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.