Ten-electron count rule for the binding of adsorbates on single-atom alloy catalysts

Single-atom alloys have recently emerged as highly active and selective alloy catalysts. Unlike pure metals, single-atom alloys escape the well-established conceptual framework developed nearly three decades ago for predicting catalytic performance. Although this offers the opportunity to explore so far unattainable chemistries, this leaves us without a simple guide for the design of single-atom alloys able to catalyse targeted reactions. Here, based on thousands of density functional theory calculations, we reveal a 10-electron count rule for the binding of adsorbates on the dopant atoms, usually the active sites, of single-atom alloy surfaces. A simple molecular orbital approach rationalizes this rule and the nature of the adsorbate–dopant interaction. In addition, our intuitive model can accelerate the rational design of single-atom alloy catalysts. Indeed, we illustrate how the unique insights provided by the electron count rule help identify the most promising dopant for an industrially relevant hydrogenation reaction, thereby reducing the number of potential materials by more than one order of magnitude.


Table of Contents
On pure transition metals, the binding energy of adsorbates correlates linear with the centre of the d-band relative to the Fermi level (Supplementary Fig. 1a-b).Because of the discrete nature of electronic states on molecular complex, the monotonic trends break down.Approaching six ligands to a transition-metal atom (Supplementary Fig. 1d) results in the splitting of its d-orbitals into two degenerate eg* antibonding orbitals and three degenerate t2g orbitals, which are usually nonbonding but can gain a bonding or antibonding character when interacting with π-acceptor or π-donor ligands respectively. 1This leads to non-monotonic trends in complex stability, which is quantified using the crystal field stabilisation energy (Supplementary Fig. 1c-e).Depending on the splitting between orbitals, the Crystal Field Stabilisation Energy (CFSE) shows as a deep V-shape curve (low spin configurations) or a shallow W-shape curve (high spin configurations) when plotted against the number of d-electrons.Low spin complexes with six d-electrons are particularly stable: this corresponds to the saturation of the t2g orbitals.When considering the two valence electrons that each ligand usually brings to the complex, the total number of valence electrons reaches 18-electrons.

Adsorption energies on Cu-, Ag-, and Au-based SAA
Adsorption energies on the top site of the SAA dopant follow trends independent of the host metal.
For clarity, we only show the adsorption energies on Au-based SAAs in Fig. 1 in the main manuscript.Supplementary Fig. 2 shows the complete set of transition metal dopants in Cu-, Ag-, and Au-hosts.For all hosts, 3d-dopants show the shallow W-shape trend while 4d and 5d dopant show deeper V-shape trends.Because of the larger spatial expansion of 5d orbitals, 5d dopants tend to bind adsorbates more strongly than 4d dopants.Substituting 4d for 5d dopants and vice versa can be used to finely tune the affinity of the dopant for a given substrate: we may want to increase the interaction for poorly reactive molecules or decrease the interaction in the presence of molecules that might poison the active site.For the adsorbates with p-electrons (C, N and O), the irreducible representations of the valence orbitals (2s and 2p) are a1 (s, pz) and e1 (px, py).This means that the dz² orbital of the dopant can interact with both the s and pz orbitals of the adatom, and thus, the three resulting MOs have a certain contribution of both the s and pz orbitals.Pre-hybridising the s and pz orbital to form two sp orbitals is an easy qualitative way to account for this mixing.One of the two resulting sp orbitals (Supplementary Fig. 5b) has a small lobe in the internuclear region, thereby poorly interacting with the dopant orbitals.This is the nonbonding nsp orbital.The second sp orbital can form a bonding and antibonding orbital with the dz² orbital of the dopant (Supplementary Fig. 5b).Similarly, the linear combination of dxz dyz with the px and py, forms two bonding π and two antibonding π* MOs.The dxy and dx²-y² orbitals do not have the suitable symmetry to form a linear combination with any of the orbitals of the adatom, hence they form non-bonding n MOs.This means for adsorbates with p orbitals, we can fill up to 6 MOs (with 12 electrons) before antibonding orbitals get populated.
For more than 10 or 12 electrons for H or p-element adsorbates respectively, antibonding MOs get filled, thereby weakening the bond, and destabilizing the system.

Electronic population analysis for clean surfaces and N adsorbed on 3ddoped Ag surfaces.
Supplementary

Role of the bonding and nonbonding orbitals
When going from left to right in the periodic table, dopants have more electrons.When the number of electrons exceeds a certain number, antibonding states start being populated: this weakens the adsorbate/dopant bond.But what drives the increased binding before that point?Nonbonding orbitals do not contribute to the stabilisation of the bond, so the origin of the stabilisation must be found elsewhere.Our calculations show that the dopant's states go down in energy as we move to the right of the periodic table.This allows the dopant's states to come closer (in energy) to the adsorbate's states.On top of this, the orbital contraction over a period allows adsorbates to come closer to the dopant, thereby strengthening the orbital interaction.This can be visualised by adding all the bonding and antibonding interactions up to the Fermi level.This is given by the ICOHP (integrated COHP signal) and the ICOOP (integrated crystal orbital overlap populations).They both show that the overlap (ICOOP) and overlap interaction (ICOHP) are extremal when the 10electron criterion is met (Tc for N).

Bader charges of SAAs
Bader charges (Supplementary Table 2) arise from the electronegativity difference between the dopant and host metals.It is a good descriptor for the electrostatic contribution to bonding.

Decomposition of the adsorption energy of H2O and NH3
Following the approach developed by Réocreux et al., 4 we can decompose the interaction energy into two terms: -an electrostatic contribution that varies linearly with the atomic charge of the dopant qd, -a covalent contribution that varies linearly as a function of the binding energy of carbon  !"# $ .The adsorption energy Eads of H2O or NH3 can then be written as a linear combination of qd and  !"# $ :  !"# =  +  " +  !"# $ (i) Fitting the DFT computed adsorption energies on 4d-doped Ag surfaces against the linear model gives the regression parameters provided in Supplementary Table 3. 3 In Supplementary Fig. 8, we plot the adsorption energies  !"# %&' of H2O (resp.NH3) as computed with DFT (black curve), the electrostatic contribution  " (light blue curve) and the covalent contribution  !"# %&' −  " (red curve).The covalent contribution shows the expected trend with minima for d 8 dopants.

NNH geometry discussion
In its linear geometry, usually considered on gold-based SAAs, NNH is isoelectronic to NO and therefore binds to the dopant with 3 electrons.On 3d dopants, its binding energy shows the usual W-shape (Supplementary Fig. 19).On 4d and 5d dopants, we find a minimum for 7 electrons (Tc, Re), as expected from the 10-electron rule.Interestingly, we could not identify such geometry for the Pt and Pd dopants, which already have 10 electrons.With the three extra electrons from diazenyle, antibonding states would get populated.Instead, during the geometry optimisation, NNH relaxes to a bent geometry.The bent geometry allows for the hybridisation of the orbitals of the molecular fragment and transforms antibonding orbitals into non-bonding, located on the fragment, that can host these extra electrons (see lone pair in Fig. 4d).In this geometry, only one electron interacts directly with the dopant, with an expected minimum for d 9 , hence its significance for late transition metals.For early transition metal dopants, a third configuration can be identified: the flat-lying geometry (Fig. 4d).To satisfy the 10-electron rule, the early transition metals try to create multiple bonds to get as many electrons as possible.In the flat-lying geometries, 5 electrons are available (Fig. 4d).DFT calculations confirm the highest stability for dopants with ca. 5 electrons (Nb, Ta, W) and such geometry is the most stable up for dopants up to 4 d-electrons (Supplementary Fig. 10).
Supplementary Figure 10.Formation energies of NNH in the linear, flat, and bent geometries compared to that of N2 on Au-based SAAs.
Regarding the relative stability of the different configurations, we can first notice the following points: -flat-lying NNH is π-bonded to the dopant, -bent NNH is σ-bonded to the dopant, -linear NNH is σ and π-bonded to the dopant.Because π -bonding is less effective than σ-bonding, the flat-lying geometry is expected to be less stable than the other two geometries.This is consistent with the general trend from our DFT calculations.A few exceptions are found for electron-deficient dopants (d 3 and d 4 ) for which flatlying NNH and linear NNH show very similar stability (within DFT error).Finally, linear NNH is usually more stable than bent NNH because of the extra π-overlap.This holds true until the π* orbitals become occupied: then, the bent geometry becomes more favourable as explained in the previous paragraph.This is completely analogous to the configurational effects seen on metal complexes with the isolobal nitrosyl ligand and rationalised by Enemark and Feltham.

Supplementary Figure 1 .
Electronic properties controlling the binding energies of adsorbates on metal surfaces (a-b) and the binding energies of ligands in metal complexes (c-e).(a) Density of states (DOS) of 4d metals.(b) Experimental adsorption energy of O adatoms as a function of the d-band centre for 4d metals. 2,3(c) Splitting of the degenerate d-orbitals into the t2g and eg* orbitals in octahedral complexes (represented in (d)).Δ is the energy difference between the two sets of orbitals.(e) Crystal field stabilisation energy (CFSE) plotted as a function of the number of d-electrons for low-spin and high-spin octahedral complexes.High-spin configurations are typically more common for 3d metals.

Supplementary Figure 5 .
a1.This means, that only the 1s orbital of hydrogen and the dz² orbital of the dopant have the right symmetry to interact and form a bonding σ and an antibonding σ* molecular orbital (MO) as shown in Supplementary Fig.5.The four other d-orbitals do not have suitable symmetry to form linear combinations; hence they form non-bonding n and nπ MOs.This means we can fill up to five MOs (with ten electrons) before the antibonding σ* orbitals get populated.Molecular Orbital diagram for the interaction of the d-orbital of a metal M with the orbitals of (a) hydrogen, and (b) p-block elements.The labels refer to the irreducible representation to which each orbital belongs in the C∞v symmetry group.

Supplementary Figure 7 .
Position of MOs for N-top adsorbed Ag-based SAAs as identified by the maximum/minimum of the COHP for bonding and anti-bonding states or the maximum of the pDOS of the respective non-bonding orbitals.Trends for integrated COHP (ICOHP), COOP and bond distances.

Supplementary Figure 8 .
Energy decomposition of the adsorption energy of H2O and NH3.10.Adsorption energy trends for halogens and hydroxyl OHSupplementary Figure9.Adsorption energy trends of fluorine, iodine and hydroxyl on Ag-SAA doped with 4d metals.

Table 1 .
Electronic population analysis (s and d states) for Ag-based SAAs.Orbital occupation for N on Ag-based SAAs doped with 3d (left panel) and 4d (right panel) dopants.On 3d dopants the π* and σ* get filled earlier than on 4d dopants.

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Regression parameters for the linear model given in Eq. (i).MIN, MAX and STD stand for minimum, maximum and standard errors respectively.