When more is less: Nonmonotonic trends in adsorption on clusters in alloy surfaces

Rationalizing and designing catalysts requires a strong understanding of how active sites behave upon modification. For alloy catalysts, it is particularly crucial to understand how active site reactivity—often measured with an adsorption energy—changes upon modifying the composition of the active site. Intuitively, we expect that as the composition of a surface site is smoothly varied, the binding strength of species to the site will vary smoothly as well. Indeed, this has been shown to be the case in many systems.^1–5 For example, density functional theory (DFT) calculations show that alloying increasing amounts of Ag or Pd into Au causes the adsorption strength of O to smoothly increase. Similarly, experiments of gas exposure to alloy single crystals often show smooth, monotonic changes in uptake as composition is changed.^2,6,7 While changes in composition could cause overall catalytic performance to change in a jagged or nonmonotonic fashion due to changes in a variety of factors (e.g., kinetics, surface segregation, reconstruction, and particle size) and the reactivity of a site of a fixed composition can be influenced by its local environment,⁸ the affinity of a particular site for a given species generally changes smoothly as composition is varied.

Small, localized ensembles of dopant atoms embedded in the surface of a host have recently gained significant attention as they can be effective catalysts for many reactions, such as selective hydrogenation.^9–11 Single-atom alloys have received particular attention, including development of models and correlations for predicting or understanding adsorption energies.^12–14 Single-atom alloys can have unusual properties, such as allowing spillover and breaking linear correlations between energies.^15–17 Furthermore, they often feature localized, sharp electronic states.^13,18,19 As this is similar to the behavior of nanoclusters (small particles with only a few atoms),²⁰ alloy surfaces with localized ensembles have been called “embedded nanoclusters.”²¹ 

In this work, we show how localized clusters of atoms embedded in the surface of a host can defy intuition and link this counterintuitive behavior to hybridization and splitting of sharp d-state peaks in these systems. By studying many dopants and several hosts, we also elucidate trends in the behavior of these systems, which allows us to develop correlations between the electronic structure and adsorption energies for single-atom alloys and embedded nanoclusters. In particular, we show that single-atom alloys have qualitatively different behaviors from dimers and trimers in how the H adsorption energy depends on the electronic structure.

Plane wave DFT calculations were performed with the Vienna Ab initio Simulation Package (VASP).^22,23 The k-point mesh was 7 × 7 × 1 with a 3 × 3 surface cell of four layers, with the bottom two layers fixed. The Perdew-Burke-Ernzerhof (PBE) exchange–correlation functional was used, with the Tkatchenko–Scheffler method²⁴ for van der Waals interactions. Plane wave cutoffs were set to 400 eV, and all calculations were spin-polarized. H adsorption energies were defined relative to gas-phase H₂, with the convention that exothermic adsorption is negative. See the supplementary material for further details.

To elucidate trends in adsorption on embedded nanoclusters, we performed DFT calculations for H adsorption on late transition metal fcc(111) surfaces substitutionally doped with one, two, and three metal atoms. We focused on Ag(111) as the host, but also examined Au(111), Cu(111), and Pd(111) as hosts, and we included 19 other d-block metals (Co, Cr, Fe, Hf, Ir, Mn, Mo, Ni, Pt, Re, Rh, Ru, Sc, Ta, Tc, Ti, V, W, and Zn) as dopants. We denote n atoms of X doped into Y as X_nY such that Cu₁Ag denotes a single Cu atom doped into a Ag(111) surface.

Doping a single heteroatom into a Ag surface nearly always strengthens H adsorption as Ag binds H relatively weakly. H prefers to adsorb in hollow sites on pure metal surfaces, and hence, we generally expect that adding more of the reactive metal to the adsorption site will further strengthen H adsorption as it can now bond to more atoms of that metal. In other words, intuition suggests that the trends across the number of dopants should be monotonic. This is, indeed, the case for Cu [Fig. 1(a)]: adding more Cu to the adsorption site stabilizes H approximately linearly as H is able to bond to more Cu atoms, and pure Cu adsorbs H more strongly than pure Ag. However, for Mo, adding a second dopant atom significantly weakens H adsorption compared to the single-Mo case, to such a degree that Mo₂Ag adsorbs H even weaker than pure Ag. This is a significant departure from intuition, given that pure Mo adsorbs H much more strongly than pure Ag. Similarly, adsorption on W_nAg follows a monotonically decreasing trend when up to two dopants are added but deviates from this trend when a third dopant atom is added.

More generally, we can elucidate trends by examining how the H adsorption energy differs between surfaces with consecutive numbers of dopants. We defined ∆E₁, ∆E₂, and ∆E₃ as the change in adsorption energy upon a change from zero to one, one to two, and two to three dopants, respectively [Fig. 1(a)]. Based on simple intuition, we generally expect that ∆E₁, ∆E₂, and ∆E₃ should be roughly similar.^1–5 This is indeed the case for many of the dopant elements. However, we found that several dopants feature the counterintuitive, nonmonotonic trends seen for Mo and W in Fig. 1(a). For example, for Mo, Ir, Ru, Cr, Tc, and Re, ∆E₁ and ∆E₂ are quite different and, in fact, have different signs [Fig. 1(b)], corresponding to unexpected weakening of adsorption upon adding the second dopant atom. For Ir, W, Ru, Ta, Re, and Pt, ∆E₁ and ∆E₃ have different signs [Fig. 1(c)], corresponding to unexpected weakening of adsorption upon adding the third dopant. Whether a particular dopant features a nonmonotonic trend appears to have no correlation to the absolute adsorption energy. For example, Mo₁Ag and Ti₁Ag have similar adsorption energies (−0.41 eV and −0.38 eV, respectively), but Mo₂Ag and Ti₂Ag have adsorption energies that differ by nearly 1 eV (+0.14 eV and −0.81 eV).

These nonmonotonic trends were also observed for some dopants embedded in other inert metal surfaces (Fig. 2). A given dopant generally behaves fairly similarly when embedded in Cu, Ag, or Au. For example, doping Mo and Cr into all these hosts gives nonmonotonic behavior, while doping Pd gives nearly linear behavior in all three cases. As a host, Pd behaves somewhat differently than Au, Ag, and Cu partially because it adsorbs H more strongly than the coinage metals. However, nonmonotonic behavior is still observed in some cases, such as Mo and Co. In these cases, adding a single dopant atom weakens H adsorption, but adding a second dopant atom strengthens it. Our results are in qualitative agreement with previous experimental studies. For example, H binding to PtCu alloys strengthens as the Pt ensemble size increases (see the supplementary material for further discussion).²⁵ 

To understand the source of the nonmonotonic behavior, we examined the projected density of states (PDOS) on the dopant atoms. Single-atom alloys often feature a single, sharp peak, somewhat similar to an electronic state in a free atom,^13,18 and the peak we observed for Cu₁Ag has a similar shape and width to the experimental photoemission spectrum for a CuAg single-atom alloy.¹³ We found that two-atom and three-atom ensembles also often have narrow d-state peaks, but due to dopant–dopant hybridization and splitting, there are often two peaks for dimers and three peaks for trimers [Figs. 3(a) and 3(b)]. This is expected based on a molecular orbital theory picture of atom-like states. There are sometimes additional peaks due to hybridization among d, p, and s states, as well as hybridization with surrounding Ag atoms.

Examination of the PDOS indicates that the splitting of these localized d states causes the nonmonotonic trends in adsorption energies. For the two-dopant cases, the d-state peaks can be split across the Fermi energy such that the upper peak becomes unoccupied, and the lower peak has a low energy, as seen for Cr₂Ag [Fig. 3(b)]. This results in a low d-band center and a low number of states near the Fermi energy, both of which lead to weak adsorption.^26–28 This splitting across the Fermi energy often occurs when the single-atom alloy’s d-band peak is less than ∼1 eV below the Fermi energy such that nonmonotonic behavior is often observed in these cases [Fig. 3(c)]. The precise amount of splitting and its precise effect on adsorption depends on the coupling and hybridization between dopant atoms and the hybridization between the dopant and the host metal atoms. This results in some scatter in Fig. 3(c). We also found that ∆E₂/∆E₁ correlates with the difference in the d-band center between the one-dopant and two-dopant cases and that it has a similar trend as Fig. 3(c) when plotted against the d-band center instead of the d-band peak (see the supplementary material). Hence, in embedded nanoclusters, hybridization and splitting of the localized d-state peaks determine trends across the number of dopants. Nonmonotonic trends in adsorption energies occur when splitting drives states significantly above and below the Fermi energy.

The link between the electronic structure and the nonmonotonic trends suggests that localized clusters will behave more counterintuitively than more “bulk-like” alloys. To test this, we calculated H adsorption energies on bulk-like MoAg and IrAg alloys in hollow sites with one or two-dopant atoms. These calculations, indeed, show that the bulk-like alloys have behavior closer to intuition than the embedded nanoclusters (Fig. S3). Hence, we generally expect the nonmonotonic behavior to be quite rare and much less significant for bulk-like alloys due to the lack of sharp peaks in their DOS.

While the d-band peaks and splitting explain trends across the number of dopant atoms, it is also important to understand trends across the type of dopant. For a given host, we found that the H adsorption energy is linked to the dopant’s group in the periodic table (Fig. 4). Dopants in the same periodic group often have similar adsorption energies, and this relationship is particularly distinct for single-atom alloys. This is consistent with previous work, suggesting that the idealized d-band filling is important in adsorption on transition metal alloys^26,29,30 and recent work on Cu-based single-atom alloys that found smooth relationships between the dopant’s group and the adsorption energy of methane, although with a different trend.¹⁹ 

For Ag-host and Cu-host surfaces, the exceptions to this similarity within a dopant group for single-atom alloys are nearly always cases where the surface has a magnetic moment. Most cases that follow the primary, U-shaped relationship have a magnetic moment near 0, while the outliers have significant magnetic moments (Fig. S1). For single-atom alloys with Au as the host, there is a systematic variation in adsorption energies within each group for groups 6–9. In this case, there is a smooth relationship for each period, with the H binding generally stronger as 5d metals > 4d metals > 3d metals (Fig. S2). This increased variation within each group is likely due to Au’s more extended d orbitals, which may lead to higher hybridization with the dopant’s orbitals and, hence, more variation among dopants of the same group.

The relationship between the H adsorption energy and the dopant’s group is U-shaped for Cu-host, Ag-host, and Au-host single-atom alloy surfaces [Figs. 4(a)–4(d)]. This is significantly different behavior from pure metal surfaces, where H adsorption is stronger on early transition metals. For example, Rh₁Ag adsorbs H somewhat more strongly than Ti₁Ag (−0.47 eV and −0.38 eV, respectively), while our previous calculations²⁶ show the opposite trend on pure surfaces: pure Ti adsorbs H more strongly than pure Rh by 0.46 eV. As the number of dopants increases, the adsorption energy vs dopant group curve changes the shape such that dopants from the left side of the d block adsorb H more strongly than those from the right side [Figs. 4(e)–4(j)]. This is closer to the expected trend for pure metal surfaces. As the number of dopant atoms increases, dopant peaks increasingly split and broaden, leading to more wider bands, more hybridization with the host, and more similar behavior to pure metals or bulk alloys. We also studied these trends for a Ag surface with one dopant in the surface layer and one in the subsurface layer [Fig. 4(j)]. In this case, there is still a U-shaped curve, but there is an increased variation within a dopant group likely due to dopant–dopant hybridization. For Pd-host surfaces, the adsorption energy curve is fairly flat and slightly S-shaped, with a similar shape for one and two dopants.

In addition to the change in the overall shape of the curve, the relationship between the adsorption energy and the dopant group also becomes less distinct in surfaces with multiple dopants than for single-atom alloys [e.g., Fig. 4(e) vs Fig. 4(a)]. Again, this increased variation within groups is likely due to increased hybridization between the dopant atoms and their neighbors in the larger ensembles, resulting in a more bulk-like PDOS and more variation among metals in the same group.

Links between adsorption energies and electronic structure properties provide key insights into changes in reactivity. To understand how the electronic structure of the surface affects the adsorption strength, we calculated band properties from the PDOS on the dopant atoms for the Ag-host bare surfaces. Broadly, these calculations suggest that the behavior of these systems is controlled by properties of the dopant’s p band and d band, as suggested by previous work.^26,29,30 However, the importance of these two bands changes for different numbers of dopants.

For single-atom alloys with a Ag host, variations in the adsorption energy are primarily controlled by the dopant’s p band [Figs. 5(a) and 5(d)]. The p-band center correlates well with the adsorption energy (R² = 0.71), while the d-band center correlates much less strongly with the adsorption energy (R² = 0.34). Most of the correlation for the d-band center comes from the two points with the lowest d-band centers, Au₁Ag and Mn₁Ag—indeed, removing Au reduces this correlation to R² = 0.16. Zn_nAg and Tc_nAg were removed from the d-band center plots because they are outliers, but including them does not change the qualitative trends (Fig. S6). As the number of dopants increases to two or three, the p-band center correlates less strongly with the adsorption energy, but the d-band center correlates more strongly. Furthermore, the correlation between the adsorption energy and the p-band center is positive for single-atom alloys but is negative for two or three dopants. Hence, adsorption on single-atom alloys has a qualitatively different dependence on the dopants’ electronic structure than adsorption on larger ensembles. This change may be due to differences in the p-band DOS: for single-atom alloys, the p band generally has two broad peaks, while for larger ensembles, the p band has many sharper peaks (Fig. S8). The relationship between the p-band center and the adsorption energy for single-atom alloys also explains the U shape for the adsorption energy vs group curve as the p-band center has a U-shaped dependence on the dopant group for single-atom alloys but decreases from left to right for two- and three-atom ensembles (Fig. S7). Overall, the d-band model generally assumes a broad, flat sp-band and that the d-band shape does not change too dramatically between surfaces,²⁸ and it is, therefore, reasonable that it may partially break down or behave differently for single-atom alloys.

Overall, the magnetic behavior of these embedded nanocluster systems can be somewhat complicated. In most cases that have a nonzero magnetic moment, adsorbed H somewhat reduces the magnetic moment relative to the bare surface (Fig. S4), as seen in previous work on magnetic nanoclusters.³¹ In a few cases, such as Mn₃Ag, H has a very large effect on the magnetic moment. For Pd-host materials, the dopant appears to induce magnetism in surrounding Pd atoms in many cases, as has been observed in previous work on impurities in Pd.³² Further discussion is in the supplementary material.

We also performed a few calculations to compare H adsorption to C and O adsorption. These calculations suggest that trends for C and O across various dopants are similar to those for H (Fig. S9). For example, Cu doped into Ag gives monotonic trends in adsorption energies for all three adsorbates, while Mo doped into Ag gives nonmonotonic trends for all three adsorbates.

We elucidate trends in adsorption on embedded nanoclusters, both across the number of dopant atoms and dopants. We find that the unusual electronic structure of embedded nanoclusters, and especially single-atom alloys, leads to a different behavior from other types of alloy surfaces. Counterintuitive nonmonotonic trends upon increasing the number of dopants are due to splitting of free-atom-like electronic states. When the single-atom d-state peak is within ∼1 eV of the Fermi energy, the two d-state peaks in the dimer may be split such that one is above the Fermi energy and the other is significantly below the Fermi energy, leading to weak adsorption. The significant changes in adsorption energy are consistent with the well-known feature of supported or unsupported nanoclusters that properties can change significantly by adding a single atom. We found that single-atom alloys display unusual behavior, even compared to larger embedded nanoclusters. Specifically, trends across the d block are different as the adsorption energy vs dopant group curve is U-shaped for single-atom alloys instead of generally increasing from left to right as is the case for larger ensembles and pure metals. Single-atom alloys also have a different dependence on the electronic structure: the dopant atoms’ p band controls variations in adsorption energy more strongly than the d band, while the d band has a larger impact for larger ensembles and pure metals. Furthermore, the relationship between the adsorption energy and the p-band center is positive for single-atom alloys but negative for two and three atom ensembles.

See the supplementary material for discussion of bulk-like alloys, magnetic effects, further methods, electronic structure effects, and C and O adsorption energies.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

The authors gratefully acknowledge support from Tulane University. A.P.M. acknowledges support from the National Science Foundation under Grant No. DMR-1852274, and M.M.M. acknowledges support from the Louisiana Board of Regents Research Competitiveness Subprogram, Contract No. LEQSF(2019-22)-RD-A-20. This research was supported, in part, with computing resources provided by Technology Services at Tulane University, New Orleans, LA, and computational resources provided by the Louisiana Optical Network Infrastructure (http://www.loni.org). The authors acknowledge useful discussions with E. C. H. Sykes.