Fig. 1: Features of the six classes of local atoms environments identified through clustering.

Visualization of the hierarchical k-means clustering results for MD simulations of Au nanoparticles with 147, 309, 561, 923, 2869, and 6266 atoms, carried out using the ML-FF trained on rPBE-DFT data. a First and second component (x- and y-axis) of the t-sne projection of the atomic expansion coefficients of 10⁴ local atomic environments randomly sampled from melting MD simulations. The colours label the six classes assigned by the hierarchical k-means clustering algorithm, as defined in the main text. The normalized average pair-distance distribution function (PDF) belonging to each class is shown and coloured accordingly. b, c Same t-sne projection as in (a). In (b), the colours indicate the nominal simulation temperature at which the local atomic environment was taken from; in (c), the number of nearest neighbours (#NNs) was computed using a cut-off of 3.6 Å.