Global Structure Optimization of Subnanoscale Magnesium Clusters at the DFT, CCSD(T) and MTP potential levels

S.K. Ignatov,1 S.V. Panteleev,1 I.S. Steshin,1 A.G. Razuvaev,1 A.E.Masunov 2

1 Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod 2 University of Central Florida, Orlando, USA


The structural, energetic, and electronic parameters of subnanoscale magnesium clusters were studied in an expanded set of 1322 structurally unique isomers found in the course of direct global DFT optimization of the structure of Mg2-Mg32 clusters at the BP86/6-31G(d) level, as well as using the global optimization of Mg33-Mg35 based on the DFT-calibrated classical moment tensor potential MTP. In order to elaborate the MTP potential parameters, the extended subsets of 10929 isomeric structures of Mg25-Mg32 found earlier in the DFT optimization was used. Several versions of MTP potential were considered, differing in the number of radial and angular parameters. The best results were obtained for the medium-size potential version (mtp16 with 4 radial functions of size 10, acting in range of 2-8A). It is shown that the use of MTP significantly improves the prediction of the cluster structure in comparison with classical metal potentials. At the same time, the differences between the individual cluster structures and energies predicted by MTP and DFT results in many cases remain significant. They strongly depend on the calibration procedure, training set, and potential version used. Elaboration of MTP parameters allowed the global optimization of larger cluster structures up to Mg55. The establishment of a complete set of isomers made it possible to construct a complete genealogical map for the formation of Mg2-Mg10 isomers, which can be considered as a fragment of the PES for the processes of formation of small clusters by sequential addition of single atom. This information was verified and refined by the full optimization of the Mg2-Mg12 structures at the CCSD(T)/cc-pVQZ level. It was shown that, as a whole, the BP86 functional predicts the structures Mg5-Mg12 rather good. Interestingly, the most significant differences between CCSD(T) and BP86 were found for the structures and energies of smallest cluster representatives Mg2-Mg4. The calculation of the electronic parameters of Mg2-Mg32 at the DFT level reveals an unusual property of the isotropic electrostatic polarizability (IEP): the dependence of the IEP of the most favorable isomers on the cluster nuclearity n is linear with a high correlation coefficient, and its value for each n is close to the minimum value among all found isomers of a given nuclearity. The found dependence is checked by predicting the IEP for isomers, the structures of global minima for which are predicted independently by the method of interatomic potentials (MTP). The calculated IEP values for the MTP-optimized global minima fall within the error limits of the regression model used for the IEP prediction. Possible explanations of the discovered dependence, its significance for quantum chemistry, and the possibility of practical application are discussed. The work was supported by the Russian Foundation for Basic Research (project 20-03-00282)