where E H 2 is the energy of a H 2 molecule, E PtH,i (x) is the energy of structure i in ensemble ε i with with a Pt 13 H x stoichiometry, and E Pt,j is the energy of structure j in ensemble ε j of a Pt 13 NP. The Pt containing energies are weighted by coefficients c ij which are determined by their normalised thermodynamic population calculated up to ensemble energetic cutoff.