Similar estimations for other dynamic transitions between the AEs within the NP can be calculated from the transition matrix of Figure in an analogous way. We note that given the time window used for the analysis we report herein (dt = 1 ns), any observed communication/exchange between the AEs involves processes happening on the ns scale or slower, thus excluding AE exchanges related to thermal vibrations (values related to p i→ j < 0.01 (i.e., 1 ×10 -2 in Figure ) should be considered as purely qualitative, as these pertain to events that are only sparsely observed along the MD simulation). We also underline that, while the exact estimated values for AEs' lifetimes, probabilities and transition rates may slightly change depending on the employed FF, tests conducted with different types of FFs provided very similar results in terms of NP dynamics, confirming the generality of our observations. We simulated the Ih 309 NP also at 400 K and 500 K by running 2 µs of MD(see also Supplementary Movie 2). We then extracted the SOAP spectra for all atoms from 1000 frames taken from the last 1 µs of MD following the same protocol used at 300 K. Figure shows the results of these additional analyses. In particular, in these analyses, we used the simulation at 300 K as the training set for both the PCA and clustering (HDBSCAN*) analyses of the MD trajectories of the Ih 309 NP at 400 K and 500 K (see Methods section for complete computational details). The PCA of Figure and Figure show how the clusters on the surface of the NP become more adjacent to each other at 400 K and 500 K than at 300 K. Moreover, the pseudo-FESs of Figure and Figure indicates that the minima corresponding to different surface AEs at 300 K tend to merge together when the temperature increases. In particular, at 500 K, the surface AEs constitute a unique large minimum, meaning that at such temperature, e.g., Faces and Edges AEs are in continuous exchange with each other and that these effectively form a unique fuzzy surface state (i.e., training the PCA on the MD trajectory at 500 K would not find at all two distinct Faces and Edges AEs, but one single environment). The communication between Faces, Edges, and Vertexes AEs increases with increasing the temperature. This is even more evident in the normalized transition matrices of Figure and Figure . The sub-square in the matrices connecting the 'Edges', 'Faces', and 'Vertexes' AEs shows that atoms belonging to these environments have larger probabilities to exchange with each other at 400 K and 500 K than at 300 K. In particular, at 400 K, such a surface atomic mobility is evident, but these atoms have still a higher probability of remaining in their environment than of jumping into another one in dt = 1 ns (p ii > 50%). On the other hand, at 500 K the residence probability for atoms in the surface AEs drops close to, and in some cases also below 50 %, suggesting that in such conditions the NP surface is pre-melting. We note that, in good approximation, the number of atoms in each environment does not vary much during the simulations at all temperatures (Supplementary Figure ). This suggests that, despite such rich atomic mobility, the Ih 309 NP surface remains structurally that of an icosahedron at all analyzed temperatures. It is also interesting to note that the transition matrix of Figure shows sparsely observed dynamic interconnections between the central atom of the NP and the surface AEs at 500 K. This does not mean that the central atom is diffusing to the NP surface, but rather that at such temperature internal voids may rarely form in the NP center, which makes the SOAP spectrum of deep bulk atoms change occasionally and become similar to that of surface AEs. This fits well with previous reports showing similar central vacancies in Ih 309 . While evidence of surface dynamics in Au NPs have been reported, obtaining clear insights as on the processes that characterize such dynamics, or on whether this is essentially due to, e.g., local atomic reconfigurations or atomic diffusion is non-trivial. Tracking the motions and the fluctuations in the SOAP spectra of the individual atoms in the NP, our approach provide clear evidence that the dynamics of these NPs is not due only to oscillations between adjacent/similar AEs, but to real microscopic atomic diffusion. As a representative example, in Figure we show the detail of the evolution during 1 µs of MD of an atom that is an Ih 309 vertex at the start of the simulation. Figure show respectively the temporal trajectory of the atom and the SOAP AEs that this visits in this time frame, revealing how even at 300 K such atom visits a surprisingly large collection of different (surface and sub-surface) SOAP AEs (Figure ). In particular, such vertex atom diffuses first to surface AEs, and then also penetrates into the sub-surface. Its diffusion is described in detail also in the plot of Figure , showing how such an atom also becomes at a certain point (∼820 ns of MD) a rosette center (pink).