Size-Controlled Electronic Structure Tuning in Ru–CrO _<i>x</i> Heteronanoclusters

Cluster-cluster heterostructures (CCheteros) are emerging as promising catalysts for alkaline hydrogen evolution reaction (HER), benefiting from coupled interfaces and functional complementarity. Among various design parameters, cluster size can be experimentally controlled and plays a pivotal role in the structure-activity relationship. However, the impacts of cluster sizes on interfacial electronic structures remain underexplored. Herein, in this paper, 20 Ru-CrO_<i>x</i> CCheteros obtained by systematically varying the sizes of Ru and CrO_<i>x</i> clusters are analyzed via first-principles simulations to derive size-dependent interfacial electronic properties based on the experimentally validated Ru-CrO_<i>x</i> CChetero, an effective HER catalyst in alkaline media. The results reveal that the interfacial electronic properties arise from nonlinear and cooperative effects of both cluster sizes. Compared to CCheteros with small Ru clusters (<15 Ru atoms), those with larger Ru clusters exhibit saturated electronic structure features, such as formation energy, binding energy, work function, and d-band center, indicating diminished tunability. Thus, maintaining a limited Ru cluster size is essential for electronic modulation. Enlarging Ru clusters increases the dipole magnitude and aligns it more closely with the interface normal, whereas increasing CrO_<i>x</i> cluster size tends to orient the dipole away from the interface normal. Furthermore, the <i>d</i>-band centers may be pinned when the Ru cluster in CCheteros is too large (>30 Ru atoms) and leading to a nontunable surface adsorption capacity. In contrast, with smaller Ru clusters, increasing CrO_<i>x</i> size downshifts the <i>d</i>-band center, suggesting the reduction of the adsorption capability. As a result, tuning cluster sizes may be an experimentally feasible way in designing high-performance CCheteros for surface science.