Descriptor for metal complex stability: synergistic effects of support, metal, and environmental conditions

Transition metal catalysts supported on oxides undergo significant structural changes under reaction conditions, which are influenced by interactions with reactants. These interactions can lead to the dispersion of metal atoms, leading to the formation of stable single-nucleus metal complexes. Understanding the stability of these complexes is essential for catalyst design. In this study, we use multitask symbolic regression to identify a descriptor for the stability of single-nucleus metal complexes with common reactants, such as CO and H₂O, on the basis of first-principles calculations. We develop a multidimensional descriptor incorporating metal‒metal, metal‒support, and metal‒adsorbate interactions, achieving high accuracy in predicting the stability of single-nucleus metal complexes. Our analysis revealed that in the absence of reactants, the stability of single metal atoms is mainly determined by the hardness (cohesive energy) of the metal. The presence of reactants such as CO and H₂O further stabilizes single-nucleus metal complexes by saturating undercoordinated metal atoms. This stabilization is correlated with the Lewis acidity of the surface oxygen in the support. Supports with lower Lewis acidity enhance metal‒support interactions, promoting CO adsorption on all metals and H₂O adsorption on complexes of hard metals. In contrast, supports with higher Lewis acidity enhance hydrogen adsorption, promoting H₂O interactions with complexes of soft metals as well as Pd and Pt. Additionally, our descriptor predicts nanoparticle (NP) dissociation into single-nucleus metal complexes or Ostwald ripening (OR) tendencies. Under CO conditions, harder metals tend to favor dissociation, whereas softer metals (e.g., Ag, Cu, and Au) are more prone to OR. Under H₂O conditions, the Lewis acidity of the support surface oxygen influences NP behavior, with supports such as CeO₂ stabilizing single-nucleus metal complexes and promoting NP dissociation. These insights provide guidance for selecting catalyst components and optimizing reaction conditions to control the stability of single-nucleus metal complexes and guide NP dissociation or OR processes.