Computational details

The molecular orbital theory program based on density functional theory (DFT) in the Gaussian 09[22] software package was used to optimize the structure and calculate the thermodynamic properties. First, use the ABC algorithm[23-25](artificial bee colony algorithm) to construct the initial configuration of (Y2O3)n(n=1-15), that is, set up different boxes for different system sizes, and add a certain number of oxygen atoms and yttrium atoms inside,automatically generates a large number of initial configurations according to the internal algorithm of the program. Then, preliminary optimization is carried out under the semi-empirical method, and the more stable partial structures are screened out according to the energy level of dozens to thousands of calculated structures for the next step of precise calculation and optimization. In order to ensure the accuracy of the ground state structure, on the basis of fully considering the spin multiplicity, for each cluster size, as many initial structures as possible are selected for geometric optimization. Finally, the global optimal structure is obtained and the frequency calculation is performed to obtain various thermodynamic properties of the cluster. In the precise calculation, the BP86 functional and mixed basis set are used, that is, the all-electronic basis set 6-311G* is used for oxygen elements. For the heavier rare earth yttrium element, the Stuttgart pseudopotential and the corresponding pseudopotential are used considering the relativistic effect[26-28]. Finally, the optimal structure of different isomers with n=1-15 and the structure with lower energy are obtained.