in which 𝐸 #$# (𝑛), 𝐸 #$# (host), and 𝐸 #$# (SAA) are the total energies of an alloy surface with a cluster of 𝑛 dopant atoms, a pure host surface, and a SAA surface, respectively. Here, we used a dopant dimer embedded on the alloy surface to represent the formation of dopant clusters in the prediction of aggregation energy, leading to 𝑛 = 2 in the above equation. Segregation energy indicates the relative stability of the single isolated dopant atom in the surface layer of the host, i.e., forming a SAA, versus immersed in the bulk host materials, and was calculated using, ∆𝐸 %&" = 𝐸 #$# (bulk) -𝐸 #$# (SAA) in which 𝐸 #$# (bulk) and 𝐸 #$# (SAA) are the total energies of an alloy surface with a dopant immersed in the bulk host slab and a SAA surface, respectively. For each dopant-host SAA combination, four different slab models, either alloys or pure metal, are essential to compute the aggregation and segregation energies (see Supporting Information or SI Figure for representative slab models). With the above formulations, a positive aggregation energy and a positive segregation energy indicate formation of a SAA. We optimized the minimum energy paths (MEPs) for CH4 dehydrogenation to *C (adsorbed carbon; * refers to an adsorption site) and C-C coupling mechanisms to ethane and ethylene using the climbing image nudged elastic band (CI-NEB) method with an artificial spring force constant of 3 eV/Å 2 along the reaction tangents.