We specifically employed variational and fixed-node diffusion Monte Carlo (FNDMC) methods , with the latter providing high-accuracy many-body electronic structure calculations by projecting the ground state from an initial trial wave function and effectively capturing electron correlation within the fixed-node approximation . Although the polynomial scaling of FNDMC (N with the number of particles) historically limited its application in surface chemistry due to high computational cost, recent advancements in codes like QMCPACK , used in this study, along with GPU acceleration, have significantly improved its practicality. Techniques such as finite-size corrections and extrapolation methods further improve the efficiency of FNDMC for catalytic systems.