Formaldehyde adsorption on the Bi-modified Pd sub-nanometer clusters: Insight into the effects of cluster size and composition on the catalytic activity

The catalytic decomposition of formaldehyde (HCHO) is of paramount importance for indoor air purification. Herein, we systematically investigate the structural evolution, electronic properties, and catalytic decomposition mechanism of HCHO on sub-nanometer bimetallic bismuth-palladium (Bi m Pd n , m+n = 2–10) clusters via density functional theory (DFT) calculations. Thermodynamic and structural analyses reveal that Bi atoms preferentially occupy highly symmetric surface sites during cluster growth. Notably, Bi 4 Pd 4 and Bi 3 Pd 6 exhibit exceptional relative stability, and their robust thermal stability at 300 K was further validated by ab initio molecular dynamics (AIMD) simulations. In-depth evaluations of electronic descriptors—including vertical ionization potential (VIP), vertical electron affinity (VEA), and chemical hardness, reveal that Bi 4 Pd 4 possesses a closed-shell-like high chemical hardness. Conversely, Bi 3 Pd 6 features a moderate energy gap and higher polarizability, thereby manifesting characteristics of "optimal activity". Calculations of the catalytic reaction network further corroborate that the Bi 3 Pd 6 cluster serves as an exceedingly superior catalyst under nonoxidative conditions: the initial C–H bond activation barrier is drastically suppressed to 0.517 eV, while the recombinative desorption of the H 2 product exhibits a nearly barrierless, facile kinetics of merely 0.177 eV. Although the desorption of CO (1.470 eV) constitutes the rate-determining step, it remains kinetically accessible under moderately elevated temperatures. Analyses of the projected density of states (PDOS) and charge density difference demonstrate that the p-d orbital hybridization between Bi and Pd precisely modulates the electronic occupancy of the active sites, effectively mitigating the repulsion during the transition state. This work not only elucidates the physical origin of the enhanced catalytic performance in Bi-doped Pd clusters but also provides valuable theoretical guidelines for the rational design of multimetallic sub-nanometer catalysts that integrate high stability with superior catalytic activity.