Guiding the design of oxidation-resistant Fe-based single atom alloy catalysts with insights from configurational space

The next generation of heterogeneous catalysts for sustainable fuel and value-added chemical production relies on the development of highly active, selective, and stable catalysts comprised primarily of earth abundant materials. Fe is one such earth abundant material with a wide range of applications given its ability to activate strong bonds: i.e., C–O bonds with use in hydrodeoxygenation (HDO)^1–3 and Fischer–Tropsch (FT) synthesis;^4,5 N–N bonds with use in ammonia synthesis;^6,7 and O–H bonds with use in water splitting.^8,9 Despite the range of applications for Fe catalysts, the wider use of this metal is limited due to rapid deactivation, particularly via oxidation when working in the presence of an oxygenated atmosphere, as shown in Scheme 1(a). The incorporation of secondary metals into Fe catalysts has been shown to prevent oxidative deactivation, but the secondary metals experimentally examined thus far are costly noble metals (i.e., Pd, Pt).^10,11 Thus, such secondary metals must be added efficiently to (1) minimize disruption to the catalytically active Fe surface, (2) increase oxygen removal, and (3) minimize catalyst cost.

Single atom catalysts—where secondary metals are either atop or alloyed into the host surface as isolated atoms—represent an ideal approach to address the problem of oxidative deactivation in Fe catalysts as the dilute secondary metal concentration will keep catalyst costs low while simultaneously adjusting the electronic and geometric properties of the surface. Many new properties emerge from the creation of chemically distinct and isolated sites within a dominant host surface. One of these is multifunctionality: the catalytic surface can easily perform multiple chemical transformations. This is evidenced by the superior performance of single atom alloy surfaces (i.e., PtCu,¹⁵ PdCu,^16–18 PdAu,¹⁹ PdAg,²⁰ and RhAu²¹) for the selective hydrogenation of a range of alkenes and alkynes.²² These single atom alloy catalysts combine the weak binding of unsaturated hydrocarbons on Cu, Au, or Ag with facile H₂ activation on Pt, Pd, or Rh. Another property of such catalysts is the introduction of significant catalytic activity to a previously inactive surface through generation of atomically isolated and undercoordinated active sites, such as seen for low temperature CO oxidation on Pt/CuO_x,^23,24 Pt/FeO_x,^25,26 Ir/FeO_x,^26,27 Au/FeO_x,^26,28 Au/CeO₂,^29,30 and Pt/CeO₂.³¹ In these supported single-site catalysts, the single-site simultaneously acts to anchor CO as well as weaken adjacent O–M support bonds, enabling the oxidation reaction at lower temperatures than seen for larger nanoparticles of supported catalysts. Meanwhile, the support material acts as an anchor for the single-site, ideally preventing loss of activity through sintering or diffusion subsurface of the active single-site. Overall, the ability of single-site catalysts to perform multiple functions motivates the creation of single atom alloy Fe surfaces to increase the surface’s oxidative resistance without negatively impacting the catalytic performance.

Increasing the oxidation resistance of Fe-based single atom alloy surfaces (denoted herein as M₁Fe) requires tuning both the secondary metal’s and surface’s properties to simultaneously weaken the problematic O–Fe interactions while leaving all other interactions, particularly the catalytically necessary H–Fe interactions, intact. As shown in Scheme 1(b), the optimum M₁Fe catalyst will primarily maintain a balance between the desired weakening of O^* adsorption energies and adversely weakening the H^* adsorption energies. This balance can be determined by (1) quantifying the secondary metal effect on the O^* and H^* energetics, (2) identifying secondary metal properties that are predictive of the surface’s performance, and (3) providing guidance for catalyst synthesis. However, any such investigations of the secondary metal effect on O^* and H^* adsorption energies must be done under realistic catalytic conditions in terms of adsorbate coverage and configuration. Previous works studying the adsorption of aromatics^32,33 and CO^34–36 on transition metal surfaces have demonstrated that the high adsorbate coverages occurring under catalytically relevant conditions significantly alter the structures and energetics of adsorbates and, consequently, the underlying catalytic activity of the system. Furthermore, Wong et al.³⁷ and Chaudhary et al.³⁸ have demonstrated that the experimentally measured heats of adsorption for aromatics can only be reproduced from theory with the inclusion of coverage effects. Thus, the inclusion of O^* and H^* coverage and configuration effects are critical to determining the true effect of secondary metals in M₁Fe single atom alloy surfaces.

Here, we characterize the effect of 13 single-atom, transition metals on the energetic and electronic properties of O^* and H^* adsorbed on M₁Fe(100) using density functional theory (DFT). To capture the effects of adsorbate coverage and configuration, the adlayer ground states determined previously for O^*/Fe(100) and H^*/Fe(100) are used as the basis for all studies as these structures represent the most probable O^* and H^* coverages and configurations to form on Fe(100). By using such structures as a starting point to examine single atom alloy effects, we are able to import realistic adsorbate coverages and configurations into our surface models and, thus, increase the accuracy of our results. Using these realistic adsorbate coverages, we probe the configurational space for each single atom alloy within the outermost surface Fe layer, identify which of the ground states remain stable for O^*/M₁Fe(100) and H^*/M₁Fe(100), and assess how their respective coverages are affected. A detailed analysis of these ground states shows that the single atom alloy effects on both O^* and H^* energetics follow clear periodic trends, where secondary metals running down either the rows or columns of the periodic table result in greater weakening of both O^* and H^* adsorption energies. At high coverage, the O^*/M₁Fe(100) adsorption energy is shown to be predicted by purely electrostatic properties (i.e., electronegativity and dipole moment), while the H^*/M₁Fe(100) adsorption is predicted by properties related to the adsorbate–surface orbital overlap (i.e., d-band center and number of valence electrons). This shows that O^* and H^* have chemically distinct methods of adsorbing onto M₁Fe(100) and suggests that tuning the surface to target O–Fe interactions is possible. Finally, we mathematically connect the DFT-based model results to catalyst synthesis and establish design criteria for choosing a single atom alloy to maximize the oxidative resistance of the Fe catalyst. Overall, this work accomplishes three major objectives: (1) establishes a new approach for determining the effects of secondary metals at the single-atom limit at catalytically relevant adsorbate coverages and configurations; (2) characterizes the single atom alloy effect on the O^* and H^* adsorption energies—i.e., the key species in the oxidative deactivation of Fe—in terms of periodic trends as well as fundamental chemical interactions; and (3) provides criteria to experimentalists for the design of oxidation resistant Fe-based single atom alloy catalysts for a range of catalytic applications.

All calculations were performed using the Vienna Ab Initio Simulation Package (VASP) code.^39,40 The core electrons were modeled with the Projector Augmented Wave (PAW) method (versions updated in 2015).⁴¹ Using the methodology of Hensley et al.,⁴² the optimal exchange–correlation functionals for O^*/Fe(100) and H^*/Fe(100) were determined to be RPBE⁴³ and optB88-vdW,^44,45 respectively. A cutoff energy of 400 eV, spin polarization, and dipole corrections in the z-direction were used. Electron smearing was performed with the Methfessel–Paxton (N = 1) method with a smearing width of 0.1 eV.⁴⁶ All calculations were considered converged at energy and force tolerances of 10⁻⁴ eV and 0.03 eV/Å, respectively. The optimum lattice constant was calculated to be 2.868 and 2.825 Å with the RPBE and optB88-vdW functionals, respectively, with a Gamma point centered k-point grid of (20 × 20 × 20). K-point grids for the surface calculations were generated automatically with the condition of 1200 k-points/reciprocal atom with the Gamma distribution. The energies for O₂ and H₂ in the gas phase were determined using a (14 × 15 × 16) Å box with one single k-point, the gamma point.

Two electronic analyses were performed to determine the predictiveness of single atom alloy properties on O^*/M₁Fe(100) and H^*/M₁Fe(100) energetics: (1) Bader charge^47,48 and (2) d-band center.⁴⁹ Bader charge analyses were performed with fast Fourier transform grids that converged the maximum absolute difference in charge by 0.05 electrons. The d-band center was calculated according to

where E, ρ(E), and E_Fermi are the electronic energy, density of states, and Fermi level energy, respectively. This definition of the d-band center considers only the occupied surface d-states; however, tests show that the d-band centers calculated with all states (occupied and unoccupied) strongly correlate with the occupied states only d-band centers (Fig. S1). Thus, the variation in electronic states, and consequently the d-band centers, is accurately captured when using the occupied states alone.

The M₁Fe(100) (M = secondary metal) surface was modeled with four layer slabs, where the bottom two layers were fixed in their bulk positions. To capture realistic adsorbate coverages and configurations, O^*/Fe(100) and H^*/Fe(100) ground states were taken from Bray et al.⁵⁰ and Hensley et al.,⁵¹ respectively. Ground states are defined as the lowest energy structures/coverages that remain stable against a constant imposed chemical potential. Each ground state is associated with a chemical potential, which is derived from its differential adsorption energy as a first order approximation. The goal here is to determine which of these structures remains stable in the presence of various single atom transition metals. To test this, we first exchange a surface Fe atom with a single secondary metal atom in each of the O^*/Fe(100) and H^*/Fe(100) ground states. To find the lowest energy single atom alloy configuration in each ground state, all symmetrically distinct (in relation to the adlayer symmetry) sites were tested. The process of scanning over these unique single atom alloy configurations is shown in Fig. 1, where two ground states, one with high adlayer symmetry and the other with no reliable adlayer symmetry, are shown as examples. In Fig. 1(a), the O^* adlayer shows two symmetrically identical regions (outlined in dashed green and magenta lines), each of which contains the same, translated mirror plane. Thus, even though there are seven potential surface Fe sites within the ground state’s supercell, only four need to be tested. The extreme case of no adlayer symmetry is shown in Fig. 1(b), where each surface Fe atom must be included in the single atom alloy configurational space scan.

To compare our single atom alloys, M₁Fe(100), to the Fe(100) systems, we compute their differential adsorption energies, $Eadsdiff$⁠, which is given as

where θ_i and ϕ_i are the adsorbate (H^* or O^*) and secondary metal coverages of ground state i, respectively; and $γsurfDFTθi,ϕi$ is the DFT surface energy (an extensive variable), i.e., the adlayer energy at 0 K without zero-point energy, defined as

where $Êθi,ϕi$ is the total calculated energy of ground state i at an adsorbate coverage of θ_i and a secondary metal coverage of ϕ_i with the hat accent, indicating that this is on a per Fe(100) surface unit cell basis; $ÊFe100$ is the total Fe(100) energy on a per surface unit cell basis; E_ref is the adsorbate reference energy (computed energy of ½O₂ or ½H₂ in the gas phase, here); and

is the effective energy contribution of a single atom of secondary metal, where $ÊM1Fe100$ is the total energy on a unit cell basis of a large p(5 × 5) Fe(100) surface (which has 25 unit cells) with a single secondary metal atom replacing a surface Fe atom. We note here that the factors of 25 and 24 arise here since the values of $ÊM1Fe100$ and $ÊFe100$ are given on a unit cell basis, noting that ϕ_i in Eq. (3) would be 1/25 ML if a single atom alloy p(5 × 5) surface were used. Equation (3) thus assumes that all single atom alloys are chemically identical regardless of coverage so long as they remain at the limit of single atoms. Since many single atom alloy configurations exist as explained above, the min(x) function is used in Eq. (2) to signify that it is the minimum energy configuration that is chosen. We choose to define surface energy in this manner because when ϕ_i = 0, Eq. (3) reduces to the same expression used to define surface energy in the reference work on Fe(100),^50,51 allowing us to faithfully compare between the M₁Fe(100) and Fe(100) systems.

Since E_diff[θ_i, ϕ_i] represents a slope in $γsurfDFTθi,ϕi$⁠, we can subtract off the slope defining the “ideal heat of mixing” [of a process where a full coverage of adsorbates and vacancies are fractionally mixed on Fe(100), here] without changing the relative ordering of E_diff[θ_i, ϕ_i]. This allows us to define a formation energy,

The advantage of E_form[θ_i, ϕ_i] over $γsurfDFTθi,ϕi$ is technical. Since $γsurfDFTθi,ϕi$ is extensive, as adsorbates are added to the system, most of the energy lowering occurs because there is simply more adsorbates on the surface. As a result, when plotted, it is difficult to discern the smaller energy changes that arise due to lateral interactions. E_form[θ_i, ϕ_i] essentially subtracts off this energy-lowering effect to reveal the more subtle energy variations that lead to the formation of ground states, allowing us to identify ground state structures more easily.

The optimum secondary metal placement within each of the O^*/M₁Fe(100) and H^*/M₁Fe(100) ground state structures was determined by constructing the convex hull for each secondary metal as a function of adsorbate coverage. This approach is illustrated using Pd₁Fe(100) as an example in Fig. 2. For O^*/Pd₁Fe(100), 26 different structures that incorporate variation in both O^* coverage and secondary metal placement were tested. From the resulting O^*/Pd₁Fe(100) convex hull [Fig. 2(a)], four ground state structures that minimize the formation energy at set coverages (i.e., 0.11, 0.57, 0.71, and 0.80 ML O^*) and electronic chemical potentials as a function of O^* coverage remained stable of the known O^*/Fe(100) ground states. Similarly, for H^*/Pd₁Fe(100), 19 different structures were tested, and two ground state structures remained stable [0.88 and 1.00 ML H^*, Fig. 2(b)]. This approach was applied to all M₁Fe(100) surfaces and enabled the identification of key adsorbate–single atom alloy configurations at each adsorbate coverage, subsequently setting the stage for (1) characterizing the single atom alloy effect on the O^* and H^* energetics and (2) determining the key properties that predict said O^* and H^* energetic single atom alloy effects. All ground state structures identified with this procedure are shown in Figs. S2–S9.

The single atom alloy effect on the O^* and H^* energetics on M₁Fe(100) was quantified by calculating the differential adsorption energy, as shown in Fig. 3. In this analysis, we examine the effect of the secondary metal type at both low and high adsorbate coverage. This includes discussion of the periodic trends as we have included a range of period 4 [Figs. 3(a) and 3(d)], period 5 [Figs. 3(b) and 3(e)], and period 6 [Figs. 3(c) and 3(f)] metals as secondary metals. We will first discuss O^*/M₁Fe(100) followed by H^*/M₁Fe(100).

For O^*/M₁Fe(100) at low O^* coverage, the incorporation of nearly any secondary metal weakens the differential adsorption energy for O^*/M₁Fe(100) relative to O^*/Fe(100), with the magnitude of the weakening trending with the secondary metal’s placement within the periodic table. Using the period 4 metals as an example [Fig. 3(a)], the differential adsorption energy in the limit of zero-coverage changes by −0.01, +0.19, +0.28, +0.26, and +0.31 eV/O^* for single atoms Mn, Co, Ni, Cu, and Zn, respectively, relative to O^*/Fe(100). This shows that heavier secondary metals located across the rows of the periodic table result in a greater weakening of O–Fe interactions even at low O^* coverage. This trend remains consistent for the period 5 [Fig. 3(b)] and period 6 [Fig. 3(c)] metals. Similarly, the zero-coverage differential adsorption energy for O^*/M₁Fe(100) weakens as the secondary metal shifts down the columns of the periodic table, with Ni, Pd, and Pt secondary metals producing changes of +0.28, +0.38, and +0.52 eV/O, respectively.

As the O^* coverage increases, the O^*/M₁Fe(100) differential adsorption energy weakens further due to (1) increased repulsive O–O lateral interactions and (2) increased repulsive O–M interactions. By comparing the differential adsorption energy trends between O^*/M₁Fe(100) and O^*/Fe(100) as a function of increasing coverage, we can ascribe the majority of this weakening to the latter effect as considerable weakening beyond that of O^*/Fe(100) can be seen. All single atom alloys besides Mn cause a weakening of the highest O^* coverage (0.8 ML) differential adsorption energy, following similar periodic table trends to those discussed above for the zero-coverage limit. On average, the single atom alloy effect on the differential adsorption energy is magnified by a factor of three at high coverage as compared to the low coverage case.

Moving our attention to H^*/M₁Fe(100) [see Figs. 3(d)–3(f)], the inclusion of a secondary metal into Fe(100) at the single-atom limit strengthens the low coverage H^* differential adsorption energy by ∼−0.1 eV on average as compared to H^*/Fe(100). This result directly contrasts that seen for the low coverage O^*/M₁Fe(100) behavior. Increasing the H^* coverage to saturation results in a significant weakening in the H^* differential adsorption energy, especially as compared to H^*/Fe(100). Similar to O^*/M₁Fe(100), moving the secondary metal down either the rows or columns of the periodic table results in a weakened H^* differential adsorption energy at high H^* coverage.

Taken together, these results present clear periodic trends in the single atom alloy effect on the O^*/M₁Fe(100) and H^*/M₁Fe(100) energetics; namely, that choosing heavier secondary metals from down either the rows or columns of the periodic table weakens the differential adsorption energy for O^* and H^*, particularly at high adsorbate coverage. Furthermore, the low H^* coverage behavior, where the single atom alloy strengthens the H^* differential adsorption energy, is in stark contrast to that seen for O^*/M₁Fe(100) and suggests that the promotional effect of single atom alloys in Fe catalysts is two-fold in that the detrimental O–Fe interactions are weakened, while beneficial H–Fe interactions are strengthened.

To enable the rapid computational design of highly oxidation resistant M₁Fe catalytic surfaces, the single atom alloy promotional effects on O^* and H^* adsorption energies must be related to easily determined geometric and electronic properties of the surface. The identification of surface properties predictive of the stability of O^* and H^* on M₁Fe(100): (1) provides critical insight into the fundamental chemistries at play between single atom, Fe, and adsorbate; and (2) allows for rapid screening of new single atom alloy Fe surfaces. Such an approach to screening for surface properties predictive of energetic behavior is conceptually similar to work developing linear scaling relations,^52–56 generalized coordination numbers,^57–59 and the d-band model^{12,49,52,53,60} in the literature. Here, the goal is to design M₁Fe catalysts that selectively weaken O–Fe interactions and either strengthen or leave intact existing H–Fe interactions. From Fig. 3, it is found that the O^* and H^* differential adsorption energies show strong periodic trends at both low and high adsorbate coverage. The question now is this: can the previously observed energetics be predicted by the properties of the single atom alloy? As pure Fe(100) has been shown to saturate with both O^* and H^* under a range of catalytic conditions, we focus our analysis on predicting the high coverage differential adsorption energies (i.e., θ_O = 0.8 ML and θ_H = 1.0 ML) where the single atom alloy has the most significant effect.

To probe a broad descriptor space as well as capture both the total surface and single atom specific properties, we chose a total of 11 possible geometric and electronic properties as possible descriptors. The geometric parameters tested include adsorbate–single atom coordination number (CN_{Adsorbate–Single}, which is related but not necessarily proportional to the single atom coverage depending on adsorbate configuration), single atom atomic radius (r_Single), and adsorbate–surface center of mass distance (d_{Adsorbate–Surface}). The electronic parameters tested include the number of valence electrons on the single atom (N_Valence), single atom electronegativity (χ_Single), total surface charge (Q_Surface), average adsorbate charge (Q_Adsorbate), single atom charge (Q_Single), adsorbate induced dipole moment (μ = Q_Surfaced_{Adsorbate–Surface}), total surface d-band center (total surface ε_d), and single atom d-band center (single atom ε_d). All charges were calculated using the Bader charge partitioning method.^47,48 By examining the single atom’s geometric and electronic properties (i.e., atomic radius, valence, electronegativity, Bader charge, and d-band center) separate from those of the total surface, we probe the effect of both the integral properties of the entire surface and the specific reactivity of the single atoms. Our approach here is to (1) calculate the correlation matrix for all possible descriptors and the high coverage O^* and H^* differential adsorption energies to identify the key properties and (2) apply multi-variable linear regression to build a simple, mathematical, predictive model of the differential adsorption energies.

The correlation matrix—an (N × N) symmetric matrix of linear correlation coefficients (R²) between all variables where coefficient values closer to unity denote greater correlation between two variables—indicates the surface properties that are most predictive descriptive of the high coverage differential adsorption energies as well as determines whether said properties are independent of each other. As shown in Fig. 4(a) for O^*/M₁Fe(100), the most descriptive properties for the differential adsorption energy are: single atom electronegativity (R² = 0.77) > single atom charge (R² = 0.73) > total surface charge (R² = 0.67) ∼ average adsorbate charge (R² = 0.67) ∼ adsorbate induced dipole moment (R² = 0.67). Examining the interdependence of these variables reveals that the adsorbate induced dipole moment correlates with the total surface charge (R² = 0.90) as well as average adsorbate charge (R² = 0.90), while the single atom electronegativity correlates with single atom charge (R² = 0.81). Thus, only two properties are statistically independent: single atom electronegativity and adsorbate induced dipole moment. This independence arises due to the fact that the adsorbate induced dipole moment—an integral property of the entire surface—contains variations in the total surface charge and the adsorbate–surface center of mass distance, the latter of which weakly correlates with the single atom electronegativity (R² = 0.34)—a single atom specific property. Additionally, given that the single atom electronegativity strongly correlates with the single atom charge (R² = 0.81) and weakly correlates with the single atom d-band center (R² = 0.16), the single atom electronegativity is primarily a descriptor of the electrostatic properties of the surface. Taken together, the single atom electronegativity and adsorbate induced dipole moment can, therefore, be used in the construction of a predictive model.

Multi-variable linear regression between the high coverage differential adsorption energies and key surface properties generates a simple, mathematical model that can be used for rapid screening of new systems. For O^*/M₁Fe(100), the most descriptive properties for the differential adsorption energy, i.e., single atom electronegativity and adsorbate induced dipole moment, were used with multi-variable linear regression to generate a predictive model [Fig. 4(a), inset]. This model has comparable accuracy to typical linear scaling relations (i.e., MAE = 0.25 eV).

A similar analysis was performed for the high H^* coverage differential adsorption energy (Fig. S10, Table S1). The correlation matrix for H^*/M₁Fe(100) showed that the number of valence electrons on the single atom (R² = 0.60), the total surface d-band center (R² = 0.59), and the single atom d-band center (R² = 0.61) were the most descriptive properties, but the total surface d-band center and single atom d-band center are correlated (R² = 0.98). Thus, the predictive model for the high H^* coverage differential adsorption energy was constructed via multi-variable linear regression using only the number of valence electrons on the single atom and the single atom d-band center, both of which are single atom specific properties.

Taken together, these results provide simple mathematical models describing the single atom alloy effect on high coverage O^* and H^* differential adsorption energies (i.e., θ_O = 0.8 ML, θ_H = 1.0 ML), which can be used for surface design and optimization. The most descriptive parameters for O^*/M₁Fe(100) combined an integral, total surface property (i.e., adsorbate induced dipole moment) and a single atom specific property (i.e., single atom electronegativity), while H^*/M₁Fe(100) is predicted by only single atom specific properties (i.e., single atom valence and d-band center). Furthermore, the descriptive surface properties themselves provide physical and chemical insight into adsorbate–surface interactions.

For O^*/M₁Fe(100), the most descriptive properties derive from purely electrostatic interactions between the adsorbates and surface. Instead of the surface d-band center, a ubiquitous descriptor for catalyst performance throughout the DFT literature, acting as a suitable predictor, the O–M₁Fe(100) interactions are determined by the single atom’s electronegativity and the adsorbate induced dipole moment. While previous work has noted the limitations of the d-band model for O^* adsorption on Pd bimetallic alloys,⁶¹ the d-band model’s descriptiveness for such systems remains significantly higher than that seen here for O^*/M₁Fe(100). Overall, our predictive model suggests that the O–M₁Fe(100) interaction strength is dictated by the degree to which charge can be abstracted from the surface by O^*. This results in the positive (negative) relation between the single atom electronegativity (adsorbate induced dipole moment) and high O^* coverage differential adsorption energy, as shown in Fig. 4.

Distinct from O^*/M₁Fe(100), the H^*/M₁Fe(100) most descriptive properties suggest that the H–M₁Fe(100) interactions are governed primarily via the overlap between adsorbate–surface orbitals (Fig. S10, Table S1). The lack of electrostatic properties descriptive of H–M₁Fe(100) interactions is surprising given that H^* becomes negatively charged (∼−0.3 electrons) when adsorbed on Fe(100). Thus, despite H^* becoming negatively charged upon adsorption to Fe(100), the H–M₁Fe(100) interaction strength is dictated by the degree of overlap between the adsorbate and surface orbitals, as opposed to the ability of H^* to abstract charge from the surface. This shows that H^* and O^* have two different methods of binding to M₁Fe(100), demonstrating that the strength of the O–M₁Fe and H–M₁Fe interactions can be separately targeted through careful optimization of the single atom alloy M₁Fe surface properties.

Thus far, we have quantified the single atom alloy effects on the O–M₁Fe(100) and H–M₁Fe(100) interaction strength as a function of adsorbate coverage, characterized the secondary metal’s periodic trends, and developed simple, mathematical predictive models for the high adsorbate coverage regimes that provide insight into the fundamental chemistries present during O^* and H^* adsorption. We turn now to address two critical questions in relation to the potential experimental relevance of this work. First, can we guide the experimental synthesis conditions for Fe-based catalysts using the observed trends in the O^* and H^* adsorption energy with adsorbate coverage and secondary metal? Second, using these DFT results, can we comment on the overall efficacy of each single atom alloy and, consequently, guide secondary metal selection and catalyst design?

To address these questions, we must first transform the degree of adsorbate–single atom interaction in the DFT models—determined by the adsorbate coverage and adsorbate–single atom coordination number—to an estimate of the single atom concentration (wt. %) in the total catalyst. This requires (1) estimating the effective single atom concentration (θ_Single) that accounts for the changes in adsorbate–single atom coordination number in the DFT models, (2) extrapolating the effective single atom coverage to the number of secondary metal atoms (N_Single) within a spherical catalyst nanoparticle, and (3) determining the number of remaining Fe atoms (N_Fe) within said nanoparticle. Here, we assume that the secondary metal atoms are purely located in the outermost surface layer, consistent with metal segregation studies with the exception of Re as secondary metal,^62,63 and that the adsorbate coverage is at saturation (1.0 ML). This allows us to convert variation in adsorbate coverage at a nearly constant secondary metal coverage to a variation in secondary metal concentration (i.e., loading). As shown in Scheme 2(a) for O^*/M₁Fe(100), the effective secondary metal coverage is proportional to the adsorbate–single atom coordination number, the latter of which was ascertained from the DFT models at every adsorbate coverage and single atom configuration. Moving from the DFT models to the spherical catalyst nanoparticle [Scheme 2(b)]—which is a suitable model of a single catalytic grain—the required number of secondary metal atoms is assumed to be proportional to the volumetric ratio of the nanoparticle’s outer surface layer to that of the p(1 × 1) Fe(100) unit cell containing a secondary metal atom, where the fraction of secondary metal is given by the ground state’s secondary metal coverage. That is,

where R_NP is the radius of the nanoparticle (taken here to be 10 nm⁶⁴); d_layer is the thickness of the outermost nanoparticle layer (1.434 and 1.413 Å for RPBE and optB88-vdW, respectively); and A_u.c. is the surface area of the p(1 × 1) Fe(100) unit cell (8.255 and 7.981 Ų/site for RPBE and optB88-vdW, respectively). All other atoms within this nanoparticle are then Fe atoms, which includes the remaining Fe atoms within the outermost surface layer (⁠$NFeSurface$⁠) as well as the Fe atoms within the core (⁠$NFeCore$⁠),

The number of Fe atoms within the outermost surface layer can be calculated as the total number of surface atoms times the coverage of Fe within that layer (1 − θ_Single), giving

The number of Fe atoms within the nanoparticle core is calculated as a ratio of the volume of the nanoparticle core (V_Core) to the volume of the p(1 × 1) Fe(100) unit cell (V_Fe) according to

where σ_Fe is a conversion factor between the number of Fe atoms and number of sites, which is equal to 1 here. Once the number of secondary metal atoms and Fe atoms within the spherical nanoparticle is known, the secondary metal concentration can be calculated according to

where m_Single, m_Fe, W_Single, and W_Fe are the mass of secondary metal within the nanoparticle, mass of Fe within the nanoparticle, atomic weight of the secondary metal, and atomic weight of Fe, respectively. Taken together, the set of mathematical transformations outlined in Scheme 2 allow us to estimate the effect of each single atom alloy on the average adsorption energy for O^* and H^* on a spherical Fe-based nanoparticle using the results from our DFT models at a range of adsorbate coverages, creating a direct connection between the fundamental and computational results presented here and experimentally synthesized catalysts.

An example of the relation between the single atom concentration and average adsorption energy over the model nanoparticle surface is shown in Fig. 5(a) for O^*/M₁Fe(100), where M are elements from the fifth period. As the single atom metal is shifted down the periodic table row, the average O^* adsorption energies are systematically weakened, with the largest difference in average adsorption energies of 1.1 eV occurring between O^*/Ru₁Fe(100) and O^*/Ag₁Fe(100) at a single atom concentration of ∼4 wt. %. Such single atom alloy effects are observed for all O^*/M₁Fe(100) and H^*/M₁Fe(100) systems (Fig. S11) and are consistent with the discussions of periodic trends in Sec. III A.

Notably, these results suggest that a key effect of single atom alloys on the O^* and H^* energetics on M₁Fe nanoparticle surfaces is the “rate” at which average adsorption energies change with a single atom concentration. Higher (more positive) rates of change indicate greater weakening of the average adsorption energies with lower single atom concentrations—i.e., less secondary metal is required to achieve the same level of protection against oxidation when its rate of change is higher than that of another secondary metal. Figure 5(b) shows the calculated rates of the average adsorption energy change with the single atom concentration for all O^*/M₁Fe(100) and H^*/M₁Fe(100) systems examined here. Both O^* and H^* systems follow similar periodic trends, where secondary metals further down the rows of the periodic table see greater weakening of the average adsorption energies. However, the secondary metal effect on O^* ranges from 1.4 to 447.0 times larger than on H^*. This suggests that the primary consideration when choosing a secondary metal in M₁Fe catalysts should be its effect on O^* adsorption energy. With the focus on the O^* adsorption energy, we can establish two design criteria for choosing a secondary metal: (1) the secondary metal must weaken the average O^* adsorption energy and (2) the average H^* adsorption energy must be relatively unaffected when compared with the average O^* adsorption energy. Using these two criteria, we can see that nearly all the tested secondary metals will enhance oxidation resistance of the Fe surface, with the period 5 metals displaying the best performance. Only three secondary metals should be avoided entirely: Mn, which strengthens the average O^* adsorption energy, as well as Zn and Re, which weaken both the O^* and H^* average adsorption energies by nearly equivalent amounts.

Taken together, these results not only connect the energetic analyses and trends observed at the atomic-scale with the DFT models to experimental catalyst synthesis conditions but enable the development of two design criteria for secondary metal selection in Fe-based single atom alloy catalysts. Such design criteria and insights are expected to significantly assist in the design of Fe-based catalysts with superior oxidation resistance as experimentalists can now (1) relate the concentration of single atoms within their catalyst to its promotional effect on the O^* and H^* adsorption energies and (2) choose single atoms that best balance metal cost and performance.

Using DFT and a dataset of O^*/Fe(100) and H^*/Fe(100) structures that were identified as the dominant ground state structures in previous work, we characterized the effect of 13 secondary metals within the outermost Fe surface layer of M₁Fe(100) surfaces on the O^* and H^* adsorption energies. The dominant O^*/M₁Fe(100) and H^*/M₁Fe(100) ground state structures were determined by mapping the configuration space for each single atom at each adsorbate coverage via construction of convex hulls. Using these ground state structures, periodic trends in the single atom alloy effect on the O^* and H^* differential adsorption energy were identified. At all adsorbate coverages, shifting the single atom metal down either the rows or columns of the periodic table resulted in greater weakening of both the O^* and H^* adsorption energies, with this effect being magnified at high adsorbate coverages due to the greater degree of adsorbate–single atom interaction. Further analysis of the high adsorbate coverage data shows that the O^*/M₁Fe(100) differential adsorption energies can be predicted from purely electrostatic surface properties (i.e., single atom electronegativity and adsorbate induced dipole moment), while the H^*/M₁Fe(100) differential adsorption energies can be predicted from properties related to adsorbate–surface orbital overlap (i.e., single atom d-band center and single atom valence). This demonstrates that the O–Fe and H–Fe interactions result from fundamentally distinct forces and suggests that their strength can be tuned independently. Finally, through a set of mathematical transformations, we connect the O^*/M₁Fe(100) and H^*/M₁Fe(100) results from the atomic-scale DFT models to the average single atom alloy effect on a model, spherical M₁Fe nanoparticle, providing guidance to experimentalists when synthesizing Fe-based single atom alloy catalysts. Specifically, using these results, we establish two criteria for choosing a single atom that will maximize the oxidation resistance of Fe-based catalysts: (1) the single atom must weaken the average O^* adsorption energy and (2) the average H^* adsorption energy must be relatively unaffected when compared with the average O^* adsorption energy. Overall, this work characterizes the single atom alloy effect on O^* and H^* energies on M₁Fe(100), providing key insight into the fundamental chemical interactions between O^*, H^*, single atoms, and Fe as well as establishing new criteria for the design of more stable Fe-based catalysts with a range of applications.

See the supplementary material for top and side views of the O^*/M₁Fe(100) and H^*/M₁Fe(100) ground state structures, correlation matrix and multi-variable linear regression model for the high coverage H^*/M₁Fe(100) system, and average O^* and H^* adsorption energies as a function of single atom concentration in a model, spherical M₁Fe nanoparticle.

A.J.R.H., G.C., and J.-S.M. were primarily funded by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences, Biosciences and Geosciences within the Catalysis Science program, under Award No. DE-SC0014560. Y.W.’s effort was supported by DOE Basic Energy Sciences (BES)/Division of Chemical Sciences (Grant No. DE-FG02-05ER15712). This research used resources from the Center for Institutional Research Computing at Washington State University. This work was partially funded by the Joint Center for Deployment and Research in Earth Abundant Materials (JCDREAM) in Washington State. PNNL is a multi-program national laboratory operated for the U.S. DOE by Battelle.

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