Using the first-principles particle swarm optimization algorithm for crystal structural prediction, we have predicted a novel monoclinic C2/m structure for ZrB₃, which is more energetically favorable than the previously proposed FeB₃-, TcP₃-, MoB₃-, WB₃-, and OsB₃-type structures in the considered pressure range. The new phase is mechanically and dynamically stable, as confirmed by the calculations of its elastic constants and phonon dispersion curve. The calculated large shear modulus (227 GPa) and high hardness (42.2 GPa) show that ZrB₃ within the monoclinic phase is a potentially superhard material. The analyses of the electronic density of states and chemical bonding reveal that the strong B–B and B–Zr covalent bonds are attributed to its high hardness. By the quasi-harmonic Debye model, the heat capacity, thermal expansion coefficient and Grüneisen parameter of ZrB₃ are also systemically investigated.

The equilibrium geometric structures, stabilities and electronic properties of Si₂Ag_n (n = 1–8) and pure silver Ag_n (n ≤ 10) clusters have been systematically investigated by using meta-generalised gradient approximation. Due to sp³ hybridisation, the lowest energy structures of Si₂Ag_n clusters for n > 2 favour the three-dimensional structure. The silicon atoms prefer to be located at the surface of the host silver clusters. By analysing the relative stabilities, it is found that the di-bridged structure Si₂Ag₂ isomer is the most stable structure for Si₂Ag_n (n = 1–8) clusters. The highest occupied–lowest unoccupied molecular orbital gaps, exhibiting a pronounced even–odd alternation, indicate that the doped clusters with even number of atoms have enhanced chemical stability than those with odd number of atoms. The results of Wiberg bond indices and electronic localisation function show that the stronger Si–Si and Si–Ag interaction may be the main driving force for the higher stability of Si₂Ag_n clusters.

By using the particle swarm optimization algorithm for crystal structure prediction, we reveal a newly orthorhombic Cmcm structure of HfB4, which is more energetically superior to the previously proposed YB4-, ReP4-, FeB4-, CrB4-, and MnB4-type structures in the considered pressure range. The phonon dispersion and elastic constants calculations confirm that the new phase is dynamically and mechanically stable. The calculated large shear modulus (240 GPa) and high hardness (45.7 GPa) imply that the predicted Cmcm-HfB4 is a potential superhard material. Meanwhile, the directional dependences of the Young's modulus, bulk modulus, and shear modulus for HfB4 are systematically investigated. Further analyses of the density of states and electronic localization function indicate that the strong B-B and B-Hf covalent bonds greatly contribute to its high hardness and stability.