To obtain more quantitative information on the complex atomic dynamics present in the NPs, we calculated the transition probabilities for atoms belonging to such AEs to remain in or undergo a transition into the different AEs in ∆t = 1 ns (same analysis of Figure , Figure and Figure , but with this new set of top-down detected AEs). The transition matrices of Figure show that deep AEs (b and ss) have diagonal entries residence probabilities p ii ∼ 1 (dark colors). This confirms the rather static behavior of the interior of the NPs at all temperatures. At 500 K the blue ss' AE starts to communicate with the surface of the NP and, in particular, with the green c and c' concave AEs. The matrices of Figure thus show that the formation of the rosettes on Ih 309 comes from such deep states, as well as (in large part) from the surface (red, s) and edge (e,e') AEs. From the transition matrices of Figure it is possible to estimate, e.g., the transition probabilities, rates, timescales, and lifetimes of all these top-down detected AEs as done from that of Figure . For example, in the Ih 309 NP at 300 K the non-native concave c' AE (light green) has a transition probability to the surface (red, s) AE of p c →s ∼ 0.4, indicating a transition rate of k c →s ∼ 0.4 ns -1 and characteristic transition timescale τ c →s = 2.5 ns (transition event observed ∼ 4700 times along 1 µs of MD: see Supplementary Figure ). Given that in the c' row of the matrix the c → s transition is by far the fastest one, in good approximation, this allows estimating the bottom limit of the lifetime of one atom in the c' AE in the range of τ c ∼ 2.5 ns. Similar estimations of the characteristic timescales for all transitions between the AEs in the NP can be easily performed from all the p i→ j reported in the transition matrices of Figure . Such analyses thus provide not only an ). (b) The Ih 309 NP before simulation start (top, 0 K), in steady state MD frames, taken from the MD simulations at temperature 300 K, 400 K, or 500 K (top-to-down). Atoms within the NPs are colored based on the dictionary AEs (a): the pie charts indicate in magenta the percentage of atoms on the NP surface that do not belong to environments native to ideal icosahedral NPs. (c) Histogram counting the average number of atoms in each cluster during the last 1 µs of MD at 300 K, 400 K, 500 K (second-left to right columns for each AE), compared to the AE populations in the ideal (0 K) Ih 309 NP (leftmost column for each AE). Black vertical lines on the top of each column indicate the standard deviation. A vertical arrow highlights when the first column is absent, hence the absence of certain AEs in the ideal Ih 309 NPi.e., environments which are non-native of ideal icosahedral temperature, emerging within them with temperature (e.g., in Ih 309 : v , c and c AEs in light-purple, light-and dark-green respectively). (d) Chord diagrams showing the interconnection between all AEs communicate with each other in Ih 309 at various temperatures. Non-native AEs emerging in Ih 309 are identified by colored arrows in the chord plot at 300 K. Chords connecting two AEs indicate that a bidirectional exchange of atoms between them is observed. The width of the chords is indicative of the flux magnitude between the two connected AEs. The color of the chord identifies the direction of the prevalent exchange events -i.e., the large red chord between the c and s AEs indicate that at 300 K more c → s exchange events are observed during the MD simulation than s → c ones (the opposite is observed at, e.g., 400 K and 500 K). (e) Normalized transition matrices reporting the probabilities for atoms in the Ih 309 NP at the various temperatures to remain in a given AE (p ii ) or to exchange into another one (p i→ j ) in the time interval of dt = 1 ns. estimation of the average composition of an NP but also, and perhaps even more interestingly for practical applications (e.g. reactivity), detailed information on the lifetime of all the native and non-native AEs populating it. In fact, the capability of an AE to activate a chemical reaction is directly related to its lifetime vs. by the characteristic time of the reaction itself on that AE.