The geometric structures, stabilities and properties of Mg₃B_n^0/-(n=1-8) clusters have been systematically investigated using the particle swarm optimization structure prediction program (CALYPSO) combined with density functional theory. The lowest energy structures were obtained at the single-point CCSD(T)/aug-cc-pvdz level based on the geometries optimized at the B3LYP/6-311+G(d) level. Mg₃B₃^- and Mg₃B₄^- were found to adopt 2D planar structures, whereas all the other clusters had 3D structures. The neutral and anionic clusters possess similar structures in the case of n=3, 6, and 8. Subsequent calculations of the average binding energies, secondorder energy differences, and HOMO-LUMO gaps indicate that theMg₃B₆ and Mg₃B₇^- clusters have the highest stability. The electronic properties of the clusters were further analyzed by calculating charge transfer and Wiberg bond orders. Based on the Multiwfn program, the photoelectron spectra, infrared spectra and Raman spectra were computationally simulated to facilitate their spectral characterization. Investigation of the thermodynamic properties showed that the heat capacity and entropy increase with increasing temperature and that the relationships between C_v(S) and T are approximately quadratic.

The study of silicon clusters has led to significant interest in transition metal atoms doped silicon clusters. In order to provide robust guidelines for future experimental and theoretical investigations of vanadium doped silicon nanomatrials, the geometric structures, stabilities and properties of V₂Si_n^-/0 (n=8~17) clusters were systemically studied using density functional theory. Firstly, the lowest and lower lying energy structures of V₂Si_n^-/0 (n=8~17) clusters were globally predicted using the CALYPSO (crystal structure analysis by particle swarm optimization) searching method via the particle swarm optimization algorithm. Geometry optimization at the B3LYP/6-311+G(d) level revealed that two vanadium atoms tend to form V₂ bonds encapsulated gradually into silicon cages with an increasing number of silicon atoms. Secondly, based on the lowest energy structures, calculations of the average binding energy, second order energy difference, and HOMO-LUMO gaps indicated that the V₂Si₁₂^-/0 clusters exhibit higher stability, respectively. In addition, magnetic properties analyses revealed that the total magnetic moment is zero for the closed-shell structures of V₂Si_n (n=8~17) clusters; However, the open-shell structures of V₂Si_n (n=8~17) clusters have magnetic moments with values of 1 μB. Upon polarizability analysis, V₂Si₈^-/0 clusters with the highest mean dipole polarizability possess stronger nonlinear optical properties. Furthermore, the simulated PES(photoelectron spectroscopy), IR (infrared), and Raman spectra can provide theoretical guidance for future experimental investigations. Finally, the lowest energy structures of V₂Si_n (n=8~17) clusters are stable thermodynamically. Moreover, the heat capacity at constant volume (C_v) increases with the increasing of temperature, and standard entropy (S) decreases with temperature increasing.