., even longer than calculated for bulk Pd.¹⁰ In contrast, Pt-Pt bond distances are generally below 270 pm, Figure 1d, i.e., only moderately extended (by ~ 10 pm) from the results calculated for the free-standing island. The average 〈M-M〉 interatomic distances for Pd₆₁ and Pt₆₁ on Au(111) are 282 pm and 269 pm, respectively. These M-M distances of M₆₁ nanoislands on Au(111) are much shorter than 295 pm, the calculated distance expected for pseudomorphic structures on Au(111).^5,10 In Figure 2a, we show average lateral (radial) distances 〈M-M〉 between individual M atoms in the shells of the nanoislands M₆₁. In general, radial 〈M-M〉 values decrease from the inner region to the edge region of the nanoislands. The average values of radial 〈M-M〉 of atoms at the edges are shorter (by 10 pm for Pd₆₁ and 5 pm for Pt₆₁) than for atoms in the inner region of the corresponding nanoislands.

Figure 2.

a) Average radial <M-M> nearest-neighbor and b) atom-projected d-band center of M atoms in the shell i of the nanoislands M₆₁/Au(111), M = Pd, Pt. Error bars show the mean absolute deviation (MAD) of the averaged property. Shell i corresponds to the i-th hexagonal ring around the center (i = 0) of the nanoisland (i = 1–4).

Next, we would like to draw attention to two key findings from our calculations. First, both Pd and Pt form compact 2D nanoislands, which are locally quite different from pseudomorphic structures on Au(111) as shown by uninterrupted overlayers of Pd and Pt on Au.^5,10 This finding is in line with those in previous computational studies^3,5–7 and recent experiments^6,8 showing that compact 2D metal nanoislands do not form pseudomorphic structures when supported on a metal substrate because of compressive finite-size effects. There is compressive stress within the Pt and Pd nanoislands on Au(111) with a strong lateral (radial) dependence.³ The stress is weaker in the inner region and stronger at the edges of the nanoislands, as shown by the significant decrease in the radial 〈M-M〉 of atoms in the inner to the edge regions of the nanoisland.

The second finding from our calculations is that Au-tensile strain effects are almost 50% larger on the structure of Pd nanoislands than on the structure of Pt nanoislands, at variance with what has been postulated in Ref. 1. The M-M distances of Pd₆₁ and Pt₆₁ nanoislands on Au(111) are 8% and 4%, respectively, longer than the average interatomic distances of freestanding Pd₆₁ and Pt₆₁ clusters. These results obtained from the analysis of Pd₆₁ and Pt₆₁ model nanoislands on Au(111) also extend to smaller and bigger model nanoislands. Figure 3 shows the average Pd-Pd and Pt-Pt⁵ nearest-neighbor distances for nanoislands on Au(111) with 19, 37, 61, and 91 atoms. For every nanoisland, Au-tensile strain effects are larger on Pd than Pt. A key difference between Pd and Pt is the fact that intra-layer (lateral) M-M bonds are weaker for M = Pd than for M = Pt. This correlates with the cohesive energies E_coh of bulk Pd and Pt; at the same level of theory they were calculated at 339 kJ mol^–1 (Pd) and 531 kJ mol^–1 (Pt).⁵

Figure 3.

Calculated average distance 〈M-M〉 between nearest-neighbor M atoms, M = Pd, Pt, of planar model nanoislands M_n (n = 19, 37, 61, 91) as a function of the number ratio, n_e/n, of the number n_e of edge atoms and the total number of atoms n of a planar model nanoisland. Results are shown for M_n in the gas phase and supported on Au(111). The calculated nearest-neighbor distance M-M of a full monolayer ML/Au of M, M = Pd, Pt, on Au(111) is also shown for comparison.

We postulate that such difference in the energetics of intra-layer Pd-Pd and Pt-Pt bonds gives rise to a different interplay between the lateral and vertical bonding of Pd and Pt nanoislands on Au(111), resulting in the higher Au-tensile strain on Pd nanoislands. To examine the interplay between lateral and vertical bonding of Pd nanoislands on Au(111), we employed a liquid “droplet” model¹⁴ and scaling relations⁵ that permit one to decouple the bonding interactions into contributions of atoms at the edge and in the inner region of the nanoislands. With that approach, the adsorption (vertical) energy and the agglomeration (lateral) energy of a monolayer nanoisland can be expressed in terms of the corresponding energy contributions E_e and E_i of atoms at the edge (e) and in the inner region (i) of a nanoisland, respectively. The quantities E_e and E_i can be determined by fitting adsorption and agglomeration energies evaluated from the results of DFT calculations; see the supporting information (SI) for details as well as our previous work.⁵ From such an energy analysis, we determine the difference between vertical (v) and lateral (l) interaction energies at the edges (ΔE_vl,e) and in the inner (ΔE_vl,i) region of nanoislands, Table 2. These results quantify the competition between vertical and lateral interactions for atoms at the edges and in the inner regions of the various nanoislands. Table S3 of the SI provides the underlying raw data.

Table 2.

Energy differences ΔE_vl,i and ΔE_vl,e between vertical and lateral interaction of monolayer nanoislands Pd_n and Pt_n, supported on Au(111). All energies per atom in kJ mol⁻¹.

System	ΔEvl,i	ΔEvl,e
Pdn/Au(111)	6	−80
Ptn/Au(111)	95	−36

At the edges of the nanoislands, vertical bonding is stronger than lateral interactions, ΔE_vl,e < −30 kJ mol⁻¹ for the two systems. At the edge of Pd nanoislands, this bonding to the support is significantly stronger than the lateral interaction. Also, the quantities ΔE_vl,i vary notably among the systems under study. For Pd_n/Au, the value ΔE_vl,i is only 6 kJ mol⁻¹, i.e., the vertical interaction is slightly weaker than the lateral interaction. At variance, the value ΔE_vl,i is 95 kJ mol⁻¹ for Pt_n/Au, suggesting that (lateral) intra-layer bonding is significantly more dominant for atoms in the inner region of Pt_n nanoislands. These differences for Pd_n and Pt_n arise because Pd-Pd bonds in general are weaker than Pt-Pt bond. These results help to understand the different Au-tensile strain effects on Pd and Pt nanoislands.

The position of the d-band center of metal surfaces (relative to the Fermi energy) correlates linearly with the width of the d-band, and an expansion or compression of the geometrical structure of metal systems results in narrower or wider d-bands, in turn, shifting the d-band center upward or downward.^2,31 As the structures of Pd and Pt nanoislands on Au(111) are different, their electronic properties will also be different. Figure 1e and 1f show the distribution of the atom-projected d-band center ε_d of Pd₆₁ and Pt₆₁ nanoislands, respectively, on Au(111). The values of ε_d(Pd) are all above −1.5 eV, and those of ε_d(Pt) are all below −1.5 eV. The averages ε_d for Pd₆₁ and Pt₆₁ on Au(111) are -1.35 eV and −1.83 eV, respectively. The values of ε_d of Pd and Pt atoms at the edges of the nanoislands are closer to the Fermi energy, by 0.1–0.2 eV, Figure 2b, than those of atoms in the inner region because of their lower CN.

The values ε_d qualitatively correlate³² with the hydrogen adsorption energy E_ads and with the change in hydrogen-free energy of adsorption, ΔG_ads, which should be zero or nearly zero for ideal HER electrocatalysts. ΔG_ads ≈ 0 eV for overlayered bimetallic systems with ε_d(M) in the range of −1.5 to −1.2 eV.³² Within the d-band center model,² both Pd and Pt nanoislands on Au are expected to be more catalytically active at the boundaries with Au, i.e., the edge region of the nanoislands, which is not the case according to the experiment.¹

Figure 3 shows estimated free-energy values ΔG_ads at 300 K for the dissociative adsorption of hydrogen (H₂) over various sites of Pd₆₁ and Pt₆₁ on Au(111). The values were determined as previously proposed,^32,33 by adding 23 kJ mol⁻¹ per H_ads to the DFT calculated dissociative absorption energy of H₂. This correction accounts for changes in the zero-point energy and the entropy of gaseous H₂ upon the dissociative adsorption on metal surfaces. On Pd₆₁ supported on Au(111), hydrogen can be adsorbed on the three-fold hollow sites, like face-centered cubic (fcc) on the inner regions of the nanoisland, and at the rim^4,9,11,12 of the nanoislands. ΔG_ads is ∼40 kJ/mol less negative on edge sites than in the inner region of the Pd nanoisland, Figure 3 and Table S4 of the SI. For the analogous model Pt₆₁, adsorbed hydrogen is stable at three-fold hollow and on top sites of the inner region, as well as at the bridge and on top sites of the edges. In both edge and inner regions of Pt nanoislands, the on top positions are stable, albeit weakly hydrogen adsorbed states,^34–36 contrasting with Pd where low-coordinated on top sites are not stable. In a previous analysis, we have traced the effect of coordination on the hydrogen adsorption on Pd and Pt to the relativistic contraction and stabilization of the valence s-orbital of Pt atoms.¹¹

The estimated ΔG_ads results for the dissociative adsorption of hydrogen suggest that under HER conditions^37,38 on Pd nanoislands on Au(111), sites in the inner regions are occupied; no further hydrogen adsorption states are available, Figure 3. The active sites are mainly located in the edge regions of the supported Pd nanoislands, where hydrogen binds weakly and the condition of ΔG_ads ≈ 0 is more easily accessible. On the analogous Pt nanoislands over Au(111), there are active sites for HER as both types of regions offer sites of weak hydrogen adsorption, Figure 3.

Figure 4.

a) Sketch showing adsorption sites of hydrogen on Pd₆₁ and Pt₆₁ over Au(111). b) Estimated free-energy values ΔG_ads at 300 K for the hydrogen dissociative-adsorption. On supported Pd₆₁. hydrogen adsorbed on sites 2, 3, 4, 7, and 8 is not stable, turning to sites 5 or 6 during optimization. On supported Pt₆₁, hydrogen adsorbed on sites 1, 4, 5, and 7 is not stable, turning to sites 2, 3, or 6. Note that the plot shows the negative value of ΔG_ads.