Structure and Properties of 1237 Low-Lying Isomers of Magnesium Clusters Mgn (n = 2–32) Predicted with the DFT Global Optimization

Unexpected polarization properties of sub-nanosized magnesium clusters

“…It was also found that the IEP for some symmetric NP shapes, namely, cubic and spherical NPs has the f values linear in a broad range of n. This allows to assume that the linearity of IEP in magnesium clusters can be connected to the more spherical shape of the most favorable structures. Indeed, it was established previously 18 that the E rel isomers of 1237 clusters of Mg 2 -Mg 32 decreases linearly when the deformation parameter DP = 2P 3 /(P 1 + P 2 ) (where P 1 > P 2 > P 3 are the principal moments of inertia of the cluster) goes to 1 which means that the spherical structures are more energetically favorable. However, this tendency is quite fuzzy, with low regression coefficient and large deviations from the linearity as it is seen on Fig.…”

“…Structures of magnesium clusters Mg 2 –Mg 32 used in the analysis were generated in the course of the direct DFT global optimization combined with graph generation algorithm and manual construction of the highly symmetric structures as was described in detail in ref. 17 and 18 . In brief, the initial structures were generated from a complete set of connected graphs with n vertices as well as using the evolutionary algorithm combined with taboo -search to avoid the generation of similar structures.…”

“…The remaining 694 structures of Mg 14 –Mg 32 were located by the similar methodology, although without achieving the limit of all possible structures, with the DFT optimization using normal optimization criteria as described in ref. 18 . Their Cartesian coordinates were published as ESI † for ref.…”

“…17 This fact allows one to explore the complete set of isomers at once (at least for some n), trying to search for the individual representatives with useful properties. In a recent study, 18 we carried out such a search in the extended set of isomers of clusters Mg 2 -Mg 32 comprising 1237 isomeric structures located in the direct DFT global optimization. The magnesium clusters are the convenient object for such studies because they are simple for DFT calculations, their ground state is a singlet spin state, and many of their properties have been published, both experimental [19][20][21][22][23] and theoretical.…”

“…The magnesium clusters are the convenient object for such studies because they are simple for DFT calculations, their ground state is a singlet spin state, and many of their properties have been published, both experimental [19][20][21][22][23] and theoretical. [24][25][26][27] In the study, 18 we considered mostly energetic and structural properties, which allowed us to locate the most stable representatives, the energy distributions for a complete set of isomers as well as the distributions for separate nuclearities. The analysis of these distributions allowed to predict that the size-and shape-selected cluster synthesis can be feasible for some n, in particular, for n = 10 and 20.…”