Single-atom alloys (SAAs), where a single active metal atom is dispersed on a more inert host metal surface, have emerged as highly efficient and selective catalysts. Unlike traditional transition metal catalysts, SAAs exhibit unique reactivity that defies established predictive models like the d-band model. The d-band model, which correlates adsorption energy with the d-band center energy, successfully explains the catalytic behavior of many transition metals; however, it fails to capture the nuances of SAAs. While density functional theory (DFT) calculations can accurately predict SAA reactivity, a simple, physically intuitive model is lacking. Existing approaches, such as machine learning models, predict adsorption energies accurately but lack the underlying physical principles governing SAA behavior. This research proposes a new paradigm shift, viewing SAAs as analogous to molecular systems and leveraging molecular orbital (MO) theory to explain their catalytic behavior. The goal is to develop a simple yet powerful predictive tool for the rational design of SAAs for specific catalytic reactions.

Previous studies have attempted to understand SAA reactivity using various approaches. The d-band model, while successful for conventional metal catalysts, falls short in accurately describing SAAs. Near-surface alloys (NSAs), related to SAAs, have been studied, with some modifications to the d-band model suggested, but these corrections are not applicable to SAAs. Machine learning methods have shown promise in predicting adsorption energies on SAAs and other alloys, but they lack explanatory power. A few studies have explored SAAs as analogs of molecular systems, hinting at the potential of electron-counting rules to understand their stability. However, a comprehensive, unifying rule for predicting adsorbate binding on SAAs remained elusive. This work addresses this gap by proposing a novel electron-counting rule based on a detailed MO analysis.

The study employed density functional theory (DFT) calculations using the Vienna Ab Initio Simulation Package (VASP) with the optB86b-vdW exchange-correlation functional (except for CO and NO adsorption, where RPBE was used). Calculations were performed on a large set of SAA surfaces, varying both the dopant transition metal and the adsorbate (O, N, C, H, H2O, NH3, CO, N2, NO). A five-layer p(3×3) slab model was used, with the bottom two layers fixed. Adsorbates were placed in atop positions, and adsorption energies were calculated. The electronic structure analysis utilized crystal orbital Hamilton population (COHP) analysis and projected density of states (PDOS) from Lobster software to understand the interaction between adsorbates and dopant atoms. Bader charge analysis was also performed to determine charge transfer. The methodology also involved constructing molecular orbital diagrams to rationalize the observed trends in adsorption energies and validate DFT results. The number of valence electrons considered for the dopant and adsorbates was based on group number and traditional Lewis structures respectively. The electronic population of molecular orbitals was calculated by integrating over the projected density of states of contributing atomic orbitals. Specific equations are provided in the supplementary information for calculating the population of bonding, antibonding and non-bonding orbitals. Visualization of charge density was done using VMD software.

The core finding is a 10-electron count rule for maximal adsorbate binding on SAA dopant atoms. This rule states that the strongest binding occurs when the sum of the dopant's valence electrons (νM) and the number of valence electrons of the adsorbate interacting with the dopant (k) equals ten (νM + k = 10). This rule is supported by DFT calculations showing that adsorption energies for atomic adsorbates (O, N, C, H) on SAAs exhibit V- or W-shaped trends across the periodic table, with minima at specific dopant elements that align with the 10-electron rule. The MO analysis shows that the strongest bonding is associated with filling of bonding and non-bonding molecular orbitals with d-orbital contributions. The weakening of the bond arises when antibonding orbitals start being populated. For p-block adsorbates, the rule is modified to account for lone pairs, leading to a slightly different electron count for maximal binding. The study also demonstrates the applicability of the 10-electron count rule to molecular adsorbates, such as CO, NO, H2O and NH3. For molecules dominated by electrostatic interactions, the rule is less applicable, and other descriptors such as dopant atomic charge, become more relevant. Application of the rule to the industrially significant nitrogen reduction reaction to ammonia revealed that d6 dopants (Tc, Re) are predicted to be most active due to favorable energetics for the rate-determining step. This prediction aligns with results from previous computationally expensive high-throughput and machine learning studies, providing an alternative explanation based on simple electronic structure principles.

The 10-electron count rule offers a significant advancement in understanding and predicting the reactivity of SAAs. The simplicity of the rule contrasts with the complexity of DFT calculations or machine learning models, providing a readily accessible tool for experimentalists and theoreticians alike. The rule's ability to explain the observed trends in adsorption energies and accurately predict active sites for industrially important reactions demonstrates its predictive power. The molecular orbital analysis provides a firm theoretical basis for the rule, highlighting the importance of orbital interactions and electron filling in determining adsorbate binding strength. The identification of d6 dopants as the most promising candidates for nitrogen reduction showcases the power of the 10-electron rule in identifying optimal SAA catalysts without needing extensive computational resources. However, the limitations of the rule for adsorbates with significant electrostatic contributions must be acknowledged. Future studies can focus on refining the rule to address other interaction types.

This study establishes a simple yet powerful 10-electron count rule for predicting adsorbate binding on single-atom alloy catalysts. The rule is supported by both DFT calculations and molecular orbital theory, offering a significantly faster and more intuitive alternative to computationally intensive methods. Its successful application to the nitrogen reduction reaction demonstrates its potential in accelerating the design of new SAA catalysts. Future work could explore extending the rule to other reaction types and refining it to accommodate interactions beyond covalent bonding.

The 10-electron count rule is primarily applicable to adsorbates where covalent bonding dominates. For adsorbates with strong electrostatic interactions, the rule's predictive power is diminished, and other descriptors may be more appropriate. The study focused on a specific set of adsorbates and host metals, limiting the generalizability of the rule. Further validation with a broader range of systems is required to fully assess its universality.