Transition metal polyborides (e.g., tetraborides or triborides) with intriguing boron configurations offer a unique combination of excellent mechanical, superconducting, optical, and thermoelectric properties. Unraveling the specific structures of polyborides is critical to understanding their underlying physical and electronic properties. Here, we perform first-principles calculations to focus on the predictions of geometrical structures, relative stabilities, and mechanical and electronic properties of vanadium tetraboride (VB4) and triboride (VB3). VB4 prefers to take Cmcm symmetry with a planar boron isosceles trapezoid, differing from earlier graphene-like or rhomboid boron arrangements in tetraborides. Upon compression, another new Amm2-type energetically favorable above 12.0 GPa and can be stabilized up to 50 GPa. Both structures are qualified into incompressible and hard materials, comparable to previous reported tetraborides. Predicted C2/m-type VB3 possesses intriguing puckered boron bilayers and graphene-like boron sheet and shows excellent mechanical properties. Analysis of electronic structure, electron density distributions, and Mulliken overlap population demonstrated the significant contributions of special planar isosceles trapezoid boron units to the great stability and excellent mechanical property for VB4. Furthermore, the universal trend of structural features and mechanical behaviors was analyzed for the available 3d transition metal tetraborides.
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