How Many Isomers Do Metallic Clusters Have? Case of Magnesium Clusters of up to 55 Atoms

About 9000 structures of magnesium clusters Mgn (n = 2–13) generated via different methods were optimized at the DFT levels in order to estimate the number of all possible stable structures that can exist for the given cluster size (∼820,000 PES points were explored in total). It was found that the number of possible cluster isomers N quickly grows with a number of atoms n; however, it is significantly lower than the number of possible nonisomorphic graph structures, which can be drawn for the given n. At the DFT potential energy surface, we found only 543 local minima corresponding to the isomers of Mg2–Mg13. The number of isomers obtained in the DFT optimizations grows with n approximately as n4, whereas the N values extrapolated to the infinite generation process grow as n8. The cluster geometries obtained from the global DFT optimization were then used to adjust two empirical potentials of Gupta type (GP) and modified Sutton-Chen type (SCG3) describing the interactions between the magnesium atoms. Using these potentials, the extensive sets of structures Mg2-Mg55 (up to 30,000 clusters for each n) were optimized to obtain the dependence of the cluster isomer count on n in the continuous range of n = 2–30 and for selected n up to n = 55. It was found that the SCG3 potential, which is closer to the DFT results, gives a number of possible isomers growing as approximately n8.9, whereas GP potential results in the n4.3 dependence.