Toward a new definition of surface energy for late transition metals

Surface energy is a top-importance stability descriptor of transition metal-based catalysts. Here, we combined density functional theory (DFT) calculations and a tiling scheme measuring surface areas of metal structures to develop a simple computational model predicting the average surface energy of metal structures independently of their shape. The metals considered are W, Ru, Co, Ir, Ni, Pd, Pt, Cu, Ag and Au. Lorentzian trends derived from the DFT data proved effective at predicting the surface energy of metallic surfaces but not for metal clusters. We used machine-learning protocols to build an algorithm that improves the Lorentzian trend's accuracy and is able to predict the surface energies of metal surfaces of any crystal structure, i.e., face-centred cubic, hexagonal close-packed, and body-centred cubic, but also of nanostructures and sub-nanometer clusters. The machine-learning neural network takes easy-to-compute geometric features to predict metallic moieties surface energies with a mean absolute error of 0.091 J m^-2 and an R² score of 0.97.