Fig. 3

Representations of potential energy surfaces constructed via the Automated Cluster Surface Scanning (ACSS) method. a, b Contour plots and c–f cluster-projected representations for the (a, c) Pt55 + H and (b, d–f) Au18 + H systems. Energies are relative to the most stable site for each system. White and red lines are the minimum energy paths connecting transition states (white triangles, contour plots only) and minima (white circles and site names). Red lines on the contour plots and the corresponding cluster-projected representations indicate diffusion paths that serve as a frame of reference for the reader. For clarity, only limited ranges of the PESs large enough to show all symmetrically unique sites are shown. Site types are defined in Supplementary Tables 4 and 7 for Au18 and Pt55, respectively. Dotted pink triangles mark the two triangular ensembles of Au atoms in Au18, identical to those in Fig. 2