Benchmarking a Molecular Flake Model on the Road to Programmable Graphene-Based Single-Atom Catalysts

Single-atom catalysts (SACs) of embedding an active metal in nitrogen-doped graphene are emergent catalytic materials in various applications. The rational design of efficient SACs necessitates an electronic and mechanistic understanding of those materials with reliable quantum mechanical simulations. Conventional computational methods of modeling SACs involve using an infinite slab model with periodic boundary condition, limiting to the selection of generalized gradient approximations as the exchange correlation (XC) functional within density functional theory (DFT). However, these DFT approximations suffer from electron self-interaction error and delocalization error, leading to errors in predicted charge-transfer energetics. An alternative strategy is using a molecular flake model, which carved out the important catalytic center by cleaving C-C bonds and employing a hydrogen capping scheme to saturate the innocent dangling bonds at the molecular boundary. By doing so, we can afford more accurate hybrid XC functionals, or even high-level correlated wavefunction theory, to study those materials. In this work, we compared the structural, electronic, and catalytic properties of SACs simulated using molecular flake models and periodic slab models with first-row transition metals as the active sites. Molecular flake models successfully reproduced structural properties, including both global distortion and local metal-coordination environment, as well as electronic properties, including spin magnetic moments and metal partial charges, for all transition metals studied. In addition, we calculated CO binding strength as a descriptor for electrochemical CO₂ reduction reactivity and noted qualitatively similar trends between two models. Using the computationally efficient molecular flake models, we investigated the effect of tuning Hartree-Fock exchange in a global hybrid functional on the CO binding strength and observed system-dependent sensitivities. Overall, our calculations provide valuable insights into the development of accurate and efficient computational tools to simulate SACs.